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Piping calculation


C h a p t e r

1

Major Codes and Standards

Overview
The world of standards may seem to many to be something like the tower of Babel—there are so many diff

erent standards, some of which are called codes, that the problem seems daunting. This book is meant to help remove some of that difficulty. One concern for any reader would be his or her geographical area. Or, to put it another way, which code does the jurisdiction for my area recognize, if any, as the one to use for my project? This is a question that can only be answered in that particular area. One can say in general that there are three main codes in the piping and pipelines realm: the ASME codes in the United States and many parts of the world; the Din codes in Europe and other European-leaning parts of the world; and the Japanese codes, which have a great deal of significance in Asia. The International Organization for Standards (ISO) standards are an emerging attempt to simplify the codification process by cutting down on the multiplicity of codes worldwide. As users of these codes and standards become more global in their reach, the need becomes more prevalent. However, there is a long way to go before we become a world where a single set of codes applies. The dominant themes here will come from the American codes and standards such as ASME. Where appropriate, we will point to other sources, some of which are specifically mentioned in the following text. The main allowance for worldwide use will be the translation to metric

? 2010 Elsevier Inc. DOI: 10.1016/B978-1-85617-693-4.00001-8

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1.? Major Codes and Standards

from the U.S. customary units of measure. The ASME codes and other U.S. code-writing bodies are in various stages of converting within their written standards. Particularly in those parts of this book where calculation procedures are given, we will show them in both methods of measure. It should also be pointed out that there are other standards-writing bodies that will be cited and their techniques used as we explore piping and pipelines. They include, but are not necessarily limited to, the following: Manufacturers Standardization Society (MSS), American Petroleum Institute (API), American Society of Testing Materials (ASTM), Pipe Fabrication Institute (PFI), and American Welding Society (ASM). In mentioning codes and standards one should also mention that in many nations there is a national standards organization. In the United States it is the American National Standards Institute (ANSI). Again, each jurisdiction may have a different format, but the main emphasis is that a code with the national standards imprimatur is the de facto national standard. In the United States once a standard has met the requirements and can call itself a national standard, no other standard on that specific subject can claim the imprimatur of a national standard for that subject. One of the relevant requirements of becoming an ANSI standard is balance. To obtain this balance as the standard is being written it must be reviewed and agreed on by people representing the major factors of the subject, including producers, users, and the public. Before it can be published it must go through an additional public review and comment phase. During this process all comments and objections must be addressed and resolved. In short, a national standard gives an assurance that all relevant aspects of that subject have been addressed. With the exception that a jurisdiction may set a requirement that a particular standard must be utilized as a matter of law in that jurisdiction, a standard is only a basis or a guideline as to good practice. As previously mentioned, it might be the law in certain jurisdictions, and it certainly can be a requirement in any contract between parties, but as a code it is not needed until one of those requirements is met. This may lead one to question what the difference is between a code and a standard. The simple answer is nothing of significance. When one reads the title of a B31 section, he or she will find that a code is a national standard. Code is a descriptive word that usually designates that the standard has some legal status somewhere. The major practical difference is that a code will have several aspects while a standard is primarily about one thing. Some standards-writing bodies call their offerings something slightly different. For example, the MSS calls their offerings standard practices (SPs). The MSS has recently started converting some of their SPs to

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Structure of Codes

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national standards. Because their membership is limited to manufacturers of flanges, valves, and fittings, they have to follow a different metho? dology to obtain the balance required by ANSI. This is called the canvass method, which is a part of the overall protocol of ANSI’s requirements. It is designed for just such a situation as MSS where their preference is a single category—that is, manufacturers—and therefore does not meet the balance requirement.

Structure of Codes
The basic structure of the ASME piping codes is fairly standard across all of the books. By following this nominal standard order a rough cross-reference between various books is achieved. Each book’s paragraphs are numbered with the number of the book section as the first set of digits. For example, for a paragraph in B31.1, the first digit is 1, while a paragraph in B31.3 has a first digit of 3, and in B31.11 it would be 11. As much as possible sequential numbering is common. This cannot be adhered to exactly because all books do not have the same concerns and therefore the same number of paragraphs. It does, however, guide a searcher to what another book says about the same paragraph or subject by leading him or her to the proper vicinity within the book. The major exceptions come from B31.8, which has a different basic order of elements. Even though this order is different, the elements that are required to build a safe system are included, albeit in a different section of the book. It is also true that there are significant differences in detail. For instance, B31.3 basically repeats certain paragraphs and numbers for different risk media. It has complementary numbering systems with a letter prefix for the number. For example, where B31.3 sets requirements for nonmetallic piping, the prefix is A3xx and the numbering again is as close to the same sequence as possible. Where applicable, in each paragraph something like the paragraph in the base code (nonprefix number) applies in its entirety or “except for,” and then the exceptions are listed. When something has no applicable paragraph in that base code the requirements are spelled out completely. Some sections of the codes are not in all codes. These are usually standalone portions of that particular book. Some have been previously mentioned. Not all codes have any reference to operation and main? tenance. The pipelines, in particular, have extensive sections that are not in the piping codes. These include things like corrosion protection for buried piping, offshore piping, and sour gas piping.

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1.? Major Codes and Standards

Code Categories
The eight major categories that the code covers are scope; design conditions; pressure design; flexibility and stress intensification; materials; standards; fabrication and assembly; and inspection, examination, and testing. Each is described in the following sections.

Scope
This is where the primary intent of the piping requirements is defined in a particular book. Scope will also include any exclusion that the book does not cover and will offer definitions of terms considered unique enough to require defining in that particular book. I repeat here that the final decision as to which code to specify for their project is up to the owners, considering the requirements of the jurisdiction(s).

Design Conditions
In this section the requirements for setting the design parameters used in making the calculations are established. These will generally include the design pressure and temperature and on what basis they may be determined. As applicable to the system considered in the scope there will be discussion of many loads that must be considered. Many of these are addressed in later parts of the code, some in specific detail and some left to appendices or the designer. All must be considered in some appropriate manner. There is also a section that defines how the allow? able stresses listed within the code are established. If allowed, a procedure for unlisted material can be computed. It will also establish limits and allowances.

Pressure Design
This section gives the calculation and methodology to establish that the design meets the basic criteria. It is probably the most calculationintensive portion of the code. There are additional parts as required by the intended scope to define requirements for service in piping components and piping joints.

Flexibility and Stress Intensification
These sections set the requirements for the designer to be sure that the piping is not overstressed from loads that are generated by other than the

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Code Categories

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pressure. They may be loads generated from the thermal expansion of the piping system and they may come from other sources such as wind and earthquake. In this section most codes give only a partial methodology after some critical moments and loads have been generated by some other means such as computer programs or similar methods. The codes also address piping support requirements for both above ground and where applicable below ground. (Part II addresses concerns that these codes may create for readers.)

Materials
This section addresses those materials that are listed and those that may not be allowed and, if allowed, how to establish them. Often, it is in this section that the low temperature toughness tests are established. This is generally known as Charpy testing, but there may be other methods allowed.

Standards
This is the section where the other standards that the code has reviewed and consider applicable to that book are listed. The listing also includes the particular issue that is recognized by that book.

Fabrication and Assembly
It should be noted that above-ground piping systems are most times fabricated in a shop in spools, and then taken to the field where they are assembled by various means such as final welding, or if the spools are flanged, bolted together. On the other hand, the majority of the time pipelines are constructed in the field with field welding. This is not to say that in both cases other methods will not be used. It does describe why some books call it construction and some call it fabrication. Needless to say, there are differences in the requirements.

Inspection, Examination, and Testing
These three elements are grouped together because they essentially define the “proof of the pudding” requirements of the codes. In some manner all systems need to be tested for integrity before being put to use. Those requirements vary from book to book, and those variable requirements are defined. The codes in general put a dual responsibility in the area of checking or inspection and examination. The examination and

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1.? Major Codes and Standards

documentation is the responsibility of the builder fabricator or contractor per? forming the work. The inspection is the responsibility of the owner’s representative and he or she may perform an examination of the product and check the documentation in order to give the final approval. With the exception of portions of B31.1 piping, namely boiler external piping, there are no requirements for third-party inspection and code stamping such as is required for some boilers and pressure vessels. This type of requirement may be imposed contractually as a certified qualitycontrol system check, but in general is not mandatory. As previously mentioned, each book may have special requirements areas for specific kinds of media or system locations. They are addressed individually in the book within that special area. Let us set the field for the different B31 sections. In the process we can give a small background for each book. The original ASME B31 Code for Pressure Piping was first introduced in 1935 as the single document for piping design. In 1955, ASME began to separate the code into sections to address requirements of specific piping systems, as follows. B31.1: Power Piping is for piping associated with power plants and district heating systems as well as geothermal heating systems. Its main concern is the steam-water loop in conventionally powered plants. More recently, it has added a chapter to require maintenance plans for the plants that produce the power. B31.2: Fuel Gas Piping Code was withdrawn in 1988, and responsibility for that piping was assumed by ANSI Z223.1. It was a good design document, and although it has been withdrawn, ASME makes it available as a reference. B31.3: Process Piping (previously called the Chemical Plant and Petroleum Refinery Piping Code) is the code that covers more varieties of piping systems. To cover this variety it has sections for different types of fluids. These fluids are basically rated as to the inherent risks in using that fluid in a piping system, so they have more restrictive requirements for the more difficult fluids. B31.4: Liquid Transportation Systems for Hydrocarbons and Other Liquids basically is a buried pipeline transportation code for liquid products. It is one of the three B31 sections that are primarily for transportation systems. As such, they also have to work with many of the transportation regulatory agencies to be sure that they are not in conflict with those regulations. B31.5: Refrigeration Piping and Heat Transfer Components is rather selfexplanatory. It is primarily for building refrigeration or larger heat transfer systems.

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Code Categories

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B31.7: Nuclear Piping was withdrawn after two editions and the responsibility was assumed by ASME B&PV Code, Section III, Subsections NA, NB, NC, and ND. This code had some very good explanations of the requirements of piping design. This book may refer to those explanations, but will not specifically address the complex nuclear requirements. B31.8: Gas Transmission and Distribution Piping Systems addresses the transportation of gases, and it too is primarily for buried piping. It is another pipeline code. The Code of Federal Regulations (49CFR) is the law for these types of piping systems. As such, that code must present complementary requirements. Also, a gas pipeline would generally cover a fair amount of distance, and this may have several different degrees of safety requirements over the pipeline as it progressively proceeds through various population densities. Also, since natural gas has so much inherent risk, it is quite detailed in its safety and maintenance requirements. B31.8S: Managing System Integrity of Gas Pipelines is a recently published book. This is a book defining how to establish a plan to handle the problems those inherent risks present. B31.9: Building Services Piping addresses typical pressure piping systems that are designed to serve commercial and institutional buildings. Because these systems are often of less risk in regard to pressures, toxicity, and temperature, they have restrictive limits on these parameters. When the limits are exceeded the user is often referred to B31.1. B31.11: Slurry Piping Systems is another transportation pipeline code that mostly applies to buried piping systems that transport slurries. It has increasingly limited usefulness as a standalone document, and may someday be included as a subset of B31.4. The expected use of slurries to transport such things as pulverized coal has not materialized. B31.12: Hydrogen Piping System—this is a new code. It is in the final stages of first development. When it is released by ASME, it will have many similar sections to B31.3 and B31.8. It is planned as a three-part code that will include transportation, piping, and distribution. It will also have a general section that will include things that need only be said once for each of the other parts of the code. A separate section for hydrogen is needed because it has unique properties that affect the materials of construction, and is generally transported at much higher pressures. It also is an odorless highly flammable gas, and as such requires unique safety precautions. A few specialty books have specific uses and are considered to be valuable to more than one code and therefore can be included by reference to that book. The oldest one is B31-G, which is currently under review

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1.? Major Codes and Standards

because of its age. There was an attempt to add elements from API-579 to make it more universal. It has been determined that that is not as necessary as bringing the existing edition up to date. It is entitled “A Manual for Determining the Remaining Strength of Corroded Pipelines” and is still used extensively in pipeline work. B31-E is a standard for the Seismic Design and Retrofit of Above-Ground Piping Systems. It is, among other things, an effort to bring continuity to piping design. It is hoped that this standard will be included by reference in various B31 books. B31-J is the Standard Test Method for Determining Stress Intensifi? cation Factors (I factors) for Metallic Piping Components. Most of the major books have an appendix stating the I factors to use for certain geometries. These are based on tests on standard components. As the technology has changed, a need has developed to determine factors for other geometries that are not in these existing appendices. To provide more objective evidence, as allowed, this standard was developed to reflect how the original intensification factors will be developed. The ASME B16 standards committee basically covers flanges, fit? tings, and valves. The most familiar of those standards would be the following: ? ? ? ? B16.5 flanges B16.34 valves B16.9 wrought butt-weld fittings B16.11 forged fittings

Details of these standards and any of the others that apply will be discussed as part of going through the calculations in the chapters in Part II and the Appendix. A similar result occurs with the standard practices that are written by the MSS. They have several, and not all are recognized by the piping codes. Some of the most familiar ones are ? ? ? ? SP-97 integrally reinforced branch outlet fittings SP-58 pipe hangers and supports SP-44 steel pipeline flanges SP-25 standard marking systems for valve, fittings, flanges, and unions

MSS has several other SPs that are quite useful but often do not require any calculation or subsequent work for the user. A particular SP applies that will be discussed in Part II and the Appendix.

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Code Categories

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API standards and specifications will be addressed in a similar manner as the need arises in the specific calculation methods. Some API standards, such as the flange standard, have been incorporated in the B16.47 and as such are no longer supported by API. The calculation requirements of elements like pipe sizing and flow will be introduced in Part II and the Appendix to give readers some insight into how to perform those calculations. The process of getting started in any piping project is not specifically covered by a specific standard in its entirety. Often there is an interplay between the process engineer and the system or pipe designer as well as the equipment designer. In all engineering situations, economics come into play regarding project initiation. One must determine, somehow, the most economical throughput, balancing any economies of scale from increased throughput and budget limitations. Then the problem becomes one of larger pipe size versus equipment size to produce the throughput. These issues are based on equivalent lengths of pipe, pipe size, fluid friction within the pipe, and so forth. Other than a rudimentary discussion and demonstration of the basics of those decisions, much of the detailed analysis lies outside the scope of this book. It is quite well covered by other disciplines and their literature. It is important for readers to note that while the various codes and standards offer what appear to be different approaches and calculation procedures to arrive at a specific solution, that difference may not be as great as it first appears. A question I have repeatedly asked myself as I complete a particular set of calculations—How does the pipe or component know which code it was built in accordance with?—has been found quite helpful in making the final decision as to whether it is proper for the situation. Mother Nature does not read codes; she just follows her laws. Of course, you must use the code’s required calculation or its equal or more rigorous requirement. More complete listings of codes relevant to piping and pipelines can be found in the Appendix of this book. The mathematics must be correct, but then the question forces the technical reviewer to face the inherent margin that the particular code he or she is working with has established. This comes from the inherent risk the fluid, temperature, and pressure offer within the area that would be affected by a failure, as well as the damage to people, property, and systems that a failure due to an incorrect calculation might incur. When you can answer that question in the affirmative, you are willing to stand behind the result of your work. Having met that challenge, we must address the contentious question of the metric system of measurement versus the U.S. customary system of measurement. For that, we move to Chapter 2.

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C h a p t e r

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Metric versus U.S. Customary Measurement

Overview
Whenever one writes anything that includes a measurement system in the United States, he or she is confronted with the problem of presenting the data and calculations. This is especially true when writing about codes and standards. Most U.S. codes and standards were originally written some time back when metrics were not necessarily the dominant world system. The metric system itself has several minor variations that relate to the base units of measure. This will be discussed more thoroughly in the following. The system has evolved to the point that basically only three countries do not use it as their primary measurement system: Myanmar, Liberia, and the United States. It is now known as the International System of Units (SI). The United States has played with converting to the SI system for as long as I have been working in this field, which is a long time. Americans have not made the leap to make it our primary system. This lack of tenacity in converting to this system is difficult to understand completely. The most plausible argument revolves around the installed base of measurement and a modicum of inertial thought regarding that seemingly inevitable conversion. To those who have worked with the SI system it is immensely preferred in its decimal conversion from larger to smaller units. What could be

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simpler than converting a length measurement from something like 1.72 kilometers to 1720 millimeters? Compare that to converting 1 yard, 2 feet, and 6 inches to 66 inches or 5.5 feet. On the other side, there is the problem of what you grew up with. It is rather like translating a language that is not your native language. You first have to get the words into some semblance of your native tongue. As one becomes fluent in another language, he or she can begin to think in that language.

