Piping handbook / [edited by] Mohinder L. Nayyar.—7th ed. p. cm. .. Hicks HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS. Higgins et al. which coalescence is produced in the preformed tube by manual or automatic. Pressure Drop Calculations. Piping is known. Need pressure drop. (Pump or compressor is not present.) Incompressible Flow a) Isothermal (ρ is constant). Piping Calculations Manual E. Shashi Menon, P.E. SYSTEK Technologies, Inc. McGraw-Hill New York Chicago San Francisco Lisbon London Madrid Mexico.
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Piping Calculations Manual. by: E. Shashi Menon, P.E.. Abstract: This on-the-job resource is packed with all the formulas, calculations, and practical tips. Editorial Reviews. From the Back Cover. Publisher's Note: Products purchased from Third Party sellers are not guaranteed by the publisher for quality. PIPING AND PIPELINE CALCULATIONS MANUAL This page intentionally left blank PIPING AND PIPELINE CALCULATIONS MANUAL DOWNLOAD PDF .
Submit Search. 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: The sizes required may have an effect on the materials of selection. The respective kinematic viscosities for metric are 0. 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. The exact definition is different but the use is similar. With few exceptions, notably the pipeline sections, there are no maintenance and ongoing requirements.
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Be the first to like this. No Downloads. Views Total views. Actions Shares. Embeds 0 No embeds. No notes for slide. Book details Author: Shashi Menon Pages: McGraw-Hill Education Language: English ISBN Description this book Presents the formulas, calculations, and tips necessary to smoothly move gas or liquids through pipes, assess the feasibility of improving existing pipeline performance, or design fresh systems.
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 None of these are accurate beyond the inherent accuracy of the conversion numbers, but they are good rules of thumb or ballpark conversions. 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.
Several documents give detailed information regarding how to convert to metric from U. SP is somewhat I. 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.
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. More is given on this subject later in Part II and the Appendix. In the piping codes themselves B Since many process industries like chemical and petroleum plants have international operations, B It is even mentioned as the normative reference code in the ISO 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 B It is hoped that they might be available in the 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. Customary Measurement In U. 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. 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. 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. 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? However, here one must be careful because some disciplines I. 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. Two lessons were learned. 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. There are some that are self-evident and need not be done in detail. 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.
Selection and Use of Pipeline Materials cific requirements in it for sour gas. As mentioned before, B In each of the codes the scope gives some more information regarding these transport materials. It defines four types of fluid: Category D service.
These must meet certain requirements and are basically low pressure, not flammable, and not damaging to human tissue. Category M service. This is the opposite of Category D fluids and therefore must be treated by separate requirements. High-pressure fluids. These are fluids that have extremely high pressures as designated by the owner and have independent requirements. Normal fluid service. 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. 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 s 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. In many instances, it also lists API 5L piping materials. One major exception is boiler external piping, listed in B 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.
So the lag exists quite naturally. Selection and Use of Pipeline Materials Table 3. 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.
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. 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. 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. 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. 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. 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. 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. 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. 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.
We will call this material Z and the necessary data to establish the trend curve ratio are listed in Table 3.
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. 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.
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. This explanation applies to the method ASME has developed to avoid the requirement for each batch of material to go through extensive hightemperature testing.
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. The criteria involve a percentage of creep over a length of time. These have been standardized in ASME as the following values: This can be described as causing a length of material to lengthen by 0. Obviously this requires many long tests at many temperatures and many stresses. Once again, many stresses at many temperatures are tried until the part breaks or ruptures. 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 I. 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 , hours would last over 11 years and several different stresses would have to be tested. Even a full hour test would take over 41 days. 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. 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.
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. The allowable stresses are set this way as well. A brief listing of how those tables vary is as follows: It is the most like the metal tables. 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. The filament-wound materials e. The specification itself defines the controlling pressureresisting dimensions and attributes, eliminating the need for any wall thickness calculation.
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. 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 B 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 I. Selection and Use of Pipeline Materials allowance is outside the scope of the codes.
There is a suggestion in B The Appendix contains a list of common materials from the U. ASTM Book 1. 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.
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. 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: 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.
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. 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.
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: They may include which material is appropriate for this system. Necessarily, there is often some interaction in the early stages of establishing these givens. 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. 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.
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. 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 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: 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 It should be noted here that a table of viscosities would most likely note 1.
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. Numerically, the metric system is all about shifting the decimal point. To say that the U. 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. At those temperatures the kinematic viscosities are 0. The conversion factor from ft2 to m2 is 0. The respective kinematic viscosities for metric are 0. For USC, it is 0. 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.
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.
Since you need to know the density to use this equation it is simpler to compute the kinematic viscosity and use Eq. 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 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 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. 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 , and then you will read either the decimal number 0. 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: The acceleration of gravity is 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.
The base equation is known as the Colebrook equation, which was developed in 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.
For those who have an Exceltype spreadsheet with a goal—seek tool, this is not as difficult as it used to be. For reference, a roughness factor for new steel pipe is 0. 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. A sample spreadsheet layout is given in the Appendix. The friction factor using the spreadsheet method described calculates to 0. 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 II. That equation is known as the Swamee-Jain equation: There is another relationship that can be used: It is deemed by chemists as sufficient for plant construction and calculations. 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. The question then becomes how does one do that? Recall Eq. It looked like this in the Darcy-Weisbach form: 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. E x amp l e C a l c u l at io n s Assume a globe valve fully open is in the line we have been working with i.
The common K factor for such a globe would be One might get a different number from a specific manufacturer. 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. The circumference of that same diameter would be 2. The ratio of area to wetted perimeter is then 0. 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. It is 0. 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. 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. 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. 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 II. 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: 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. 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. So for a very wide range of temperatures and a wider range of pressure the average is 1. To simplify the tables that compute these factors, including a factor called super-compressibility, run to six volumes long.
The Pacific Energy II. 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. 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. 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 II. 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.
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: 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. One of the many ways that speed of sound in gas can be calculated is by the following formula: Molecular weight of methane is 16, so Rg in USC is The universal gas constant can have many different units; in USC units it is customarily taken as Then, in some formula where mass is involved rather than pound force, for the acceleration of gravity 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. The velocity then is 1. 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.
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 II. There is a generally agreed-on method of calculating