Hard versus Soft Metric Conversion
All of this is a descriptive example of some of the difficulties of converting an ASME code into a metric code. The generic classification of this problem is hard versus soft conversions. The terms hard conversion and soft conversion refer to approaches you might take when converting an existing dimension from nonmetric units to SI. “Hard” doesn’t refer to difficulty, but (essentially) to whether hardware changes during the metrication process. However, the terms can be confusing because they’re not always consistently defined and their meanings can be nonintuitive. It’s simplest to consider two cases: “converting” a physical object and conversions that don’t involve an object. When converting a physical object, such as a product, part, or component, from inch-pound to metric measurements, there are two general approaches. First, one can replace the part with one that has an appropriate metric size. This is sometimes called a hard conversion because the part is actually replaced by one of a different size—the actual hardware changes. Alternatively, one can keep the same part, but express its size in metric units. This is sometimes called a soft conversion because the part isn’t replaced—it is merely renamed. If the latter sounds odd, note that many items’ dimensions are actually nominal sizes—round numbers that aren’t their exact measurements— such as lumber, where a 2 × 4 isn’t really 2 by 4 inches, and pipe, where a 0.5-in. pipe has neither an inside nor an outside diameter of 0.5?in. With pipe, the international community has come to a working solution to this anomaly because comparable SI pipe has different dimensions than does U.S. schedule pipe. An even more difficult problem comes about when one is determining nonproduct-type decisions while making pipe calculations. For instance, how does 1720?mm compare to 5.5?ft in your sense of the two distances? That is to ask, which is longer? The answer is 1720? mm converts mathematically to 5.643045? ft. However, for few of us, even those who have worked with but are not

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SI System of Measurement

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fluent in metrics, the answer is not obvious—until we do the conversion. We may sense that they are close. In some calculations 5.643045 may not make a significant difference. In others, it may make the difference between meeting or not meeting a certain requirement. This points to another problem in working with things developed in one system as opposed to other systems. As it relates to conversion, there can be many decision-like problems. If for some reason we were deve? loping a U.S. customary design and arrived at an answer that came to 5.643045?ft, we might call it any of several dimensions in our final decision. This would depend on the criticality of the dimension in the system. Where we are concerned with a dimension that only needs to be within the nearest 1 8 in. to be effective, we might chose 5 5 8 (5?ft, 7.5?in.) or 5 3 4 (5?ft, 9?in.). The original 5.643 can be converted to something within 23 1 32 of an inch as 5?ft, 7 32 ?in. Mind you, all this is for converting 1720?mm into U.S. customary dimension. A similar exercise could be presented for converting something like 5 3 4 (5?ft, 9?in.) into millimeters, which would be 1752.6?mm. One would then have to make comparable decisions about the criticality of the dimension.

SI System of Measurement
It was previously mentioned that there are several metric systems. Fortunately, they are not as complex as the U.S. customary system (USC). For instance, in distance measurement the name and unit of measure changes with the size of the distance. We have miles, furlongs, chains, yards, feet, inches, and fractions of an inch, all of which can be converted to the other, but not in a linearly logical base 10 fashion as the SI system does. The different systems in metric are centimeter, gram, and second system. Another is the kilometer, kilogram, and second system. It can be noted that the major difference in the base unit system is a different length, which essentially just changes the prefixes, as the decimal relationship is constant. It is just up from centimeters to kilometers or down from kilometers to centimeters. The International System of Units (SI) includes some other base units for use in other disciplines: 1. Meter, the distance unit. 2. Kilogram, the weight and force unit. 3. Second, the time unit. Interestingly, a second in France is the same as a second in New York. 4. Ampere, the electrical unit.

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2.? Metric versus U.S. Customary Measurement

5. Kelvin, the temperature unit. Since most of us live and work in the atmosphere, the Celsius measure is more commonly used. But a degree in either is the same; the difference is the 0 reference point. Absolute 0 in Kelvin and in freezing water in Celsius is a difference of some 273.15 (often the .15 is ignored). 6. Candela, the measurement of light, or similar to the U.S. term candlelight, the luminous intensity of one common candle is roughly one candela. 7. Mole, basically the measure of atomic weight. The exact definition is different but the use is similar. These, then, are the metric (SI) system. Converting back and forth between the two systems is at the least time consuming. In the Appendix there is a conversion chart as well as a chart that focuses on the conversion that applies to the type of calculations commonly used in piping. Some standard charts don’t give those calculations and the dimensional analysis to make them can be quite time consuming if not nerve racking. There is also a chart that lists the common prefixes as one goes up and down in quantity. Many need to be used only rarely, but it is often maddening not to find them at the moment you need them. It is also good to have a calculator with some of the fundamental conversions built in. Baring that, there are some common conversions that should be committed to memory so one can quickly move from one to the other. For example, there are 25.4? mm in an inch and 2.2? lbs in a kilogram, and a degree in Celsius is equal to 1.8°F, and there is a base difference at the freezing point of water from 0°C to 32°F. None of these are accurate beyond the inherent accuracy of the conversion numbers, but they are good rules of thumb or ballpark conversions.

Methods of Conversion from One System to the Other
It is also a good idea to get a conversion program for your computer. There are several good ones that are free on the Internet. It is quite handy as one works calculations at the computer to just pop up the conversion program and put in the data and check. From the previous discussion, the conversion of 1720?mm to a six-place decimal was made in less than a second on such a computer program. Several documents give detailed information regarding how to convert to metric from U.S. customary units. The most general one, which includes guidance and conversion charts, is the ASTM SI-10. SP-86 is somewhat

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Methods of Conversion from One System to the Other

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simpler and was developed by the MSS to guide their committees that chose to add metric to their U.S. customary dimensions. It has a very good discussion of conversion, the implied precision in conversions, and is written in plain language for users who are somewhat at a loss regarding conversion other than the strictly mathematical multiply-this-by-that chart or calculator. The ASME B31 piping codes and standards are in various stages of converting their codes to metric. Not all codes lend themselves to metric conversion urgency, so the pace in the various book sections varies according to international usage. Some are quite local to the United States and therefore lag in conversion. Many of the B16 fittings and flange standards have converted. In most cases the B16 conversions have made the determination that the metric version is a separate standard. This is a direct result of the problems just described. When making a practical conversion some of the dimensions are not directly converted or are rounded, and are in tolerance in a manner that means that a component made from one set of the dimensions might not be within tolerance of the other set of dimensions. Where that is the case, the standard or code has a paragraph establishing this fact. The paragraph points out that these are two separate sets of dimensions—they are not exact equivalents. Therefore, they must be used independently of the other. In the flange standards this created a much more mixed set of dimensions. For tolerance and relevant availability the metric version of the flange standards kept U.S. bolt and bolt hole sizes. The standard metric bolting not only did not offer equivalent heavy hex nuts but also since bolting is important in calculations of pressure ratings and metric bolts that are not necessarily the same exact area create significant diffi? culties in establishing ratings and margins. More is given on this subject later in Part II and the Appendix. In the piping codes themselves B31.3 is probably the most international of the codes. Since many process industries like chemical and petroleum plants have international operations, B31.3 has broad worldwide usage. It is even mentioned as the normative reference code in the ISO 15649 standard. For that reason, it is probably the most advanced in its establishment of a metric version. The main remaining pieces of the puzzle in the conversion of B31.3 are the stress tables, which are not yet completely established. It is hoped that they might be available in the 2010 version of that code. This is not necessarily a given, as to be included in the code many things need to happen and not all of them have yet happened. However, various committees are working to accomplish this goal. Stress tables create an almost double problem for the codes. The tables are presented material by material in what is a regular temperature range.

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2.? Metric versus U.S. Customary Measurement

In U.S. customary units that range is 100° in the lower temperature ranges and 50° steps as the temperatures get higher. These are in Fahrenheit, and the fact that they do not directly translate to Celsius causes a problem. Also, the stresses are in thousands of psi (pressure per square inch) and again not evenly translated into MPa, creating another problem. These two problems make a requirement for a very large amount of interpolation, which in turn has to be checked for accuracy by an independent interpolation. This, coupled with the 16 temperatures and hundreds if not thousands of those interpolations, means a slow process. The notes in the stress tables indicate the methodology that can be used in getting an equivalent stress from the current U.S. customary tables. Where a metric stress is required those notes will be used to establish an allowable stress for the example problems in this book. The code books themselves already establish any changes in metric constants that may be required to complete calculations. The intention is to convert the codes to metric completely. This of course cannot realistically happen until the United States takes that step. As previously noted, for reasons that can only be surmised, it hasn’t happened yet, but it will happen. When one buys a container of bever? age, the metric equivalent is often noted. Those who work with automotive equipment might need a new set of metric wrenches to work on newer devices. Likewise, if one is into antique cars, he or she might need an older set of U.S. customary wrenches.

Challenges for Converting from One System to the Other
One of the vexing problems is when one is doing calculations that include standard elements such as the modulus of elasticity, moment of inertia, section modulus, universal gas constant, and other similar standard elements. When one is accustomed to working in one system, he or she may not know all of the standard units that are used in the other. This causes some concern when working a particular formula to get the correct answer in a working order of magnitude. Inevitably, the question is: What unit do I use in the other system? One example could be the section modulus, Z in most B31 codes. It is often used in concert with moments and stresses and other calculated parameters. Not infrequently there is a power or a square root involved. Which values should be used in such calculations? The best advice is to use a consistent unit of measure such as meters or Pascals, which are defined in Newtons/m2 when converting from USC or something like inches. However, here one must be careful because some disciplines

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Challenges for Converting from One System to the Other

19

develop the formulas in foot measurements when converting from SI to USC. Fortunately, the way the world is going, most conversions are from the USC system to the metric. The saving grace in all this is that whichever system you are working in you can calculate the result in it and then compare what you get to the result you get in the system to which you are converting. This will essentially develop your own conversion factor for that combination of units to which you had converted the components. Here again, Mother Nature has been kind to us even if the measurement gurus have not. The stress, for instance, is the same order of magnitude no matter which set of units you calculate in. When I was first learning how to do beam calculation, one of the problems given as an exercise was to calculate the size of a ladder rung that would hold a man of a certain weight on a ladder a certain distance wide. I had to calculate it in both the USC system and what was then the metric system. After the weight was converted to kilograms from pounds, the width from inches to millimeters, the moment of inertias calculated, and so forth, the size of the rung came out 1 inch (or very close) in USC. To my, surprise, the rung in millimeters was 25 (or very close), because in the calculation we used integer numbers in the weights, widths, stresses, and so forth, so the answers came out in whatever accuracy that the slide rules allowed. Nowadays, the same exercise would most likely give an answer for the rung diameter in several decimal places. The wise engineer would make the very close decision to make the rung 1? in. in diameter, and in metric make it somewhere near the standard size of round wood in his or her geographical region. Two lessons were learned. One, Mother Nature doesn’t really care what system of measurement you use. If your math is right you will get the same special diameter and you can call it what you want. Second, unless you are in some high-precision situation, you can pick the nearest standard size that is safe. It is hoped that someday there will only be one set of unit-sized equipment. However, it is unrealistic to think that all of the older equipment will disappear overnight should that conversion occur. The calculations will be done in both U.S. customary and metric units in any sample problems that are presented in this books, of course, when it is necessary to walk through the calculations. There are some that are self-evident and need not be done in detail.

I.? INTRODUCTION

C h a p t e r

3

Selection and Use of Pipeline Materials

Overview
When one thinks of materials for use in the piping codes the usual thought is about the materials that make the pipe, fittings, and supporting equipment—the materials that the codes address. However, there are more materials than that to be considered. The material that the piping will be immersed in is important. In aboveground piping, that is usually just air, and is not always significant. Even then one has to consider the environment—for example, the humidity levels and whether the location has extreme weather such as temperature and wind. If the location is earthquake prone, that has bearing on the design calculations and the construction. Buried piping has another set of concerns. One has to know the topography and soil conditions that the pipeline is routed through. Usually there is need for some kind of corrosion protection. Does the route cross rivers, highways, canyons, or other things that can cause special problems? All these questions must be considered, and they are not usually spelled out in the piping codes. They may be mentioned as things that must be considered; however, there is often little guidance. There is a whole new set of code requirements for offshore and underwater pipelines. The pipeline codes explain those requirements in detail. One also needs to consider the fluid or material that the pipe system will be transporting. Often, the code’s title is the only indicator of the fluid. B31.8 is specifically for gas transmission. That code does have spe-

? 2010 Elsevier Inc. DOI: 10.1016/B978-1-85617-693-4.00003-1

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3.? Selection and Use of Pipeline Materials

cific requirements in it for sour gas. As mentioned before, B31.1 Power Piping is primarily involved with steam-water loops. In each of the codes the scope gives some more information regarding these transport materials. B31.3, because of its broad range of application to a variety of process industries, has the most information about transport fluids. It defines four types of fluid: 1. Category D service. These must meet certain requirements and are basically low pressure, not flammable, and not damaging to human tissue. 2. Category M service. This is the opposite of Category D fluids and therefore must be treated by separate requirements. 3. High-pressure fluids. These are fluids that have extremely high pressures as designated by the owner and have independent requirements. 4. Normal fluid service. This is not your everyday normal Category D fluid service, but it does not meet the requirements in 1, 2, or 3, and is generally called the “base code.” One can use that base code for Category D fluids, as it is sometimes simpler when Category D service is over the entire project. This gives a flavor of what the various transport fluids can be.

Selection of Materials
By and large what the fluid a project is for comes as a given. The specifier or designer then chooses an appropriate material to handle that fluid under those conditions. In general, codes do not have within their scopes which material should be used in which fluid service. However, they may limit which materials can be used in certain system operation conditions, like severe cyclic conditions or other effects that must be considered. Many of these do not give specific ways to make those considerations. Some methods are discussed later in this chapter. At this point, given a fluid and the need to calculate which piping material should be used, there comes a little bit of interaction with regard to sizing the pipe. This is especially true when there is the opportunity to have more than one operating condition in the life of the system. In those multiple-operation situations, a series of calculations must be made to find the condition that will require the thickest pipe and highest component pressure rating. For instance, it is possible that a lower temperature and a higher coincident pressure may result in use of heavier pipe than a higher temperature and a lower pressure. This combination may not be

I.? INTRODUCTION



ASTM and Other Material Specifications

23

intuitively obvious. Such considerations will be discussed and demonstrated in much more detail in Part II and the Appendix. The sizes required may have an effect on the materials of selection. All components may not be available in materials compatible with pipe materials. This conundrum was common when higher-strength, high-temperature piping was developed in the late 1990s for hightemperature service. Material to make components out of similar material was not readily available for several years. It is also true that when newer materials are developed the fabrication skills and design concerns take a little time to develop. New techniques are often required for a result in the same net margins one is used to with the older materials. That and similar problems explain why the adoption of new materials proceeds at a less-than-steady pace. Having explained generically some of the material problems, we can turn our attention to the materials of construction for a pipe system. Each code has what is generally called listed materials. These are materials that the various committees have examined and found to be suitable for use in systems for the type of service that that book section is concerned with. It stands to reason that those books that work with a wider variety of materials have more types on their “preferred” list.

ASTM and Other Material Specifications
In piping these are most usually ASTM grades of materials. For ferritic steels, they usually are ones from ASTM Book 1.01. In many instances, it also lists API 5L piping materials. One major exception is boiler external piping, listed in B31.1, which requires SA materials rather than ASTM. It is basically true that one can substitute SA for ASTM materials of a similar grade. The SA materials are often the same as ASTM materials of the same grade, as in SA-515 or A-515. Section II of ASME’s Boiler and Pressure Vessel Code (BPVC) is the materials section, which reviews the ASTM materials as they are developed for applicability to the boiler code. There is a little hitch that always occurs when one standards-writing body adapts or references another’s standard for their purposes—a time lapse problem. If standard group A issued a change to their standard, the adopting group B cannot really study it for adoption until after the publication date. And then they can’t necessarily get it adopted in time for their next publication date, which is most likely to be out of sync by some amount of months or possibly years with the change. So the lag exists quite naturally.

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24

3.? Selection and Use of Pipeline Materials

Table 3.1? Unlisted Materials
Book B31.1 B31.3 B31.4 B31.5 B31.8 B31.9 B31.11 Listed Yes, including SA Yes Yes Yes Yes, with specific types Yes Yes Unlisted Yes, with (non-SA) limitations Yes, with limits Yes, with limits Not addressed Addressed in types Yes, with limits No Unknown No No Yes, with limits on fluids Not addressed Addressed in types Structural only Not addressed Reclaimed or Used Not allowed Yes, with limits Yes, with limits Yes, with limits Yes, with limits Yes, with limits Yes, with limits

In addition, sometimes the change made by group A is not necessarily totally acceptable to group B. Specifically for the SA/ASTM problem there are some SAs that say this is the same as the ASTM of a specific edition with an exception. Or they might just keep the earlier edition that they had adopted. Because of this inherent lag, standards groups spend a fair amount of effort letting you know which edition of a standard they have accepted is the one that is operative in that code. Typically, B31 and other standards will list the standard without an edition in the body of their code. Then they will offer an appendix to the code that lists the editions that are currently approved. Every attempt is made to keep the inherent lag in timing to a minimum. In addition to these listed materials, sometimes unlisted materials are accepted with certain limitations. Also, some discuss unknown materials and used or reclaimed materials. Table 3.1 shows what each B31 book section generally will say. Other standards have materials requirements that often point back to ASTM or an acceptable listing in another standard. This helps to eliminate duplication of effort and the lag problem is again minimized. Some standards develop their own materials. The most notable of these is MSS SP-75, which has a material called WHPY that has a defined chemistry and other mechanical properties.

Listed and Unlisted Materials
The listed materials are those in the B31 books, which list the allowable stresses at various temperatures for the materials that they have listed.
I.? INTRODUCTION



Listed and Unlisted Materials

25

So, because in their applications there is a wide range of temperatures utilized in their systems, they need these tables. Over a wide range of temperatures the yield and ultimate strengths will go down from ambient temperatures. In addition, at some temperature, time-dependent properties, such as creep and creep rupture, become the controlling factor. To establish the allowable stresses at a specific high temperature could require expensive and time-consuming tests. The ASME determined a method that, while it doesn’t completely eliminate the tests, reduces them to an acceptable level. It uses them to establish the allowable stress tables. In cases where the material one wants to use in a project is not listed in the particular code, the first step is to determine whether that code allows the use of such a material. Some guidelines of where to look are in Table 3.1. B31.3 is the most adaptable to unlisted materials, so a brief discussion of that procedure is given. It is important to note that the code does not give one license to use it in compliance with other codes; however, it is a rational method to determine acceptable stresses for temperatures where there isn’t a published table of allowable stresses. The nonmathematical part is to select a material that is in a published specification. This is quite probable because of the proliferation of national or regional specifications that for one reason or another have not been recognized by the codes in either direction. That is to say, the code from one country does not specifically recognize another country’s or region’s material specification. There is progress in the direction of unifying these different specifications, however slow. To be useful, they must specify the chemical, physical, and mechanical properties. They should specify the method of manufacture, heat treat, and quality control. Of course, they also must meet in all other respects the requirements of the code. Once the material is established as acceptable, the next priority is to establish the allowable stress at the condi? tions, particularly temperatures in which the material is intended to be used. This discussion assumes one is intending to use that material at a temperature that is above the “room” temperature or temperature where normal mechanical properties are measured. Measuring mechanical properties at higher temperatures is expensive and can be very time dependent if one is measuring such properties as creep or creep rupture. The ASME code, recognizing that this process is difficult, developed a trend line concept to avoid requiring such elevated-temperature mechanical tests for each batch of material made, as is required for the room temperature properties. This is called the trend curve ratio method. The method is relatively straightforward. Some of the difficult extended temperature tests have to be made. While as far as is known there is no set number of tests, it stands to reason that there should be more than two
I.? INTRODUCTION

26

3.? Selection and Use of Pipeline Materials

data points to ensure that any trend line that is not a straight line will be discovered from the data points. It also stands to reason that the temperature range of the tests should extend to the higher temperature for which the material is used. This eliminates extrapolating any curve from the data and limits any analysis to interpolation between the extreme data points, which is just good practice. Obviously, if the intended range extends into the creep or creep rupture range, those tests should be run also. This decision becomes a bit of a judgment call. As a rule of thumb the creep range starts at around 700°F or 371°C. However, depending on the material, that may not be where those temperature-dependent calls control the decision. So now one has a set of data that includes the property in question at several different temperatures. For purposes of illustration, we make an example of a set of yield stresses. This is not an actual material but an example. The data for listed materials can be found in ASME Section II, Part D, and these are already in tables so there is no need to repeat that data here. We will call this material Z and the necessary data to establish the trend curve ratio are listed in Table 3.2. Given these tables, a regression on the temperature versus the computed ratios can then be established. It should be noted that the original data might be in the same degree intervals that the table is intended to be set up in, but in general this is not the case. Therefore, a set of data that ranges from the room or normal temperature to the highest intended temperature can then allow a regression that is basically interpolative rather than extrapolative. It is unlikely that the material supplier has test data at the exact temperature at which one is going to use the material. One might note in delving into Section II of the boiler code, which is the basic material and stress section, that these yield temperature charts rarely go above 1000°F. This is accompanied by the general fact that this is a temperature that is usually within the creep range and that yield is

Table 3.2? Material Z Test Data for Trend Curve Ratio
Room Temperature, °F 70 100 300 500 600 800 Tested Yield, kpsi 32 32 29 24 20 10 Ratio to Room Temperature Yield 1 1 0.906 0.750 0.625 0.3125

I.? INTRODUCTION



Allowed Stress Criteria for Time-Dependent Stresses

27

the less dominant mechanical property. Yield above that temperature is not as critically needed. Regardless, the regression yields formulas that allow one to predict the yield at any intermediate temperature. For the previously presented data one regression is a third-degree polynomial that has a very high correlation coefficient. That formula is Ratio at temperature ( Ry ) = 1.00361 ? ( 2.08E ? 0.06 ) T ? ( 9.5E ? 0.07 ) T 2 ? (1.58E ? 10 ) T 3 One might think that the latter terms might be ignored, but if one thinks of, say, a temperature of 500, that 500 is cubed; therefore, that small constant changes the yield by over 500 psi in the current example, and that is a significant change in stress. This explanation applies to the method ASME has developed to avoid the requirement for each batch of material to go through extensive hightemperature testing. A test of tensile and yield at room temperature (generally defined as 70°F or 20°C) satisfies the requirement. The temperature values is that room temperature value multiplied by the appropriate temperature, Ry or Rt. The same general technique is used for both yield and tensile properties.

Allowed Stress Criteria for Time-Dependent Stresses
The other criteria for establishing allowable stresses are that of creep and creep rupture. The criteria involve a percentage of creep over a length of time. These have been standardized in ASME as the following values: 1. 100% of the average stress for a creep rate of 0.01% per 1000 hours. This can be described as causing a length of material to lengthen by 0.01% in 1000 hours when a steady stress of a certain amount is applied at a certain temperature. Obviously this requires many long tests at many temperatures and many stresses. 2. 67% of the average stress for a rupture at the end of 100,000 hours. Once again, many stresses at many temperatures are tried until the part breaks or ruptures. 3. 80% of the minimum stress for that same rupture. Again, many stresses at many temperatures are tried. These criteria are basically the same over all the ASME codes. The double shot at the rupture criteria (2 and 3) comes about to eliminate any

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28

3.? Selection and Use of Pipeline Materials

possibility of having a test that gives a wide variability of highs and lows. It is essentially an analogy for having a rather tight standard deviation in the data. One can also assume that there are expedited testing methods for the creep-type tests. A full-length test of 100,000 hours would last over 11 years and several different stresses would have to be tested. Even a full 1000-hour test would take over 41 days. Having assembled all that data, the decision for any given tempera? ture is then made to allow the lowest stress. The tensile stress has a percentage applied to it that is set, as much as possible, to ensure that the material has some degree of ductility. The main stress factor is yield stress. The percentage of yield that is allowed is dependent on the code section. Generally, the two most often used criteria are 67% of yield and a divisor of 3.5 on the ultimate tensile stress, all at the desired design temperature. The creep criteria are included in this survey, and the one that yields the lowest stress is established as the allowable stress at that temperature. This is not true in the books where the applications have a limited range of operating temperatures, mostly in the pipeline systems. In those, they simply set the specified minimum yield of the material as the base allowable stress. Their calculation formulas then have a few variable constants based on the pipeline’s location class and the temperature and any deviation for the type of joint that is employed in making the pipe. It is noted that the temperature range for pipe containing natural gas, for instance, would be quite small. On the other hand, that pipeline can go through a wide variety of locations.

Stress Criteria for Nonmetals
When one comes to nonmetals the presentation of stresses is considerably different. Nonmetals have a much wider set of mechanical properties with which to contend. There are several types of nonmetallics. Those recognized by the various codes are thermoplastic, laminated reinforced thermosetting resin, filament-wound and centrifugally cast reinforced thermosetting resin and reinforced plastic mortar, concrete pipe, and borosilicate glass. One doesn’t need to be an expert to recognize that they represent a wide range of reactions to stress or pressure. The allowable stresses are set this way as well. For instance, B31.3 refers to five different stress tables for the above-mentioned materials. A brief listing of how those tables vary is as follows: 1. The thermoplastic pipe table lists several ASTM designations and allowable stresses over a limited temperature range for each ASTM designation. It is the most like the metal tables.

I.? INTRODUCTION



Corrosion and Other Factors

29

2. The laminated reinforced thermosetting pipe table lists an ASTM specification with a note stating the intent is to include all of the possible pipes in that specification. That specification gives allowable usage information. 3. The filament-wound materials (e.g., fiberglass piping) table lists several ASTM and one American Water Works Association (AWWA) specification with the same note as that in item 2. 4. The concrete pipe table lists several AWWA specifications and one ASTM, and it states the allowable pressure for each pipe in the specification. The specification itself defines the controlling pressureresisting dimensions and attributes, eliminating the need for any wall thickness calculation. 5. The borosilicate glass table lists one ASTM specification and an allowable pressure by size of pipe. This is the way ASME has chosen to handle the nonmetal materials that they list. B31.3, which for now is the only high-pressure design for pipe code, has a separate allowable stress table for the limited number of metals that are recognized for use at those high pressures. Those tables do have an unpredictable difference in allowable stress values for common temperature. Like everything in the chapter, they are mandatory to comply with the code once a piping system has been defined by the owner of the system as a high-pressure system. Many times it is asked: What is high pressure? The general requirements are that it can be anything, with no specific lower or upper limit. It is high pressure only if the owner specifies it as so. For purposes of writing the chapter the committee used the definition as any pressure and temperature that are in excess of the pressure at that temperature for the material as defined in the ASME B16.5 pressuretemperature charts as Class 2500.

Corrosion and Other Factors
A main remaining consideration in material selection is what is called the material deterioration over time, commonly referred to as corrosion allowance. That corrosion can occur on the outside of the pipe due to the environment the pipe is in, and can come from the inside due to the fluid and the velocity and temperature of that fluid. The amount of corrosion allowance to be allowed is dependent on the rate the corrosion will occur over time and the expected lifetime of the particular system. The calculation effort, after the corrosion allowance is set, is addressed in Chapter 5 to calculate pressure thickness. Setting that

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3.? Selection and Use of Pipeline Materials

allowance is outside the scope of the codes. There is a suggestion in B31.3, Appendix F, Precautionary Considerations, that points the reader to publications such as the National Association of Corrosion Engineers’ “The Corrosion Data Survey.” This would help guide the setting of corrosion allowance. The Appendix contains a list of common materials from the U.S. ASTM Book 1.01, which by far lists the vast majority of the materials used in piping. As was mentioned, the ASME has its Division 2 listing of materials, which have an SA or SB designation. By and large, they are ASTM materials that have been adopted. Some have restrictions on elements like the chemistry, or some other portion of the current ASTM material may be invoked when adopting them. Those restrictions are noted in the listing. The primary purpose of these materials is for use in the boiler code sections; therefore, they are not treated in this piping-related book more than they have been already. There are materials standards from other geographical sections of the world. Many of them are similar to ASTM materials, but some are quite different. It appears on cursory examination that often these standards have a greater number of micro-alloyed materials. The mélange of materials has not been resolved into some simple—“these are the materials of the world”—standard. There is considerable work going on in that area, but it might take a long time to get to the finish line in that effort. For those who feel the need, there are books that attempt to be conversion sources to compare world materials—for example, Stahlschussel’s Key to Steel. It is quite expensive and most detailed, and works primarily with European steels but lists many regional steels. I have used it with success in untangling the web of various steels. There is a little more to consider in preparing to do the calculations required by or suggested by the codes: the business of sizing the pipe for a particular system. This includes the flow in the system and the attendant pressure drops, which, as mentioned, are not really a code-prescribed concern. However, a basic understanding of the methods employed in this process is background for the user of the codes and as such is addressed in Chapter 4. A description of the calculations and examples with certain parameters are given rather than an explanation of the development of those parameters. The reader will note that the metals listed as acceptable are often ASTM standards. One of the interesting things about ASTM steels is that they are segregated into different forms. The steel might have almost exactly the same chemistry, and therefore in the casual reader’s eye be the same material. This could be considered true. Certainly, it is true if the various elements in the steel are within the chemical tolerance of the specification for the particular form being reported. However, the chemistry is not the only thing that ASTM and other standards would specify. The major

I.? INTRODUCTION



Corrosion and Other Factors

31

forms of the same material would most likely have different mechanical properties and minimum stresses. Those things depend to an extent on things like the method of manufacture and postmanufacture treatment, as well as the chemistry. It is true that chemistry is the main ingredient; however, the other factors will make a difference and that is why the same chemical material would have a different number depending on the form the material takes—pipe, plate, or forging or casting.

I.? INTRODUCTION

C h a p t e r

4

Piping and Pipeline Sizing, Friction Losses, and Flow Calculations

Overview
After reading this chapter, you should be acquainted with the complicated field of fluid flow or, as it is known, fluid mechanics. You will be aware of the basics and have an understanding of the important issues in this discipline. If you choose to delve deeper into the subject, Elsevier has many titles to choose from that can give you more understanding. For the most part the following issues will be treated as givens in the final design and erection of a system of pipes: fluid, pressure, and temperature, and how they will vary during the life of the process that is involved. They may include which material is appropriate for this system. Necessarily, there is often some interaction in the early stages of establishing these givens. As the project is in its formative stage certain trade-offs are made, including considerations from an economics point of view to establish the cost/revenue returns the project might require. Often these trade-offs involve fluid mechanics considerations. It is the intent of this book to provide a level of understanding of those fluid mechanics considerations to the subsequent systems designer. Understanding how they may have arrived at a certain set of givens makes the business of moving forward somewhat easier. At the least, one can move forward with more confidence.

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4.? Piping and Pipeline Sizing, Friction Losses, and Flow Calculations

Fluid Mechanics Classes
There are two major classes of fluids. The first is incompressible fluids, which are generally liquids. The second is compressible fluids, which are generally gases. We discuss the incompressible fluids class first, as many of the techniques are transferable from that type to the compressible fluids class. In fact, we find that in some instances some compressible fluids can be treated as incompressible. There are other differences that we will discuss as well. There are differences within each of the classes, which we will point out. For instance, in incompressible fluids there are Newtonian fluids and non-Newtonian fluids. In compressible fluids there are the perfect gas laws and the degree that the fluid differs from a perfect gas. These differences will also be pointed out. In all cases some calculation procedures are given and explained. Many of these procedures are complex. In some cases a simpler, less accurate or precise procedure is pointed to for simple rule-of-thumb calculations or ballpark estimating. When appropriate, charts and graphs are provided in the Appendix for many of the issues. Since this is basically a manual, readers who are already familiar enough with the fluid mechanics field may skip this chapter. There is little in the other chapters that will require the calculations given here. In most cases these givens are brought to the table when performing the other calculations. If necessary, the reader is referred back to this chapter or the appropriate chart or graph in the Appendix. Now we must familiarize ourselves with the fluid mechanics terms. Following is a discussion of the less common terms along with a short description of that characteristic of the fluid. Those discussed are important to successful calculation. Where appropriate, there are some supporting calculations. At the end of the list there are examples that put it all together for a small piping system.

Viscosity
The short definition of viscosity is the resistance of a fluid to flow. Many of us are familiar with the expression “as slow as molasses in January.” This of course has more meaning to those who live in northern climates, where January is often very cold. Its deeper meaning is that the resistance to flow is dependent to a great degree on temperature. It has, for the most part, very little dependence on pressure. A more scientific definition of viscosity involves the concept of fluid shear. Many readers who have worked with metals or other solids under-

II.? CONSTRUCTION AND DESIGN FABRICATION



Viscosity

37

stand shear as the force that causes a material to be broken along a transverse axis. Fluid, being fluid, doesn’t really break—it moves or flows. Naturally, being a fluid, it has to be contained, say in a pipe, and when the force is along the free axis of the containment, flow occurs. The containment material has some roughness on its surface that causes the fluid to “drag” or move more slowly at that surface and more rapidly as it moves away from that surface. The net result is that for any small section of the fluid, the velocity pattern is a parabola. There are two basic measures of viscosity. The first is kinematic viscosity, which is a measure of the rate at which momentum is transferred through the fluid. The second, dynamic viscosity, is a measure of the ratio of the stress on a region of a fluid to the rate of change of strain it undergoes. That is, it is the kinematic viscosity times the density of the fluid. Most methods of measurement result in dynamic viscosity, which is then converted by dividing by the density when that is required. We use the following symbols in this book: ? Dynamic viscosity, ?. ? Kinematic viscosity, v. ? Density, ρ. Therefore, the basic viscosity relationship is v=

? ρ

E x a m p l e C a l c u l at i o n s
The dynamic viscosity of water at 60°F is 2.344; the units are lbm.s/ft2 (pounds mass per second/ft2) × 10?5. You will notice the lb has an m, which means those units are in slugs, or what we normally think of as weight divided by the acceleration due to gravity (which for engineering purposes can be 32.2?ft/sec2). The density of water in slugs at 60°F is 1.938, which means that the specific weight of water at that temperature is calculated as 62.4. Therefore, the kinematic viscosity of water at 60°F is 2.344/1.938, which comes out to 1.20949 on a calculator. Those units are ft2/sec × 10?5. It should be noted here that a table of viscosities would most likely note 1.20949 as 1.210. The same procedure in the metric system would most likely give you the following numbers at 20°C, which is the nearest even degree for the

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4.? Piping and Pipeline Sizing, Friction Losses, and Flow Calculations

Celsius scale. One could do some interpolation between, say, 10 and 15, but the changes are not necessarily linear, so the calculation is more complex and there is some concern about the necessity for increased accuracy in a rough calculation. Dynamic viscosity = 1.002?N.s/m2 × 10?3 Kinematic viscosity = 1.004?m2/s × 10?6 Water density = 998.2

With the preceding we begin to see some of the differences between the U.S. customary system (USC) and the metric system. Numerically, the metric system is all about shifting the decimal point. The major difference between dynamic and kinematic viscosity is the ?3 and ?6 exponents of the numbers. The density doesn’t change much by the design of the system. To say that the U.S. customary system was designed is to stretch one’s credibility. The units tend to stay the same size, but there is little or no numerical significance. It is interesting to convert from one to the other system after calculating. However, in converting final calculations from charts one must be sure that the temperatures are the same. On many charts for water the only temperature that is the same is the boiling point, or 100°C and 212°F. At those temperatures the kinematic viscosities are 0.294 × 106 for metric and 0.317 × 105 for USC. The conversion factor from ft2 to m2 is 0.093, and in the other direction it is 10.752. The respective kinematic viscosities for metric are 0.294 × 10?6, which converts to 0.316 × 10?5 against a 0.317 on the comparison chart. For USC, it is 0.317, which converts to 0.295 × 106. The error is very small. This gives readers an idea of why the business of fluid mechanics, as well as moving between metric and USC units, is computationally complex. And we have not even discussed the many different forms of viscosity units that exist. The Appendix contains a discussion and a conversion means of many of those units. It also begins to explain why such techniques as CFD (computational fluid dynamics) programs and their skillful users are in demand. The programs are essentially finite analysis programs and beyond the scope of this book. Suffice it to say, this is not where the non–fluid mechanic wants to spend much time in turning the crank, which explains many if not all the charts, graphs, and other assists that are available. However, we have other fish to fry before we leave our discussion of fluid mechanics.

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Reynolds Number

39

Reynolds Number
The Reynolds number gets its name from Osborne Reynolds, who proposed it in 1883 when he was 41 years old. It is a dimensionless number that expresses the ratio between inertial and viscous forces. This set of dimensions often occurs when one is performing a dimensional analysis of fluid flow as well as in heat transfer calculations. The number in flow defines the type of flow. There are several types for a low Reynolds number (Re) when the viscous forces are dominant. This is characterized by smooth, more or less constant fluid flow. As the Reynolds number gets higher, the inertial forces begin to dominate and the flow then becomes turbulent. This flow is characterized by flow fluctuations such as eddies and vortices. The transition from laminar to turbulent is not at a specific number. It is also gradual over a range where the types of flow are mixed up and in general become indeterminate as far as being a reliable predictable level as to what happens in the pipe or conduit. This range is not even specific, but in general is Re > 2000 < 5000. In its simplest form for flow in pipes the Reynolds number is Re = VD v



(4.1)

where V is the velocity, ft/sec or m/sec D is the internal diameter of pipe, ft or m v is the appropriate kinematic viscosity, SI or USC matic Since we know the relationship of dynamic viscosity to kine? viscosity, Eq. 4.1 can be rewritten in terms of the dynamic visco? sity as



Re =

ρVD ?

(4.2)

where one just substitutes the density and dynamic viscosity. Since you need to know the density to use this equation it is simpler to compute the kinematic viscosity and use Eq. 4.1.

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4.? Piping and Pipeline Sizing, Friction Losses, and Flow Calculations

E x a m p l e C a l c u l at i o n s
Using the kinematic viscosities of water found previously in the “Viscosity” section, and adding the information that we are using an 8 NPS schedule 40 (S40) pipe with water flowing at 7 ft/sec, we make the following calculations: 8 NPS S 40 pipe ID = 7.981 in. or 0.665 ft or 0.203 m 7 ft sec = 2.13 m sec Kinematic viscosity at 60°F = 1.210 USC Kinematic viscosity at 20°C = 1.004 ; at 10°C = 1.307 , both at 10 ?6 The USC Reynolds number is 0.665 ? = 384, 711 7? ? ? ? 1.2105 × 10 ?5 ? The SI Reynolds number is At 20°F : 2.13 × 0.203 1.004 × 10 ?6 = 430 , 667 At 10°F : 2.13 × 0.203 1.307 × 10 ?6 = 326 , 167 Interpolating up as 60°F = 15.55°C, one gets Re to be 384,269.

This basically shows that by using the appropriate units in either system one will get the same or dimensionless Reynolds number. It is important to be sure to convert the temperature exactly. One would get a slightly different number if the interpolation were made on the kinematic viscosity. As one might expect about something that has been around since 1883 there are many forms of the Reynolds number, but they all eventually boil down to these results, and the other forms are left to your exploratory inclinations.

Friction Factor
The drag of a fluid at the contact between the fluid and the container (mostly pipe in this discussion) is caused by what is called a friction factor. In fluid mechanics there are two major friction factors: the Fanning fric-

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Friction Factor

41

tion factor and the Darcy-Weisbach factor, which is sometimes called the Moody friction factor. The two factors have a relationship where the Darcy factor is four times larger than the Fanning factor. This can cause confusion when using the factor. It is important to be certain which factor one is using, or the answer one achieves will not be correct. In laminar flow the factor doesn’t change over the range of laminar flow, so when one in using a chart or graphical solution it is fairly easy to determine which factor is presented. The Fanning factor in laminar flow is 16 Re where the equation for the Darcy factor is 64 Re So it is easy to determine which factor one is using. If one is using a chart, simply read the factor for an Re of 1000, and then you will read either the decimal number 0.064 or 0.016, which will give you the factor being used. The factor used changes the form of the head loss equation that one uses to calculate the pressure drop in a pipe section or line. It is common for chemists to use the Fanning factor, while civil and mechanical engineers use the Darcy factor. So if you are a civil engineer and get a Fanning factor chart, multiply the factor by 4 and you will have the factor you need, or use the Fanning formula for head loss. The two equation forms used with the proper form of the head loss equation will give the same loss for that line segment of pipe: Darcy-Weisbach: Fanning: where L is the length of straight pipe, ft or m D is the pipe interior diameter (ID), ft or m V is the average velocity of fluid, ft/sec or m/sec G is the acceleration of gravity, in the appropriate units F is the appropriate dimensionless factor for the form being used hf is the head loss, ft or m In both cases all symbols are the same except for the f factor, which changes. hf = f hf = L V2 D 2g (4.3) (4.4)

2 f V 2L gD

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E x a m p l e C a l c u l at i o n s
Use the pipe and velocity in the Reynolds number example (i.e., pipe 8 NPS S40 and 7?ft/sec velocity) and the appropriate SI dimensions. The acceleration of gravity is 32.2?ft/sec2 in USC and 9.81 m/sec2 in SI The length of pipe is 100?ft or 30.5?m Re = 1000 Darcy-Weisbach calculations: USC : h f = 0.064 × (100 0.665) × (7 2 2 × 32.2) = 7.32 ft SI : h f = 0.064 × ( 30.5 0.202) × ( 2.13 2 2 × 9.81) = 2.23 m Fanning calculations: USC : h f = 2 × 0.016 × 7 2 × 100 ( 32.2 × 0.665) = 7.32 ft SI : h f = 2 × 0.016 × 2.13 2 × 30.5 (9.81 × 0.202) = 2.23 m

From the example, the formulas give the same answers in both unit systems and either equation form if the appropriate factor is used with the form. Chemists and civil engineers will get the same answer whichever method they choose. This example was for a laminar flow regime and most regimes are not in laminar flow. In the case of turbulent flow the calculation of the factor is not so simple, which was one reason that Moody, for whom the Darcy factor is sometimes named, developed his graph. This was for many years the preferred way to establish the factors. The graph is developed for both the Darcy form and the Fanning form. In the remaining chapters, we will work with the Darcy factors and forms. The graph in the Appendix is presented mainly for reference. The advent of computers and calculators has reduced by a significant amount the work involved in calculating that factor. This is because the calculating equations involve what used to be tedious work, like computing logarithms or making an iterative calculation. Both are done much more simply by today’s electronic wizardry. The base equation is known as the Colebrook equation, which was developed in 1939. It is a generic equation and is based on experiments and other studies, but it can be used for many if not all fluids in the turbulent region. It is not useful for laminar flow, and as discussed, for it to be effective one must first calculate the Reynolds number.

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Friction Factor

43

One drawback of the equation is that it has the unknown factor f on both sides, so it must be solved iteratively. For those who have an Exceltype spreadsheet with a goal–seek tool, this is not as difficult as it used to be. The equation is 1 ? 1 ? ? ε ? 2.51 = ?2 log10 ?? + f ?? 3.7 ? ? D ? Re f ? ? ? (4.5)

where the symbols have the previous meanings given with the exception of ε, which is the roughness factor for the pipe material. For reference, a roughness factor for new steel pipe is 0.00015. As might be expected, this is not a precise factor. It is a reasonable estimate for a particular material. Several materials have different factors and some sources give different estimates. A table of reasonable factors used in this book and by several sources is given in the Appendix. One way to calculate the factor in spreadsheet form is to make a column for all the variables in the formula. Set up three different cells. In one cell set the formula for 1 f In the other cell set the formula for the right side of the equation. Then in the third cell set the difference between the two cells. Then use the goal– seek function to make that third cell zero by changing the input cell for f. This will let the computer do the iteration. If your spreadsheet doesn’t have the goal–seek function, you can perform the iteration manually by changing the cell for the variable f. A sample spreadsheet layout is given in the Appendix.

E x a m p l e C a l c u l at i o n s
Using a roughness factor of 0.00015 and the diameters and Reynolds numbers calculated previously for a speed in the turbulent regime, the Darcy factor calculates as follows (for USC): The friction factor using the spreadsheet method described calculates to 0.016032 with the difference between the two sides at 2.9 × 10?5. Before spreadsheets were developed there was a need to find a direct solution to the Colebrook equation. That is the sort of thing that mathematicians do—fiddle with expressions to make them either simpler or more difficult. In this case, at the price of some accuracy, another equation was developed. When a statement at the price of some accuracy is utilized one must recall that that may not be a major problem given such things as the uncertainty of the roughness factor that was used in the original calculation. In fact, the natural deviation between the two is quite small and for all

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4.? Piping and Pipeline Sizing, Friction Losses, and Flow Calculations

practical (engineering) purposes, zero. That equation is known as the Swamee-Jain equation: f = 0.25
2 ? ε ? 5.74 ? log10 ?? + 0.9 ? ?? 3.7 D ? Re ?

(4.6)?

When one computes this in USC units the factor calculates to 0.016108, which is a minuscule 0.000076 difference and far inside the probable uncertainty of the roughness. This uncertainty is expected to be in the +10 to ?5 percent range.

There is another relationship that can be used: the rough-and-ready relationship. It is deemed by chemists as sufficient for plant construction and calculations. It can be found in Perry’s Handbook so one must recall that it is in Fanning factor form. For purposes of this book it has been converted to the Darcy format; the formula is f = 0.04 ( 4) Re0.16 (4.7)

As such, it calculates to 0.0204 as opposed to the more exact calculations presented before with Colebrook and Swamee-Jain. It is conservative in that it is approximately 25 percent high. This higher factor would give one a need for either higher pumping energy or larger pipe. However, it can be a very quick field-type estimate that would rarely if ever be low. It must be pointed out that all of the previous equations and discussions relate to the line flowing full. That is, it is assumed that there is an incompressible fluid touching all of the inside surfaces of a round pipe. This is not always the case in the real world. The problem is handled by introducing the concept of equivalent diameter, or as it is technically known, hydraulic radius. This will be discussed later in this chapter. This then is the process for straight pipe. But how does one handle the pipe for situations where valves, elbows, tees, and other elements are added to that pipe? This is covered in the next section.

Equivalent Pipe Lengths
The previous discussion covered calculating the friction and head loss for straight pipe. However, any pipe system has elements in it that also add friction, such as valves, fittings, entrance changes in direction, and so forth. So a method is needed to work with those sets of frictions as well.

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Equivalent Pipe Lengths

45

Basically this is to compute an equivalent length of pipe for each of those elements and then add them to the length of straight pipe. The question then becomes how does one do that? Recall Eq. 4.3 in the last section that calculated the friction loss in a section of straight pipe. It looked like this in the Darcy-Weisbach form: hf = f L V2 D 2g

It is relatively simple to break the formula into two parts. The last part of the right side is V2 2g which is known as the velocity head. The rest of the right side is basically the friction component per length of pipe. The method is to simply replace that with a new factor, often called K or the resistance coefficient. Manufacturers and others have run tests and developed the K factor for their product, or one can use common K factors (see the Appendix). Multiply the appropriate K factor by the velocity head and you have an expression for the head loss for that element. If the run is horizontal, all the elements and their respective K factors can be added and then multiplied by the velocity head to get the total head loss for that horizontal run. Elevation losses need to be added separately. If there is a need to calculate the equivalent length, one can just substitute the head loss achieved by the K factor method and solve for L in Eq. 4.3.

E x a m p l e C a l c u l at i o n s
Assume a globe valve fully open is in the line we have been working with (i.e., 8 NPS S40 with a velocity of 7?ft/sec). The common K factor for such a globe would be 10. One might get a different number from a specific manufacturer. USC : Head loss = 10 × (7 2 2 × 32.2) = 7.608 ft SI : Head loss = 10 × ( 2.13 2 2 × 9.81) = 2.312 m USC : Equivalent length = 7.608 × 0.665 × 2 × 32.2 (0.016034 × 49) = 414.7 ft SI : Equivalent length = 2.312 × 0.202 × 2 × 9.81 (0.016034 × 4.537 ) = 125 5.95 m

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4.? Piping and Pipeline Sizing, Friction Losses, and Flow Calculations

A globe valve was picked for demonstration because it has a high and therefore dramatic effect that shows how important it is to include these “minor losses.” The losses are called “minor” mainly because they are independent of the Reynolds number for calculating purposes. As one can see from the example, they may not be minor in terms of actual size. Saying they are not dependent on the Reynolds number applies only if you do not convert to equivalent length. When one converts to equivalent length the Reynolds number and the kinematic viscosity come into play in the computations.

Hydraulic Radius
The discussion so far has been in regard to round pipe that is flowing full. This is not always the case when doing fluid flow problems with liquids. Sometimes the pipe is not full and the geometry is not a circle. There is a method to use these formulas and techniques for flow in noncircular devices, which is what the hydraulic radius is all about. The basic definition of a hydraulic radius is the ratio of the flow area to the wetted perimeter of the conduit in which it is flowing. For starters, consider the hydraulic radius of the round pipe flowing full. For illustration purposes assume an inside diameter of 0.75?m and calculate the flow area to be 0.442? m2. The circumference of that same diameter would be 2.36?m. The ratio of area to wetted perimeter is then 0.1872, which then is the hydraulic radius numerically. How does that relate to the diameter that we started with and used in the previous calculations? This is one of those anomalies of language. Geometrically the diameter of a circle is twice the radius of the circle. Twice 0.1872 is clearly not the 0.75 starting diameter. It is 0.7488, which rounds to 0.75. That says the hydraulic diameter is four times the hydraulic radius. It also points out the vagaries of numerical calculations. If one had used 3.141592654 for pi in the calculation procedure, the ratio would have come out to 0.1875, which when multiplied by 4 would have been 0.75 exactly. For this reason it is somewhat more customary now to speak of the hydraulic diameter and define it as four times the area of the wetted perimeter ratio. This eliminates the language confusion of the different radius meanings. However, old habits die hard, so one must remember that hydraulic radius is different than geometric radius by a factor of two. It is fortunate that for full flowing pipe the two diameters are the same. The same fortunate relationship works out when one considers a full flowing square tube. The flowing area is the side (S) squared and the wetted perimeter would be 4S. That ratio would then be S over 4, and using the definition of four times the ratio, the hydraulic diameter becomes S, the length of the side.
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Compressible Flow

47

W

H

Figure 4.1? Rectangle flowing partly full

This becomes only slightly more difficult mathematically when the conduit is not full. It also makes if fairly easy to calculate the hydraulic diameter of a channel that is not fully enclosed as a pipe or tube. Consider a rectangular device that is flowing partly full (Figure 4.1). The flowing area would be W × H and the wetted area would be W + 2H. So the hydraulic diameter would be WH W + 2H If the rectangle were a square of dimension 5 and the height were 4, then the hydraulic diameter would be 6.15, whereas it would be 5 if it were flowing full. Observation shows the flowing area denominator is smaller and the wetted perimeter is even smaller, so the ratio of those smaller diameters is more than 1, which predicts that the hydraulic diameter would be larger by that ratio. The fundamental expression for hydraulic diameter (Dh) is 4 flowarea wettedperimeter and works in all situations regardless of the geometric shape and amount of flow. Some specific formulas for common shapes are provided in the Appendix.

Compressible Flow
The information provided so far in this chapter is all about incompressible flow that changes to compressible flow when some of the factors change. In general, compressible flow means a gas, and as such it means
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4.? Piping and Pipeline Sizing, Friction Losses, and Flow Calculations

that it is primarily subject to the ideal or, for old-fashioned folks, the perfect gas law. Most readers are aware that for the perfect gas there is a relationship among the pressure (P), the volume (V), and the absolute temperature (T). That relationship has two proportionality constants: the first is mass (m) and the gas constant (Rg), and the second is the number of moles (n) and the universal gas constant (Ru). As might be expected, the two proportionality constants are strongly related. And given the proper use of units, they are the same in both measuring systems. The relationship is as follows. The gas constant Rg is the universal gas constant divided by the molecular weight, and 1 mole is the molecular weight in mass. This means that if you work in a unit of 1 mole with the law, it is not necessary to know the molecular weight until you start to work with the actual flow rates. And the perfect gas law can be stated as PV = Rg T (4.8)

It is important to remember that the absolute temperature is either in degrees Kelvin or Rankine depending on the unit system being used. This relationship can be utilized to tell the temperature, volume, or pressure at another place in an adiabatic system by writing the equation in the form P1V1 P2V2 = T1 T2 where 1 is considered the upstream point and 2 is the downstream point. If you know the upstream point you can calculate a downstream point characteristic when any of the other two are known. This can be helpful in calculating pressure drop. It must be pointed out that most gases only approach being a perfect gas, and therefore a modifying factor called the compressibility factor has been added for most accurate calculations. This factor is highly developed in the gas pipeline industry and is called the Z factor. As an example, air at 1 bar pressure from the temperature ?10°F to 140° has an average Z of 0.9999, and at 100 bars the average across those same temperatures is 1.0103. So for a very wide range of temperatures and a wider range of pressure the average is 1.0051. This is not to say that other gases don’t have a wider range, but to point out that unless one is striving for high accuracy like those who are measuring thousands if not millions of cubic feet or meters of a substance flowing through their pipeline, it is reasonably safe to ignore the Z factor for common engineering calculations. To simplify the tables that compute these factors, including a factor called super-compressibility, run to six volumes long. The Pacific Energy

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Compressible Flow

49

Association developed an empirical formula that estimates the Z factor. That equation also requires some additional adjustment for the highest degree of accuracy. It is given without the subsequent adjustments for things like the inclusion of CO2 and other nonvolatiles (see Appendix). The degree of accuracy is important in the measurement and selling of things like natural gas in pipelines; however, it is usually for the flowing conditions and those who measure the amounts, and the like, rather that the designers. Before we begin to discuss seriously the fluid calculations for friction loss in compressible flow it is important to point out that it may require no change in calculation technique. Many authorities assert that if the pressure drop from pipe flow is less than 10 percent, it is reasonable to treat that fluid as incompressible for that pipeline. Further, it is generally acceptable if the pressure loss is more than 10 percent but less than 40 percent based on an average of the upstream and downstream conditions. Recall that the specific volume changes with the change in pressure by the relationship previously discussed. Having given that caveat it stands to reason that there are left only large pressure drops, which imply very long pipe. This of course means pipelines where the length of the pipe is often in miles. Therefore, we must talk more specifically about what is important in the design and sizing of such longer pipes. Probably the most important thing after, or maybe even before, the topography and the selection of the exact route is how many cubic feet of gas need to be available and/or delivered. All pipe systems are designed for the long term, but in plants and such, that pipe is just a portion of the project; in the pipelines, pipe and the pumping or compressor stations are the project. Determining the pipeline route is the job of surveyors and real estate people. As such, they will not be discussed here. For those with a long memory, the Alaskan pipeline stands as evidence of the time it takes and the struggles that intervening terrain causes in that process. The existing pipeline is for crude oil, not gas. Along with politics and other such problems surrounding natural gases, a pipeline for this hasn’t ever been started, even though they were thinking about it at the same time as the construction of the oil pipeline. There are miles of existing and planned gas pipelines to reference for these compressible flow problems. Suffice it to say that the design elements used are not as simple as those of incompressible flow. For one thing they would fall into the category of a pressure drop of more than 40 percent, where the two simplifying uses of the Darcy-Weisbach formula and its friction factor, along with velocity head, are not common. We discussed earlier how the comprehensibility factor was not particularly important. The average compressibility factor of air was used as an example of how little error would be introduced in considering the factor

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4.? Piping and Pipeline Sizing, Friction Losses, and Flow Calculations

to be 1 and therefore not playing a part in such a calculation. This is not quite the same when dealing with millions of cubic feet of gas, which is measurably more compressible than air, delivered over several miles at a higher pressure. The compressibility factor is most often a measured factor that is then published in tables. Even then, they often require extensive manual correction factors. Several formulas have been developed that are helpful in computing the factor. One of the simplest for natural gas was developed by the Pacific Energy Association. In this method a super-compressibility factor is first calculated and then the compressibility factor is calculated from that. That formula is where Fsc is the factor itself k1 and k2 are factors dependent on specific gravity of the gas Tf is the temperature, degrees Rankine G is the specific gravity of the natural gas Since natural gas can have a large range of specific gravities depending on what else is found in the well, there is a table of k1 and k2; it along with an example of the calculation and some other methods and examples is in the Appendix. As stated, the purpose of the book is to familiarize you with fluid mechanics, not to make you a fluid mechanic. Similar types of highly complex ways to calculate other properties of gases are available either in chart form or, in some cases, empirical formulas. We will not go into specifics of these as they are beyond the scope of this book, which is not to say they are not important. Natural gas is the most common gaseous medium that we work with, so there is more discussion addressing it. There are several formal methods to calculate what is usually desired by pipeline owners and operators: the pipeline’s capacity to flow in millions of standard cubic feet (or meters) per day. Those formulas are the Weymouth, Panhandle A, and Panhandle Band, but there are several others. These equations can be and have been modified to eliminate the friction factor. In fact, there are several proposed friction factor equations, but the Darcy-Weisbach equation is applicable to any fluid. It has some inherent conservatism that may be best for the estimating uses most readers will be involved in. Before approaching the ways to calculate these millions of standard cubic feet or meters of gas, there is another element of gaseous flow that must be presented. Gas has a limit—the speed of sound in that gas—to the velocity at which it can travel. This can most simply be described by saying that the pressure waves can only travel at that speed of sound.
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Fsc =

k1 p g (10 5 k2G ) Tf3.825



(4.9)



Compressible Flow

51

Therefore, as the pressure drops further none of the fluid upstream can receive the pressure wave signal of a further change in pressure. This is a little like Einstein’s thought experiment about moving away from a clock at the speed of light. As he surmised, he would never see the clock’s hand move, so for the ride time it wouldn’t change. One of the many ways that speed of sound in gas can be calculated is by the following formula: Vs = kgRg T where k is the ratio of specific heats, and for methane (close to natural gas) it is 1.26. Molecular weight of methane is 16, so Rg in USC is 96.5 (1544/16) and in SI it is 518.3 (8314.5/16). The universal gas constant can have many different units; in USC units it is customarily taken as 1544 (1545.349 more precisely). Then, in some formula where mass is involved rather than pound force, for the acceleration of gravity (32.2?ft/sec2), as in the speed of sound formula above, one must multiply or divide depending on the exact formula to get the value in mass units, or slugs. As noted, one of the advantages of the SI system is that somewhat awkward conversion is not required because of the definitions. In that case the g is dropped out of the velocity formula. T is assumed to be 40°F or 500° R for absolute temperature and 277.5° for SI. The velocity then is 1.26 × 32.2 × 96.5 × 500 ≈ 1400 ft sec in USC 1.26 × 518.3 × 277.5 ≈ 427 m sec in SI This might seem quite high and not likely inside a pipe, and that is reasonable. But one must remember that as the pressure drops, for the flow to continue absent any dramatic change in temperature, the volume of gas must expand and that can only happen with an increase in flow velocity. The previously mentioned flow equations are in use in the United States and may be in use worldwide, but rather than discuss them here, we will talk about the fundamental equation of flow in compressible gas. The equations mentioned are all in some way a variation of the fundamental equation through algebraic manipulation or a change of factors (like the friction factor). For instance, the fundamental equation has a correction factor for converting to “standard conditions.” However, these vary. For instance, some data have a standard temperature of 0°C, others 20°C, and in United States it might be 60°F or 68°F. All have to be converted to absolute values. Goodness only knows how many different units are recorded in some of the other properties. The fundamental equation is

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Q=C

Tb 2.5 ? P12 ? P22 ? D e? ? LGTa Za f ? ? Pb

0.5



(4.10)

where C is the constant, 77.54 (USC units) or 0.0011493 (metric units) D is the pipe diameter, in. or mm e is the pipe efficiency, dimensionless f is the Darcy-Weisbach friction factor, dimensionless G is the gas-specific gravity, dimensionless L is the pipe length, miles or km Pb is the pressure base, psia or kilopascals P1 is the inlet pressure, psia or kilopascals P2 is the outlet pressure, psia or kilopascals Q is the flow rate, standard cubic ft/day or standard cubic m/day Ta is the average temperature, (?R) or (?K) Tb is the temperature base, (?R) or (?K) Za is the compressibility factor, dimensionless It should be noted that in these equations it is customary to use the arithmetic average temperature across the length of the pipeline. There is a generally agreed-on method of calculating the average pressure. These two averages are used in calculating the compressibility factor. The average pressure equation is Pav = 2? PP ? P1 + P2 ? 1 2 ? ? 3? P1 + P2 ?

An SA comparison was made between several formulas given the same conditions, which were ? ? ? ? ? ? 10-in. pipe ID 100-mile pipeline P1 of 550 psia and P2 of 250 psia Temperature is 95°F Standard condition of 60°F and 14.7 psia Gas-specific gravity is 0.65

For purposes of comparison, the efficiency of 1 was used. For the two calculations, a calculated friction factor of 0.01344 was used. For the Weymouth and Panhandle A calculations, the form of equation that had eliminated the friction factor by including it in the

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Table 4.1? Comparison of Various Gas Pipeline Calculations for Millions of Standard Cubic Feet per Day
Weymouth formula Panhandle A Fundamental equation with f as 0.01344 18.96 × 106 23.63 × 106 19.9 × 106

Note: The Weymouth and Panhandle formulas are adjusted empirical formulas that eliminate the need to develop a friction factor. They are implied as some factor divided by the Reynolds number to some power. As such, they can be shown as higher or lower than a flow by the fundamental equation, which has a more rigorously calculated friction factor. All are estimates.

constant employed was utilized. The results of that comparison are shown in Table 4.1. Since everything is at an efficiency of 1 it is obvious that the only difference is in the accuracy of the constants used or the friction factor. The efficiency factor is usually based on some value between 0.9 and 1.0. It comes from experience, and a designer could use some value based on his or her experience.

Pipe Sizing
As a quick means to size pipe for the fluid flow one can use a simple relationship between flow in cubic feet per second as a starting point. As an example, take the flow of 2 × 106 standard cubic feet per day, which the table shows as the general equation for standard conditions. This translates to 231?ft3/sec at those conditions. We know from the parameter of the problem that the gas never sees standard conditions of 14.7 psia in the pipe, as the lowest pressure is 250 psia and the average pressure shown by the last formula is 418.7 psia. Since that was the pressure used to calculate properties such as viscosity it is a good one to use. It is also one that would be available when the starting and ending pressures were established. So converting the 231 to that pressure and assuming no change in temperature from the averages used, the flow would fall to 8.11?cfs (0.230?m3/sec). The next issue is what is the target velocity? For discussion let the assumption be that the target velocity is 15?fps (4.6?m/sec). Some tables and discussion of target velocity are in the Appendix. The size of the flow can now be estimated using the following formula: ID = C F V (4.11)

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where ID is the calculated internal diameter, in. or mm C is a constant that is 13.54 in USC and 1133 in SI F is the flow, ft3/sec in USC or m3/sec in SI V is the velocity, ft/sec in USC or m/sec in SI Then calculate ID = C ID = C 8.11 F = 13.54 = 9.95 in. in USC V 15 F 0.230 = 1133 = 254 mm in SI V 4.75

Both of these equations would lead one to pick a pipe close to the NPS 10 or DN 250 pipe given in the sample problems. When the fluid is a liquid, one is not concerned so much with the conversion to or from standard conditions as one is with gases. The volume in gas is highly dependent on pressure and, for that matter, temperature. It is not so dependent in liquids. Once the trial size is chosen based on the desired amount of flow, the friction losses and amount of horsepower for pumping or driving the fluid over the length of the pipe can be estimated and the economic calculations made. As the pipe size goes down the friction and therefore energy requirements grow higher. As the pipe size and its fixtures grow the energy required goes down but the capital costs increase. At some point an economical decision can then be made. Of course, there are many more ways to calculate these hydraulic mechanics concerns. One of the most difficult aspects is being sure that one is using the correct set of units. In charts and tables from other sources, they are using different approaches. The universal gas constant includes energy, time, temperature, and space or distance units. For such, a constant should be reasonably standard and have one constant for SI and one for USC, and usually this simply is not the case. One source listed 24 different values for the universal gas constant. This is of course the same constant expressed in different units. Readers are cautioned to read very carefully which data units, and on what basis, they are using to make their calculations. Confusing the data unit will give an incorrect numerical answer. Any data found in the Appendix of this book will specify this as completely as possible. That, along with the conversion chart included and a good dimensional analysis when one is not sure, will give the best opportunity to get the numeric calculation correct. Simply let it be said that when going through calcula-

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tions like this, the changes in the numbers can be drastically affected by the units used in the calculations. In my experience, using the wrong constant has caused more problems than almost any other consideration. Often it is relatively easy to avoid and sometimes quite hard to find. For instance, the universal gas constant is known as 1545.35 when one is using pressure in lbs/ft2 and volume in cubic feet as the units of measure. But change to pressure in lbs/in.2, and the universal gas constant becomes 10.73. Close examination reveals that the 144 conversion from a square foot to square inches is the difference. That is, divide 1544.35 by 144 and you get 10.73. Finding that when it is buried in the calculations may be difficult. By the way, that comparison was assuming the temperature involved was in Rankine, not Kelvin, and that gas computations were in degrees absolute. Change your temperature to Kelvin, keep the pressure in psi and cubic feet, and the R is now 19.3169. In the SI system it is a little simpler. Quite often it is just a matter of shifting the decimal point correctly as one moves between measures such as cubic meters and cubic millimeters. However, it still requires a great deal of attention. Some of the discussion here will be repeated in Chapter 14, on valves. Since this one is a chapter that can be skipped, and some of the calculations for valves use some of the calculations just presented, the background necessary to understand valves is repeated there as needed.

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C h a p t e r

5

Piping and Pipeline Pressure Thickness Integrity Calculations

Overview
One of the primary issues in pipe design is the minimum wall thickness for pipe sizes when exposed to given temperatures and pressures. To establish that wall thickness the material and its allowable stress at those conditions are the first consideration. In discussing the B31, establishing the allowable stress is different for different books, as was discussed in Chapter 3. There are two ways to choose the basic allowable stress with variations, which are also discussed. If the same material is used and the same service conditions apply, that basic stress may still be different. This comes about because of the different levels of concern for the pipe to be in a safe condition at that service state. There is also some allowance for the level of analysis of the pipe as it is being designed. It is common to discuss the margin between a design, say right at the yield point and at a lower point, by calling that the safety factor, which of course it is, but the level of safety is dependent on the knowledge of the condition one is designing for. That knowledge comes from the certainty that the loads used in the equations are accurate, the allowable stresses are correct, and the method of analysis utilized all of the possible variations in computing the results. So the size of the safety factor can correctly be called a measure of what you don’t know.

? 2010 Elsevier Inc. DOI: 10.1016/B978-1-85617-693-4.00005-5

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The base codes are usually simplifications, meaning that in their analytical approach they strive for conservatism. When setting the allowable stresses, they use (as does ASTM or ASME) the minimum values to ensure that the real property is somewhat above that value. The amount of analysis is dependent on what is perceived as the need for more consideration. There are two basic approaches to setting the stresses. One is to give a table of allowable stresses for a given material form over a relevant and wide range of temperatures. This is because the major properties change with temperature changes. As the temperature goes up, the strength goes down, and at some temperatures the strength may not be the controlling factor. As temperature changes, the material begins to creep with no increase in load and thus distorts. Sometimes that distortion even involves what is called creep rupture, where for instance a pipe will just burst. Those codes that give you tables over a temperature range indicate what the controlling factor, be it strength or temperature-dependent properties, determines the allowable stress to be. Some of the newer chemistries of piping materials actually have no perceptibly stronger strength properties but excel in creep. When they are used in higher temperatures, they have higher allowable stresses and can require less actual material to make the same high-temperature pipe. It must be pointed out that this is not a free lunch—the base material is more costly and often it requires a more costly fabrication, but when the total cost is less the material will be chosen. The other major set of book sections operate over a very small temperature range, so they basically work from specified minimum yield strength (SMYS) and control any variation by factors against that SMYS. In the case of B31.4 and B31.11, they only have a temperature range up to 250°F (121°C), whereas B31.8 will allow up to 450°F (232°C), so they have a temperature correction factor. Each of the codes establishes a limit on the amount of shear and bearing or compressive stress that may be used. This is some percentage of one of the allowable stresses that was already established. And in some manner each code tells you how to use materials that are not on its preferred list. That manner varies from “thou shall not” to here is how you compute the stress for this material. A sample of some of those calculations is shown in the Appendix.

Basic Wall Thickness Calculations
In calculating the wall thickness for pipe the basic formulas for the primary (hoop) stress have been around for ages. There are many varia-

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tions. At last count there were more than 20. Each of these addresses the basic problem somewhat differently to account for the variations in failure modes that can occur. But there are two fundamental differences: the thin-wall approach, which we call the Barlow equation, and the thick-wall approach, which we call the Lame equation. This then raises the question: When does a thin wall become thick? When the problem is thought about, it is not too hard to figure out that the pressure is higher on the inside of the pipe than on the outside. That may not be true if the pipe is buried in a very deep underwater trench. There, the outside pressure can be higher than the inside or at least the same order of magnitude. From that logic for the more general case a man named Barlow surmised that if the pipe is thin one can assume that the thinness of that wall allows one to average the stress across the thickness (see Figure 5.1). So he devised a simple formula by splitting a unit length of pipe through the diameter. He then said the pressure across that diameter creates a force equal to the pressure times the diameter, and the two unit thicknesses create the area that resists that force. Thus, the stress equation becomes S= PD 2t
Figure 5.1? Barlow force diagram

Internal Pressure

Resisting Stress

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This is the basic equation that the code presents. Since the goal is to find the unknown thickness, the formula is rearranged to solve for t given the other three parameters: pressure, outside diameter (OD), and allowable stress. The formula then becomes t= PD 2S

One can note many things from this simple formula. For instance, for a given pressure the stress is proportional to the ratio D t This is sometimes called the standard dimension ratio (SDR). It can be manipulated to represent outsidediameter insidediameter and offers many interesting ways to think about the stresses and pressures in a pipe. Some B31 code equations have added a factor Y to adjust and mathematically move the actual average toward the middle of that thickness. This movement depends on the material and the temperature. They also have an E factor to correct or allow for the efficiency of the way the pipe is made. Recently, a W factor was also added to those codes that operate at high temperatures. This is to make a correction on certain welds when they will be in high-temperature service. This W factor was the result of some unpleasant experience from not taking into account the fact that most often the weld and its attendant heat-affected zones do not have the same strength as the parent material. In spite of the adjustments they are the same basic equation with frills for things that have become known over the nearly hundred years the code has been in effect. Mr. Lame developed the thick-wall theory of pipe. His surmise was that knowing that the pressure on the inside is different than the outside, and as the wall gets thicker, that difference becomes important enough to consider. His formula is somewhat more complicated. It is built mathematically around radii rather than diameters. A simple form of that equation is S= Pb 2( a 2 + r 2 ) r 2( a 2 ? b 2 ) (5.1)

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where S is the equal stress at intermediate radius r a is the outside radius of pipe b is the inside radius of pipe P is the pressure Note two things: When calculating the stress at the point where r equals the inside radius of the pipe the stress is higher than the pressure only, and that if r is set at the outside radius the stress continues to have a component from the inside pressure, and the difference of the two components is the pressure. This issue applies no matter how thick or thin the pipe wall might be. So we now have a tool to begin to answer the question of when does a thin wall become thick. A general answer is when it becomes more than 10% of the inside radius. We have a tool to check that. Simply use the Lame equation on any inside radius and make the thickness 10% of that and find that maximum stress when on the inside. Say the pressure is 150, the inside radius is 3, and the wall thickness is 0.3, making the outside radius 3.3. You will note that leaving the units off the measurement system only requires that you keep all the units compatible with the system you use. The maximum stress on the outside wall is S= 150 × ( 3 2 + 3.3 2 ) = 1578 ( 3.32 ? 32 ) 150 × 6.6 = 1650 2 × 0.3

Now calculate by Barlow S=

which comes to an approximate 5% difference. In the conservative directions, assuming an E of 1, seamless pipe, and low temperature, Y would be 0.4 and W 1, the code equation would give you a somewhat lower stress of 1594. By changing the Y factor and keeping the same thickness the stress drops to 1544, and by making the Y factor 0.5 the stress is 1575. It appears the Y factor adjustments do a pretty good job of calculating the maximum stress per Lame. As in all comparisons like this, the scale factor, higher stress, and so on, may change the relative values, but the adjustments to the simple formula seem to work. Again the careful reader will note that we were comparing stress results from the formulas. In conventional practice we are given a pressure and temperature along with the material. The temperature allows us to determine the allowable stress by one of the methods described. So stress is not a regular calculation made in the code; it is thickness. Recall that the ratio D t

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Table 5.1?Ratio of Maximum Stress to Barlow (Average)
K1 Ratio2 1.1 1.05 1.2 1.10 1.4 1.23 1.6 1.37 1.8 1.51 2.0 1.67

t . internalradius 2 The ratio is the maximum stress calculated by Lame divided by the stress by Barlow (average).
1

K equals the expression 1 +

can be related to stress, and with some algebraic manipulationthat can be related to the thick/thin puzzle. A relationship between the thickness and the internal radius can be derived, and then this expression can be established: 1+ t internalradius

From that one can establish an index of the maximum stress to the internal stress and get an index of how much that maximum stress exceeds the simple Barlow equation (not the code-adjusted Barlow). Then, keeping in mind that the allowable stresses are established at a margin below yield, one can determine the severity of using the simpler equation. In Table 5.1 you can see that the K factor representing a thickness of 10% or less of the internal radius represents a maximum Lame pressure of 5% or less than the average pressure. B31.3 has an enigmatic note in its equation that says that t < D/6 and does not require any further consideration, but if it changes to t > D/6 one must consider other things such as theory of failure, effects of fatigue, and thermal stresses. This is related to the thick/thin problem. Interestingly, the standard pipe dimensions (i.e., schedule pipe in the United States and more or less adopted by ISO) do not have t thicknesses that exceed D/6 above the three double-extra strong schedule. A chart showing the SDR (D/t) ratio of common pipe is in the Appendix. It is as we get into nonstandard pipes that the problem can occur. This then is the general discussion of calculating which pipe thickness to use under given conditions. There are other equations than the code and even a few within the codes. We will discuss these in the following section.

Basic Code Equations
As discussed, the codes offer several variations of the equations. The equations presented in each book section are listed in the code equations table and are discussed individually as well as in general. Within certain
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parameters the different results can narrow considerably when one sets up the conditions properly. The differences are the code books’ responses to the particular problems in the type of service that the specific book was written for. There are some special code equations for high-pressure design in B31.3 (Table 5.2). There are basically three different equations. The third equation is specific materials, such as solution heat-treated austenitic
Table 5.2? Code Equations
Code Designation B31.1 B31.31 B31.41,2 B31.51 B31.83 B31.9 B31.111,2 OD Formula tm = t= t= PDo +A 2 (SE + Py ) ID Formula tm = t= Pd + SEA + 2 yPA 2 ( SE + Py ? P )

PD 2 (SEW + PY )

PD 2 (SEW ? P (1 ? Y ))

PD 2S PD t= 2 (S + Py ) P= tm = t= 2ST ( FET ) D PD +A 2SE

N/A t= Pd 2 (S + Py ? P )

N/A Option B31.1 N/A

PD 2S

Note: The symbols are the same across the various book sections: P is the pressure; D and Do are the outside diameter of the pipe (not the nominal diameter); D is the inside diameter; y and Y are the adjustment factors as discussed in the general equation section; A is basically the same as c, the sum of mechanical tolerances; E is a weld joint efficiency factor for some welded pipe and is given in the books (seamless pipe has an E of 1); and W is the weld joint efficiency factor for longitudinal welds when the temperature is in the creep range as defined in the code. The current edition of B31.1 tells what the factor is under certain conditions and leaves the designer to determine when to use it. When the temperature is below the creep range, that factor is 1. 1 These have a separate formula to calculate the minimum acceptable t, which is tm = t + c where c is the sum of mechanical tolerances like thread depth, corrosion, or erosion allowance.
2 These equations adjust the stress by multiplication of specified design factors and, if applicable, an efficiency factor for some pipe that is not seamless. The proper stress to use in the formula is the adjusted SMYS. 3 The B31.8 formula is given in pressure terms for various reasons. It can and is rearranged to solve for t. As the pipeline is monitored over its use the t may vary, and an allowable operation pressure is recalculated using this formula among other lifetime calculations.

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stainless steel and others at specific temperature, that utilize the von Mises stress criteria and strive to initiate yielding on the outside surface. As such, readers are referred to the codes and other sources before using that formula. They all take a form similar to the Lame equation. The equation for the thickness using the outer diameter is t= D ? 2co ? ?P ? 1 ? exp ? ? S ? 2 ?

( )

This equation eliminates the need for the Y factor adjustment and is therefore slightly more accurate. It has an algebraically manipulated form for ID calculations. In standard pipe the constant dimension is the OD, and as the schedule or thickness changes, so does the ID. The ID forms of the equations are more for convenience when for internal reasons one purchases the pipe to a specified ID. As might be expected the equations for nonmetallic piping are different. Some differences are obvious. The E factor for those metal pipes that are not cast or seamless is not required. This is because all code recognized for nonmetal pipe is seamless, so the factor would be 1 and is not necessary. The W factor for welded metal in the creep range is not necessary. This is because, while nonmetals might creep, they are not welded in the same sense as metals, nor are they used at the temperatures where the effects that W is intended to correct for occur. Finally, there is no use of a Y factor to correct for the stresses moving through the thickness of the wall. The basic nonmetal ASME formula is t= PD 2S* + P

The asterisk (*) indicates that for some materials, such as reinforced thermosetting resins and reinforced plastic mortar, a service factor needs to be included. This multiplier in the code sense is established by procedures established in an ASTM D 2992. The designer is to set that service factor after evaluating the service conditions fully. The code limits the maximum service factor depending on whether the service is cyclic or static, but not otherwise. For comparison purposes we calculate the thickness by the different formulas and comment on the rationale for any difference discovered. To be fair, the calculations will be done for two different conditions: one in the lower temperature ranges that are compatible with pipeline service and the other in the non-high-temperature service. The second set will address the higher-temperature and higher-pressure service that mainly only affects the first two codes. These comparisons are found as charts or tables in the Appendix. Naturally, when one is working with a particular code it is important to use the code equation from that code to establish any values, such as

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thickness for a given pipe at a given pressure and temperature for a given allowable stress, from that code’s rules. This is especially true when converting from one system to another. A particular code as shown by the different formulas for B31 codes will give slightly different answers based on the formula and the requirements of that book section. The same is true for any other code. However, it is a truth of nature that the material does not know which code was used to calculate the thickness. Within the accuracy of our knowledge the stresses at the same conditions are the same regardless of the code. As an aphorism on this it has often been asked: How does the pipe know which code it was calculated for? It is often the case that one might want to know the maximum pressure for reasons other than a code calculation. The differences might not be significant in the decision that the question is intended for. For that reason one of the tables in the Appendix gives the pressure at one unit of stress. It may not be the same exact pressure one would calculate in a code, but it is useful in back of the envelope calculations and as a check against the code calculation made or reported from a computer. The only thing one must do is multiply the factor by an allowable stress. It is an independent measurement system. The table uses standard NPS and DN dimensions as a start. It is time to remind readers that the discussions so far have been about hoop stress only. One will note that most of the codes either require a specific identification of mechanical allowances, including manufacturing tolerance, to determine the minimum required thickness, or advise you that through their modification factors they have taken into account such things and that the nominal pipe size is the result calculated. Manufacturing tolerance in standard pipe is usually 12.5% of the thickness and is therefore an important inclusion. If the pipe is made from plate, which usually has a much smaller tolerance, it is still important but is not as significant. It is important to remember that the word minimum means minimum, and in using things like manufacturing tolerance, it means one has to be sure that what they are using is within that tolerance. This is also the basis of some codes allowing measured thickness. They define in some manner how the measurement must be made. Other mechanical allowances include corrosion allowance and erosion allowance. Both of these are usually beyond the scope of a particular code. They both have little or no influence when the pipe is new and the system is just starting up. They do, however, have a significant influence on the life of the pipe. As a pipe corrodes or erodes it loses strength and material. If no material is added to allow for this loss when the service causes it, the pipe soon will not have the required strength to withstand the service. Sometimes the amount of corrosion or erosion is learned from experience in that service.

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The National Association of Corrosive Engineers (NACE) offers publications that give guidance on the corrosion that may occur. Erosion can be quite heavy in flow that has entrained solids like sand. I am aware of conditions of highly erosive flow that caused failure through a highpressure drop device such as a valve in hours rather than years. There are basically too many variables in erosive quantities to predict a rate. The best one can do is to increase the bend radii as much as possible, add protective coatings or linings in the pipe, and/or work on the hard coating. In the rapid erosion mentioned, a very hard weld coating was added to the device that increased the life to a matter of days rather than hours. Even so, the process was never deemed economical. Other mechanical allowances would be the depth of any threads in the pipe or grooves and other incursions on the integrity of the pipe wall. The formulas of these are simple—one just adds the material to the calculations. This means that you have extra material for the stretches of pipe that do not have threads, grooves, or the like. This may not be economical for the entire length of the pipe. The designer should then consider other means or components to achieve what those threads and grooves provide. One solution might be to insert a pup piece of the thicker material for a short distance. This discussion has to this point been concerned with hoop stress in a steady state or temperature. This is not always the case. In some cases system is designed to go up or down in temperature or pressure. In daily operation these changes may occur in an unplanned way. Such things as changes in flow may cause some severe pressure shocks. They will be discussed in detail in Chapter 12, on fluid transients. Many of the other loads are considered in the flexibility analysis, including longitudinal stress calculations. Flexibility and fatigue analysis is a subject by itself and as such has a chapter devoted to it (see Chapter 7). Longitudinal stresses do have a component coming from the pressure equal to half of the hoop stresses in the simple calculations. They have other components that create moments and other stresses, so they will be discussed in Chapter 7, on flexibility. What we have examined so far is straight pipe. In a piping system there is rarely only straight pipe. Piping has elbows, bends, tees, and other branch connections. The methods of calculating stresses in straight pipe are not sufficient to establish the thickness or stresses in these components. In some cases there are standard fixtures that in some test or other proof provide the fixture with adequate mechanical strength for the situation. These are often covered in a separate standard that is then considered by the various code committees. They determine that when the particular component is in accordance with the code requirements it is acceptable without further proof. This still leaves certain components that require some design input to determine their compliance with the particular section of the code. The calculations for these will be the next few calculations discussed.
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Pipe Turns or Bends
One can ask about the difference between elbows and pipe bends. The answer is relatively simple: Elbows are by definition covered by some standard. As such, they have limitations as to size, bend radius, and resulting angle, usually 90° or 45°. Any other similar product is a pipe bend. In any system there are usually some bends and some elbows resulting from a need for one of the characteristics to be different from something that is covered by one of the standards. The basics of pipe bends are relatively simple. First, if it is a bend, it is not a sharp corner. Subject to material and thickness constraints there is a limit to how small a radius can be bent in a given pipe. Depending on the method of bending there are further constraints. These constraints will be discussed in Chapter 13 on fabrication and examination. The discussion is about the design and considerations of the designer in his or her calculations for compliance with the stress constraints. The nomenclature of a bend is shown in Figure 5.2; it is the same whether the component is a bend or an elbow. There are two basic criteria to determine an allowable pipe thickness. These criteria can be utilized to determine if the resulting bend is compliant with the code. They are based on the fact that that as the pipe is bent two things happen: 1. On the extrados the wall of the pipe thins by some amount dependent on the bend radius. 2. On the intrados the opposite occurs and is also dependent on the bend radius.

Extrados

Figure 5.2? Nomenclature of pipe bend

Bend Radius

Intrados

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These two events are predictable to a certain degree and are the natural result of the neutral radius of the bend, which is the place along the bend that the thickness remains constant during the bend. As indicated by the nomenclature this is usually considered to be the centerline of the pipe. It becomes evident that neither the extrados nor the intrados is this neutral radius. The amount of thinning is as important as the amount of thickening. Finite-element analysis of such bends varies of course as the bend radius varies with the pipe diameter, but some published studies have shown that the actual hoop stress on the intrados may be as much as 75% higher than the stress on the extrados. The changes in geometry as the pressure or fluid moves around the bend cause the changes in stress. The hoop stresses on the outside (extrados) become lower, and the inside (intrados) stresses intensify. It seems that what happens naturally is what Mother Nature knew would be required because the change in wall thickness is in concert with the change in hoop stress. This concert of phenomena if done properly in the bending process allows the bend to maintain the full pressure capacity of the straight pipe for which it is matched. All of the codes put restrictions on the bends. Some, like pipelines, specify minimum bend radius for the field bend. These minimum radii are of such length that the changes in thicknesses are minimized. In essence, the pipe behaves as if it were straight or nearly so. The older method of controlling the bend required that the minimum thickness after the bend match the minimum thickness of straight pipe. This required that the bender start with pipe that is thicker enough than the straight pipe so that when it is bent the thinning results in a wall that is still above the minimum wall computed for straight pipe. This can create some problems of matching up the bent and the straight pipe unless sufficient straight tangent pieces are included in the bend. It also leaves open the question of the need for the intrados to be thicker for the increased stress there. Some thickening will occur, but there is no definition of what thickening is required to keep the bent pipe compliant with the stresses. A newer method is one that has been adopted by the two major codes, and is under consideration by others. It gives a method of determining what those minimum thicknesses should be. This is accomplished by introducing a factor, called I in the B31 codes that have adopted it. This factor is a divisor to the allowable stress used in the system. It is based on the amount of increased stress or decreased stress depending on where one is checking. Naturally, when one increases the allowed stress the required thickness is reduced and vice versa. The two formulas are

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? R? 4? ? ?1 ? Do ? I= ? R? 4? ? ? 2 ? Do ? ? R? 4? ? +1 ? Do ? I= ? R? 4? ? + 2 ? Do ?

for intrados

(5.2)



for extrados

(5.3)

In both cases, R is the bend radius, usually a multiplier of Do Do is the nominal outside diameter, which is considered the same for standard pipe in DN and NPS If one stays with those rules the factors are the same. In whatever way one calculates the thickness one divides the allowable stress by the appropriate I factor as calculated to find the stress, and from that the thickness.

E x a m p l e C a l c u l at i o n s
Use the simplest equation to calculate the thickness for a 6 NPS pipe (6.625 Do) at 875? psi pressure and allowable stress of 23,000? psi. Then the thickness required is t= 168.275 × 6032.913 = 3.200 mm in SI 2 × 158 , 579 t= 6.625 × 875 = 0.126 in. in USC 2 × 23 , 000

Assume you want to bend the pipe with a bend radius of three times the nominal size, or 18? in. in diameter. Using Eqs. 5.2 and 5.3 the intrados I factor is 1.1 and the extrados factor is 0.928. Note that in SI, DN can be considered to be the same as NPS or 6, so the factors in standard pipe would be the same. Thus, the new thicknesses required would be t= 6.625 × 875 = 0.139 in. in USC 23 , 000 2× 1.1

and 3.531?mm in SI for the intrados.

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The same procedure would be used to calculate the thinner wall on the extrados; substituting the 0.938?in the previous equation, the results would be 0.117?in. in the USC system and 2.972?mm in SI. Note that you will be reminded from time to time that a wall thickness carried out to three decimal places is borderline silly. It is done because the U.S. system in spite of all efforts is still basically a U.S. system, and we carry the walls to three decimals in inches and do other things that make little sense in the SI system. It is obvious that a true soft conversion (starting with the SI units one would probably round the wall as calculated from 2.972 to 3? mm) would make a difference in the inches wall of 0.001 on an inch, which is not a significant change from an engineering point of view. This is not to say that one can go below the minimum of the specifying code. It is just to remind the reader that mathematical conversions from one measurement system are not necessarily law, but the code written is law. This is especially true when the code, as many U.S. codes are, is mixed. Any comments on the different manufacturing methods are reserved for Chapter 13, on fabrication. There are some differences that have a real impact on the operation, from both flow and safety.

Miter Bends
In spite of the increasing ability to bend pipe there are just some situations where a bend can’t be made. This may be because of bending equipment sizes or tooling availability. This is especially true as the size of the pipe gets larger. The larger sizes usually don’t have enough demand to justify the huge tooling expenses involved in machine bends. It may be because of the size and wall thickness that the pipe involved is not strong enough to withstand the bending forces without creating ovality or flat spots, which are not acceptable in the finished bend. These do not mitigate the need for changing the flow direction in the piping system. A frequent solution to this directional change is the choice of a miter bend. A miter is succinctly defined in B31.3 as “two or more straight sections of pipe matched and joined in a plane bisecting the angle of junction so as to produce a change in direction.” Normally, it is considered that when that angle is less than 3° no special consideration is needed as to the discontinuity stresses that might be involved in the joining weld. Care should be taken here to be sure that when one is speaking of an angle in a miter there are actually two angles involved. The first angle is called θ, which is the angle of the cut on the pipe. Naturally, for the pieces to mate properly for welding the same angle cut needs to be made on the mating piece of pipe. When joined, this creates the second angle, α, which

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T Mean Radius r

q

q

N

Effective Bend Radius R D

Figure 5.3? Miter bend nomenclature

is sometimes called the total deflection angle of the pipe. See Figure 5.3 for an example. It is usually considered that if θ is more than 22.5°, problems are going to happen. That is, unless it is a single miter for a total deflection of more than 45° but less than 90°. B31.8 does state that if the operating pressure creates a hoop stress of 10% or less of the SMYS, you can have a miter where the total angle is not more than 90°. There are two different kinds of miter bends. The first is a single miter, as just mentioned. The second is a multiple miter, where the direction change needs to be of a higher degree. Multiple miter bends come in two varieties, closely spaced and widely spaced. As we examine the way to determine the minimum thickness of the miters we will begin to understand the difference. It comes about as the length of the individual sections get longer. The difference comes when the centerline of the section in question changes from less to more than the mean radius times the factor (1 + tan θ). This is the definition of closely spaced. The reasons for this change can be dictated by constraints on the narrowness of the crotch or smaller length of the section of surrounding requirements, or by the resulting equivalent bend radius.

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Only two of the B31 code books give a specific formula for calculating wall thickness for the miter section. The rest of the codes give you limits to the pressure that may be utilized along with the percent of allowable stress that may be used with that pressure. These are fairly consistent, and are limited to the pipeline or low-temperature codes where one doesn’t have to make significant adjustments for the mechanical property changes that occur as the temperature rises. Basically these constraints limit the pressure that can be utilized or the amount of hoop stress that pressure can develop in the pipe. The theory is that the increased stresses that may occur due to the discontinuities from the changes in direction will not raise the stress in a miter so much that it will make it inappropriate to use the same wall thicknesses that were calculated by using the lower stress for the pipe thickness sizing. Cursory mathematical examination of possible situations indicates that the increased stresses expected in the miter will not be over the limit. Some judgment has to be made in performing such checks, as the radius and other factors can change the resulting climb in the stresses. Suffice it to say, the prudent engineer would also perform some analysis and/or increase the thickness by some percent, and thus the need exists to determine that percent by analysis. B31.1 and B31.3 take different approaches, and both will be explained and discussed in the formulas and calculations. As suggested, the prudent engineer might perform some calculation to be sure that the restriction as applied to the actual system under consideration does not violate stress limits. One might ask why not use the same technique of arbitrary restrictions with B31.1 or B31.3. After reflection, the answer would seem evident: Both of those codes are for systems that, unlike pipelines, do not expect to have continuous operation at one state. Their systems might not work by lowering the pressure, whereas in a pipeline lowering the pressure may be economically undesirable. However, the net result is primarily only less flow, but there are not many intentional state changes as in the process industries. In power plants, lowering the pressure may change the quality as well as the pressure of the steam, which might have a very serious effect in the turbines. And lastly, in many of their tempe? rature regimes lowering the allowable stress further might make the system one that can’t be constructed economically, since as the temperature climbs the allowable stresses fall, sometimes rather steeply. The result is they must calculate the thicknesses and pressures for the given conditions. Before we examine the two methods of calculating this thickness we need to look at the nomenclature of the miter bend so the various new symbols in the resulting analysis are understood.

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The equations have the look and feel of empirical equations that revolve around the somewhat arbitrary function of a θ, which is a saw cut and equals ? pipe deflection. There are two equations for the sections under the θ. The first check covers a single miter for deflections from 3° to 45°. The second check uses that equation plus a second equation that is dependent on the equivalent bend radius, which might be the controlling factor depending on that radius. There is a minimum equivalent bend based on an empirical constant and the pipe diameter. The third equation applies again to single miters for a θ over 22.5°. This situation could make economical sense if one needed a deflection larger than 45° but less than 90° (probably several degrees less), where the extra cutting and welding would increase the cost of construction. This might sound quite complicated, but it is a relatively simple decision-making process and will become clear as we work through the example. The checks mentioned are basically a check on the maximum pressure the miter can take at the allowed pressure given the θ and some new thicker component. You will recall that the other methodology is to limit the pressure to some amount less than what the calculated straight pipe thickness would allow. This method turns the logic around and asks: What new thickness is needed for this particular miter to be stressed at the allowable amount? The calculations then become iterative and presented in much the same way that they were when calculating the friction factors in fluid mechanics that we discussed earlier in Part I. Thank goodness for modern spreadsheets and calculators, which can be set up to perform the iterations in a painless way. Following are the relevant equations that are used in B31.3. They are somewhat more comprehensive. This is especially true as the pressures get higher, since B31.1 places limitations on the pressures that are allowed before allowing an increase in thickness to compensate. where c is the total mechanical allowance E is the pipe efficiency rating Pm = Pm = SEW (T ? c ) ? T?c ? ? (T ? c ) + 0.643 tan θ r (T ? c ) ? r2 2 ? ? Pm = SEW (T ? c ) R1 ? r2 r2 R1 ? 0.5r2 (5.4) (5.5) (5.6)

SEW (T ? c ) ? T?c ? ? (T ? c ) + 1.25 tan θ r (T ? c ) ? r2 2 ? ?

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Pm is the maximum allowable internal pressure for miter bends R1 is the effective radius of the miter bend r2 is the mean radius of the pipe S is the allowable stress T is the miter pipe minimum wall thickness W is the weld strength reduction factor θ is the angle of miter cut The minimum value of R1 is established by a formula where R1 is dependent on the final thickness calculated, and its smallest amount is the equivalent of 1?in. larger than the pipe radius at less than 0.5?in. (13?mm), and goes up from there. This adder varies according to a specified formula that causes one to add 1?in. (25?mm) at the thin thickness to 2?in. (50?mm) at 1.25?in. (32?mm) thickness. If one is doing an actual code calculation the specific formula check is recommended. For demonstration purposes we treat the minimum R1 as 2?in. (50?mm) over the pipe radius. A little explanation of the usage of the formulas is required. Before setting up an example, Eqs. 5.4 and 5.5 are both used in multiple miter calculations where θ is 22.5° or less. One calculates the maximum pressure by both methods and then uses the lesser pressure as the appropriate pressure. If one is only intending to use a single miter where θ is less than 22.5°, then Eq. 5.4 is the only calculation required. Finally, if one is intending to utilize a miter cut of over 22.5°, only a single miter is allowed and the minimum pressure is calculated by Eq. 5.6. It is a known fact that the thickness of the miter pipe is required to be more than the thickness of the straight pipe to which it will be attached. Often this requires an educated guess or repeated calculations. Once again, setting up a spreadsheet and using a goal–seek function will save a lot of time calculating several different miter bends. This is discussed more in the Appendix; for now, let us explore a set of sample calculations.

E x a m p l e M i t e r C a l c u l at i o n s
First establish the data for the problem. Assume a multiple miter with θ of 22.5° and the following: ? ? ? ? Design pressure (for straight pipe) is 400?psi (2750?Kpa) Pipe OD is 48?in. (1220?mm) W and E are 1 Wall thickness is nominal, 0.5?in. (13?mm)

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? Corrosion allowance is 0.06?in. (1.5?mm) ? Allowable stress is 23,000?psi (158.5?MPa) Step one: Calculate the mean radius of the pipe at 23.75?in. (603.5?mm). Note that the layout geometry requires an R1 of 30?in. (762?mm), which is well above the required minimum. For calculation purposes, make a guess at the required thickness to meet the pressure and then check for the radius that will work. For this example, guess that the required thickness is 0.8?in. (21?mm). First, use Eq. 5.4 to calculate the minimum pressure it will allow.

( 0.8 ? 0.06 ) 23 , 000 × 1 × 1 × ( 0.8 ? 0.06 ) ? ? ? 23.75 ? ( 0.8 ? 0.06 ) + 0.643 × 0.414 23.75 × ( 0.8 ? 0.06 ) ? ? = 415.5 psi ( 2864 Kpa )
This will certainly handle the proper pressure for the bend. We must make a check using the 30-inch radius and Eq. 5.5 to find which formula yields the minimum allowed pressure. Unfortunately, that check shows a much smaller allowable pressure. A careful reading of the formula shows that increasing the minimum radius will increase the allowable pressure by that calculation. So we will estimate a new R1 and run that formula. For this run, we will do it in SI units to be fair to our metric readers and then convert back to USC. Our guess is 1020?mm R1. Using Eq. 5.5, the calculation is 148.5 × 1 × 1 × 1000 ( 21 ? 1.5 ) ? 1020 ? 603.5 ? = 2782.4 Kpa ( 403.5 psi ) ? ? 1020 ? 0.5 × 603.5 ? ? 603.5

Note that megapascals were converted to kilopascals and that there are subtle differences in converting back and forth between the systems due to rounding, and so forth. Now the designer has to determine if the space in the layout can fit the larger R1 required. If not, he or she must determine what to do. There are options, such as using a different material with a higher allowable stress. That would entail other considerations. The designer could possibly use Eq. 5.6 and create a single miter for a larger θ. This might cause pressure drop problems as the fluid flows through the miter, which causes higher erosion or other considerations. From a pressure-only view, let’s assume that the final required change in direction is 80°, which in a single miter means a miter cut of θ is 40°. Apply Eq. 5.6; a quick check shows that the thickness of the miter would have to be 2?in. (51?mm). This thickness in

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itself might cause problems. From this basis it seems that the designer might have to take a closer look at the layout and possibly make the corrections there. It stands to reason that a different layout might be the answer. As noted previously, B31.1 puts restrictions on pressure and many other things. However, if the pressure is over 100? psi (690? Kpa), some calculation is allowed. First, the code refers to its paragraph, 104.7, which among other things leads one to things like FEA, testing, or calculations. Those calculations might lead one to go to the formulas in B31.3. However, formulas are provided for the minimum wall thickness that is acceptable regardless of what the calculations show would work. Those formulas are dependent on what are called closely spaced miters and widely spaced miters. These spacing definitions are based on the centerline cord of the miter section. If that cord is less than the quantity (1 + tan θ) times the mean radius of the pipe, it is considered closely spaced. Conversely, if it is larger than that figure it is considered widely spaced. The definition is the same in both B31.3 and B31.1. It is also used to differentiate the stress intensification factor. The use and calculation of this factor is discussed in Chapter 7 on flexibility analysis. B31.1 also defines the effective radius of the miter bend differently than B31.3. In a closely spaced miter, R is defined as the centerline cord times the cotangent θ divided by 2, and the radius of the widely spaced miter as the quantity (1 + cot θ) times the mean radius divided by 2. This means, of course, that to change the effective radius of the miter bend, one merely changes the length of the centerline cord, which is true. The formula for the minimum thickness of the pipe for the two types of miter bends is similar to Eqs. 5.4 and 5.5 without the portion that converts the result of the calculation into a minimum allowed pressure. For closely spaced, the formula is r R ts = tm r 2 ?1 ? ? ? R? 2? For widely spaced, the formula is r? ? ts = tm ? 1 + 0.64 tan θ ? ? ts ? Again, note that the widely spaced formula has the same factor ts on both sides of the equation, which requires an iterative solution or, with manipulation, a quadratic solution. The spreadsheet solution is quite simple with the goal–seek function.

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If one experiments with the formulas for both, the inescapable conclusion is that there is a vast difference in the results to make a given miter design’s geometries have a required thickness. One can only assume that is because of the difference in the design philosophies of the two com? mittees regarding the safe margin in a given design. The differences lessen as the sizes of the pipe change. It is also true that the different fluids, and so on, that are used are the basis for those differences. It is hoped that the mechanical design committee, whose mission is to establish a standard, can find a way to minimize those differences. There are of course other differences depending on the other analysis that one does in calculating the acceptability of the miter for that code. It seems that the simple thing to do is use the B31.3 approach and check against the minimum thickness formulas given in B31.3. It goes without saying that building an FWEA model is acceptable, but that is an advanced methodology. Nevertheless, as the technology advances it may be the simple way. Setting up B31.3 formulas in a spreadsheet gives one both speed and flexibility in calculating. As mentioned, this is discussed in more detail in the Appendix. The foregoing is a discussion of the methodologies to determine the pressure that a given pipe will sustain at a given temperature. Or, what size pipe is required for that temperature and pressure given the pipe and its material? However, one might recall that in every case the discussion revolves around pressure that is internal to the pipe. What happens when the pressure is external to the pipe? The first thing to note is that the tensile formulas will work, but there is another failure mechanism. Called by many names, basically it is buckling- or instabilitybased where failure doesn’t occur in the same manner. There is a second check that does not necessarily have to occur in every situation but should occur, and the designer or engineer needs to be aware of the situations where that happens. Therefore, we move to the case of solutions for external pressure.

External Pressure
When we are dealing with internal pressure we are dealing with the tensile properties of the metal as the pressure is trying to expand the metal or, as one person put it, tear the pipe in two. With external pressure just the opposite occurs. It compresses the material and tries to squeeze it together. As you may know, steels in particular have very similar properties in tension and compression. In that case the questions become: What is the big deal if the compressive strength is similar in size to the tensile strength?

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What difference does that make? While it is true that the yield points and thus general distortion and ultimately failure can occur, another phenomenon can occur in compression where the failure is well below the yield point. We are so used to thinking of the failures being proportional to the load applied that we tend to neglect the failure from buckling instability. This is well known in columns and is described in many strength-ofmaterials books by using the Euler formula, where a column loaded in compression has a critical load, where the column can fail before the load that would fail, that column in tension. That column will “buckle” and fail in a compressive load. This is based on the cross-section of the column, the modulus of elasticity, a constant based on the end supports of the column, and, most important, a factor called the slenderness ratio. The slenderness ratio of the column is the length divided by the radius. There are many variations of the computational ways to determine what the critical load is, but for the details of a column, readers are referred to a strength-of-materials book such as Roark’s Formulas for Stress and Strain. The buckling of pipes and tubes has a very similar buckling phenomenon based on the OD, wall thickness, external pressure (net), and length of pipe between adequate supports. One might ask, When is this a problem? Well, just consider the OD of a pipe or tube with a very thin wall. Surely you have handled an aluminum soda can, which you can shake up and free the entrapped CO2 while the can is sealed; therefore, it can withstand a fairly large internal pressure. However, one can squeeze the can (especially when empty) and it will collapse. The question is at what pressure (squeeze) does that occur and with how large a can. Now, consider a pipe with a vacuum where the external pressure could be 15? psi (≈ 100? Kpa), double-walled piping with pressure in the annulus, piping underwater, pipe inside a pressurized vessel, fire tube, and so on. In other words, it can happen to pipe with some regularity. ASME Division 2 has an extensive set of graphs and charts for several materials that allow one to calculate an allowed external pressure. A sample of these charts is in the Appendix, but not the entire set. Here we work through the analytical aspects that were basically used to develop these charts. It should be pointed out that the calculation method here is only appropriate for one material at 300°F (150°C) or lower. Regressing the other temperatures and materials would be an arduous task and the charts for those are available through ASME. The piping codes reference these ASME charts for their requirement to check compliance with their codes. It is suggested that if the condition one is checking for this material is sufficiently resolved by these calculations, one can safely assume they have met the intent. However, unambiguous compliance with the code might require use of the graphs and tables.

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A two-lobe form of a tube collapse is the one calculated. This is the lowest pressure that would cause this type of failure. The next higher pressure would be 2.66 times higher, and if the situation was not sufficient for this two-lobe failure, it is of no consequence as the pipe has already failed. It is important to point out that the development of the formulas introduced here is fraught with considerable highly technical mathe? matics, which are not shown. What we are working with is the resulting derivations from that math, substantiated by experiment. The length of the pipe is important; like the slenderness ratio, it does come into consideration. It is defined as the distance between two end supports of a pipe. For instance, consider a length of straight pipe with a flange on the end of the spool and a valve some distance away. That distance between the flange and the valve would be the length under consideration. In the absence of any stiffener similar to the valve or flange, one could add a stiffening ring around the pipe. The determination of what is an appropriate distance is based on the results of the investigation, which in effect is a trial-and-error situation in the ASME methodology. The chart/graph methodology is to establish a factor A with a graph or chart using as the independent variables the ratio length L previously described and the OD of the pipe as the first variable. The second variable is the OD of the pipe divided by the wall thickness. Using those two variables one can read factor A. Then one checks for the appropriate material chart and uses factor A as a variable. Read the chart, which has a different line for that material at different temperatures, and from those two variables you get a factor B. Using that factor B one can calculate the allowed external pressure. If that pressure is higher than the design external pressure your estimated length and wall thickness for that size pipe is adequate. Since the length is usually established by the geometric layout if the pressure is not high enough one starts with a new thicker pipe and repeats until there is a sufficient solution. Subsequently, there is a need to determine the size of the stiffening rings, which will be discussed after going through this abbreviated (due to one material temperature) calculating procedure. The first calculating step is to calculate the critical length. This is important, because above that length there is a different calculation procedure for below that length when calculating factor A. The formula is as follows; note that it is the same in inches or millimeters. Do t



Lc = 1.11Do

(5.7)

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5.? Piping and Pipeline Pressure Thickness Integrity Calculations

Lc is the critical length Do is the outside diameter t is the wall thickness An example with 6 NPS S40 pipe is 1.11 × 6.625 × 1.11 × 168.275 6.625 = 35.77 in. 0.280 168.275 = 908.558 mm 7.112

This then is used to determine what factor A to use for a length that is more than the Lc: ? t ? Factor A = 1.1 ? ? ? Do ? 0.280 ? 1.1 × ? = 0.001965 in. ? 6.625 ? For factor A in millimeters multiply by 25.4 = 0.04991. Note: If one is using Eq. 5.8 in millimeters, factor 1.1 changes to 27.94, which eliminates multiplying by 25.4 to get from USC to SI units. If the length is less than the critical one, the formula for factor A changes: ? t ? 1.30 ? ? ? Do ? Factor A = L Do
1.5 2 2

(5.8)





(5.9)

A specific L is needed to calculate this. To dramatize the difference in the two factor A’s, the following example uses an L of 35?in. (889?mm). Using Eq. 5.9 at the specified length, factor A becomes 0.280 ? 1.30 × ? ? 6.625 ? 35 6.625
1.5

= 0.002138 in.

As before, if one uses the millimeter units in the calculations, factor 1.3 changes and becomes 33.02, which gives a factor A of 0.05431?mm. This merely states mathematically what is intuitive: As the tube gets longer it

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takes less external pressure to buckle. Of course, it is also true that OD and the thickness of the wall play important roles in determining the buckling pressure. Once factor A is determined, it is used to determine what ASME calls factor B, which is really the allowable stress for the material. This stress is not like the allowable stresses that are in the stress tables in the B31 books. It is based on what is called the critical pressure—the pressure at which the pipe or tube actually begins to collapse or buckle with appropriate safety factors for such things as out of roundness of the tube and other imperfections that are not known at the time of the design, as well as conservatism. There have been many analytical ways to marry the fact that the actual pipes are not perfectly circular, thick, or smooth. These have involved empirical work done over the years. The analytical work has been done for over 100 years. There is a book, Textbook on Strength of Materials written by S. E. Slocum and E. L. Hancock in 1906, that has a lengthy discussion of the theoretical calculation of this critical pressure, and then a subsequent chapter that develops the theoretical formula into what Mr. Slocum calls a more practical method. Roark’s sixth edition of Formulas for Stress and Strain has the same formula and lists it as approximate and attributes it to a 1937 book. These various theoretical and practical calculations vary somewhat wildly with the ASME charts. The ASME charts are based in part on work done at the University of Illinois in “Paper 329.” Those charts were done without any allowances for experimental data. The knockdown factors and allowances to account for experimental results and shape factors were included in the development. That base formula is ec = where ec is the critical stress ER is the tangent modulus E is the modulus α is a knockdown factor to accommodate the differences between tests or experiments αe is the theoretical stress In short, a lot of work has gone into the development of the charts. There are 21 pages of graphs, most of which have four different materials, each with a variety of temperature lines to read factor B. Then the ASME added some charts that in effect digitize the answers to factor B. One ER αα e E

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should use them to determine the exact knockdown factors and which exact theoretical form they used. To calculate the theoretical stress is at best difficult. In addition, the graphs and charts are made with a margin of 4. And even when one gets a factor B, it needs to be converted to a margin of 3 by multiplying by 4/3. If one repeatedly uses the same materials at the same temperature it is possible to make a regression on those charts and then use that regression to calculate B from the calculated A with the formulas we used before. For this book and personal use, that regression was made for two carbon materials, called CS1 and CS2 by ASME, for carbon material up to a yield of 30,000? psi and for those with a yield of over 30,000? psi, respectively. These regressions were only for above the 300°F line. Since the charts are not in SI units, further discussion is only in USC with apologies to the SI purists. It is emphasized that any code calculation should be checked with the actual graphs and charts. The work is not official. This would be especially true if the calculation created concern by being close to failure. There may be commercial programs that have codified the work required. That being said, readers are informed that more information is in the Appendix. Using that data and the factor A calculated earlier, one gets the results shown in Table 5.3. The allowed pressure is calculated using the formula from ASME Boiler and Pressure Vessels, Section VIII, paragraph UG 28 for cylinders: Pallowable = 4B D 3 o t

( )

where the symbols retain the same meaning as before. Assuming that the pressure you are testing for is only a vacuum where the external pressure is 15? psi, you are done with the calculation. If the

Table 5.3?Regressed Factor B for Selected A Factors Using Regression on Chart CS2
Calculated A* 0.001965 0.002138 0.002993 Factor B 14,989 15,261 16,184 Allowed P (psi) 845 860 912 Critical P (psi) 2534 2580 2736

*The first two A factors are either side of the critical length and close; the third is at two-thirds the critical length.

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external pressure exceeds the allowable pressure, the first thing is to try a thicker wall. Depending on many factors, that may be expensive or difficult. And again, depending on the situation, another way to accomplish that is to shorten the L distance. As noted earlier, shorter is inherently stiffer. The last concern would be the moment of inertia. Whatever holds the ends of the section of pipe being considered in the external pressure would have to be sufficient to handle the loads imposed by that set of external forces. Those stiffeners can be flanges, valves, structural shapes, or just plain rectangular rings. The moment of inertia calculations are standard calculations, so they are not further discussed here. The major question is, What moment of inertia is required? The following formula allows one to calculate the appropriate moment of inertia: Irequired =
2 Do L A t + s Factor A 10.9 L

(

)

(5.10)

The familiar symbols have the same meaning as before. The new symbol As is the area of steel that is involved in the calculation. One might question the 10.9 factor, as it is somewhat different than a typical moment of inertia factor. It is an allowance for using the pipe between the stiffener as part of the calculation. If that pipe is not used, the reader is directed to ASME UG 28 and further discussion of the other alternative. For purposes of simplification, Figure 5.4 shows the arrangement and relationship. The figure shows a simple cross-section of a rectangular ring. If one uses some other arrangement it will alter the actual moment

b

d 0.5 L

0.5 L

Max 1.1 (D/t ) 0.5

Figure 5.4? External pressure stiffener example

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calculation. But success is when the calculated moment is larger than the calculated required moment. Note that the actual calculation may require repeating if the first attempt to size the moment of inertia does not meet the requirement, since the size of the ring is also part of the requirement calculation. This is just another case where experience and judgment may be required.

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C h a p t e r

6

Straight Pipe, Curved Pipe, and Intersection Calculations

Overview
This chapter covers the basic requirements for establishing the appropriate wall thickness for the proper diameter of pipe, and the material chosen for the type of service. In effect, it establishes the pipe pressure temperature rating. If the piping system was just straight pipe or, as necessary, curved pipe that was welded together, the pressure portion of the design would be complete. However, it is the rare pipe system indeed that doesn’t have intersections and for that matter places along the pipeline where something is used, most often flanges, to break the continuity of the pipe run. The intersections include such things as tees, wyes, laterals, branch connections, and, rather than bent pipe, such fittings as elbows. In fact, there are a myriad of fittings that can be used to accomplish the even larger varieties of ways that pipe can be put together. Those fittings that are ubiquitous can be standardized; in fact, there are many that are codified into standards. These are often called dimensional standards since the most obvious thing they do is establish a set of dimensions that define how they would fit into the piping system. By preestablishing these “take-out” dimensions they perform an important function in allowing the standard piping system design to proceed long before the actual purchase of the components. They even allow in a

? 2010 Elsevier Inc. DOI: 10.1016/B978-1-85617-693-4.00006-7

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somewhat more limited sense the opportunity to precut the individual pieces of pipe that are to be fitted into the puzzle of the system. One of the secondary issues in developing these standards is that these fittings are also subject to the same temperature and pressure requirements of the parent pipe to which they are attached. This gives rise to the need to establish the pressure rating of the fitting or component itself.

Code Standards
Each of the B31 code books has, as one of its responsibilities, the function of reviewing the various standards that are available and listing those that meet the requirements of that code. Naturally, many of the more common standards are recognized by all code books. Not all are for obvious reasons. One of the things that those committees look very hard at is the way any particular standard approaches the business of pressure ratings in conjunction with the requirements of the process for which they are most concerned. When a standard gets “blessed” by a code book the meaning is simple—users of a product from that standard need only be concerned about the compliance of that product with the requirements of the standard. If it meets the standard, it meets the code. One can use a product from another standard that isn’t on the approved list. However, in using that standard some compliance with the code must be established. There are several ways to do this, including using the traditional area replacement calculating method, or some other method that is deemed to give the same margin of safety that is embedded in the code. Many codes have a paragraph or refer to some other means of proving the code. Both of the general methods also apply to products that are not covered by a standard but are special. Oftentimes, such a special might be a variation of a standard that doesn’t in some manner completely comply with the standard. This noncompliance needs to be agreed on between the manufacturer of the product and the purchaser, and that agreement should include some explicit understanding that it meets the pressure temperature rating as if it complied in all respects with the original dimensions.

Definitions
When a code defines what is necessary to meet its requirements, the approved methods are often spelled out, including things such as the following: 1. Extensive successful service under comparable conditions, using similar proportions and the same material or like material. This

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rather begs the questions: How did one get that experience, what is extensive, how close is similar, and what is like material? It is basically a “grandfather” clause for items that have historically been used. Then the question is, How did it get into codes that have been around for years? 2. Experimental stress analysis. 3. Proof test in accordance with .?.?.?. There is a list of accepted proof tests ostensibly to cover various shapes and situations. The B31 technical committees have been working to develop a universal standard proof test. 4. Detailed stress analysis such as the growing use of finite-element analysis. One should be sure the analysts know what the special needs are. For instance, analysis in the creep range is significantly more restrictive. Plus, one asks: Does the analysis of one size cover other sizes? What are the acceptance criteria? The preceding paraphrases some of the existing lists. The comments are not intended to point out that the list is not sufficient. When done properly, any of the methods is more than adequate to define compatibility. The comments basically point to the fact that the use of the method is not sufficient unto itself. This is especially true of the user/purchaser’s acceptance of the use of one or more of the systems. It points to the reasons that the technical committees are working on the universal procedure. I was privileged to read a report from one of those methods. To paraphrase, “We tested it, it passed.” Now if that had come from a source that one knew well and was familiar with over a broad range of situations, it might be marginally acceptable, but even then I would ask by how much and what was tested, etc. There is more discussion on this later.

Intersections
The point so far is to say that the code acceptance of a product that is other than a piece of straight or bent pipe is somewhat more complex than the computation of a minimum wall thickness to establish the product’s pressure temperature rating. The fundamental philosophy of such intersections should revolve around this fact. Nothing should be added to the pipe that reduces its ability to safely perform its duty of transporting its designated fluid through the designed system at the designed pressure and temperature. This is a rather wordy way of saying that a chain is as strong as its weakest link. That weak link in the piping system should be the pipe, and we are discussing here the minimum pipe. Of course, there is nothing that says

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the designer can’t use and, in many cases for many reasons, will use stronger pipe. For instance, if one calculates that a minimum wall of a 6-in. pipe needs to be 0.3, the designer has a decision to make. The minimum wall of an S40 pipe is 0.245? in. (0.280 × 0.875 manufacturing tolerance), while the minimum wall of an S80 pipe is 0.378?in. The designer might petition to lower the pressure temperature rating, which is unlikely to happen. Therefore, he or she might specify a special pipe size, which might be cost prohibitive. Likely, he or she will choose the S80 pipe and have a strongerthan-necessary pipe. This particular dilemma may follow the designer through the course of this pipe spool design. Many of the components, as mentioned, are standardized and for that reason it is often more cost efficient to use a standard-size component that has a pressure rating higher than the particular system for which it is being specified. However, when an intersection is going to be made in the base pipe other considerations are necessary. It is classic that U.S. piping codes and other countries’ codes will have something like the following statement: “Whenever a branch is added to the pipe the intersection weakens the pipe. Unless the pipe has sufficient wall strength beyond that required without the branch, additional reinforcement is required.” See Figure 6.1 for an example. Then the codes proceed to tell you what kinds of reinforcement can be used. All piping codes also have the ability in certain circumstances to use other methods. Some of those methods discussed are already methods that require work or calculation that is not required by the approved or listed standard.

Stress Level

Stress Level

Internal Pressure

Figure 6.1? Intersection stress increase diagram

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The grandfather method known by most pressure code users and many nonusers in general is what is known as area replacement. Area replacement, although simple in concept, is somewhat complex within the different codes. We discuss it here in regard to a generic concept that will describe the fundamental process. Readers are left to choose a particular code and follow its specific process. Many of these differences in methodology are brought about by the fact that some of the pipeline codes work with nominal walls in their calculations, while others work with minimum walls. In addition, some have restrictions on what you can and cannot use regarding sizes and methods. The fundamentals are that one knows the required wall for pressure on both the run and the branch. As Figure 6.1 shows, the increased stress in the assembly extends in a decreasing manner as one moves away from the discontinuity. Those distances are not the same. There are very complex theoretical analyses that determine the distance of such discontinuities. They are important in limiting the area where any reinforcement is particularly effective. The codes’ intentions were to make the assembly safe. So they rather simplified the analysis. Looking at Figure 6.1, how far should one go for the acceptable decreased stress intensification? The expression that defines the amount of stress existing as one moves from the center of the hole out is rather simple:

σ=

1? x2 x4 ? 4 + 3 + 3 ? ? 4? r2 r4 ?

(6.1)

where σ is the stress at distance x from the hole and r is the radius of the hole.

Asme Standards
Given those factors, the decision to be made is how far along the run should the distance x be set as acceptable. ASME decided to make that distance one diameter of the opening in either direction. Noting that one diameter equals two radii, let us check what occurs at the edge of the hole where it would be highest and then at the two-radii distance. One should note also that the use of 1 in the numerator of the fraction 1 4 in Eq. 6.1 is a unit substitution. If one were doing a real calculation, that 1 would be replaced by the nominal l hoop stress that was calculated for the unbranched pipe. Assuming an opening of 6?in. at the edge (one radius from the center), the stress would be 1? 32 34 ? + + 4 3 3 ? ? = 2.5 4? 32 34 ?

II.? CONSTRUCTION AND DESIGN FABRICATION

90

6.? Straight Pipe, Curved Pipe, and Intersection Calculations

So whatever the nominal stress is, it is 2.5 times the stress at the edge of the hole. Now moving out to the diameter (2r) from the center, what is the stress? 1? 62 64 ? + + 4 3 3 ? ? = 1.23 4? 32 34 ? At this point the stress is 1.23 times the nominal. One would note that if the reinforcement were there and completely integral, the new stress would be somewhat lower because of the additional material. A good question might be, How far does one have to go to get the stress absolutely to 0 by this simple calculation? Well for this size hole, it turns out that the distance to 1 is ≈ 92?in. For smaller holes it is less, and for larger holes it is more. That is one of the complexities. But how far up should one go along the branch from the run? Here again, there is a simplification of the complex math that can be used. This factor involves the use of Poisson’s ratio and, indirectly, the Young’s modulus (modulus of elasticity) and the moment of inertia, as well as the radius. Without going through the rigorous math, that ratio in terms of Poisson can be expressed as the allowed length up the branch equal to 1 β where rt 1.285

β=

This equation was worked with Poisson’s ratio set at 0.3, which is for steel. This is sensitive to both the radius and the wall thickness. ASME decided to use the thickness as a guide and to note that the walls of standard pipe can be very roughly equated to 10 percent of the radius of that pipe, especially in the standard and extra-strong wall dimensions. This 10 percent wall thickness calculates out as follows. Setting r equal to t/0.1 and rewriting the preceding equation for l in terms of t, we get the following: t2 0.1 1.285 This equation gives the same answer as setting t in the previous equation to 0.1r. That result is 2.46. ASME chose 2.5 times the header wall thickness or a combination of branch and header walls as the standard. Without the variations per book, and understanding that in most cases we are talking about the minimum required wall thicknesses, the reinII.? CONSTRUCTION AND DESIGN FABRICATION



Asme Standards

91

forcement zone is defined as one diameter of the opening on either side of the center of that opening and 2.5 times the thickness above the surface of the pipe. It should be noted that all material within the established reinforcement zone is usable. The basic idea is simple. When you cut an opening you remove an amount of metal that has an area through its diameter that is equal to the required thickness of the pipe from which you have cut the hole times that diameter. Then you calculate the necessary reinforcement zone with the rules just established. The material that is originally required for the two pieces—branch and run—is within that zone; however, the required for pressure integrity is not available because it has been removed. So you must add an equal amount of metal to the area that is removed within the reinforcement zone. There are at least four areas of potential reinforcement within that zone: 1. Excess metal in the run from which you have just made the opening 2. Excess material on the branch pipe 3. Material in any ring pad added 4. Attachment welds If one designates the metal cut out as AR and the excess metal in the areas as A1 + A2 + A3 + A4, the area replacement becomes a simple calculation of making those two sets equal. Some of the ASME codes add an additional factor for cases where the nozzle is inclined away from the 90° intersection with the centerline of the pipe by an angle. This is called θ and is defined as the angle from the centerline of the run pipe—that is, the calculated diameter is multiplied by the factor of (2 ? sin θ). This manipulation changes the area required to an equivalent of the major axis of the ellipse that is formed when a cylinder is cut on a bias. So the designer goes through the steps, as indicated in Figure 6.2. As a reminder one must always actually use the specific requirements of the code the designer is working with, as each has idiosyncrasies specific to the code. We will keep the generic focus in the example. Assume that we are preparing to put a 3 NPS (80 DN) S40 branch on a 6 NPS (150 DN) S40 run. The respective minimum walls are 0.189 and 0.245?in., based on the U.S. manufacturer’s tolerance being deducted. The design temperature is 350°F (175°C) and the material allowed stress is 23,000?psi (158?mpa). The pressure of the system is 1750?psi (11.8?mpa). This basically uses all of the minimum wall of the 150 DN pipe, and therefore, only uses 0.129?in. of the 80 DN pipe. The opening cut in the run for a set on branch is a 3.068-in. diameter, so the area required is AR = 3.068 × 0.245 = 0.752? in.2. There is no excess metal in the run and the height of the allowed reinforcement zone is 0.245 × 2.5 = 0.6125? in. The excess of the branch is 0.189 ? 0.129, or 0.06 × 0.6125, or the inherent is 0.036?in.2. Now the designer has to decide what to do.
II.? CONSTRUCTION AND DESIGN FABRICATION

92

6.? Straight Pipe, Curved Pipe, and Intersection Calculations

Required thickness calculated per the ASME code.

Reinforcement zone: Only excess metal in this zone is considered reinforcing.

Genereal Procedure

Area of metal removed from run pipe that must be replaced in zone for reinforcement.

1. Calculate area of metal removed by multiplying required thickness by the diameter of hole; adjust for angle as allowed.

2. Calculate total area of excess metal in reinforcement zone; this includes attachment welds.

3. Increase pad, run, or branch wall until item 2 is equal to or greater than item 1.

Figure 6.2? Generic area replacement

One solution is to change the run to S160 pipe. The minimum wall of S160 pipe is 0.491?in., which is twice the 0.245?in. of the required wall of 6 NPS pipe. That could, depending on the geometry of the spool piece, be a short length of that pipe. C

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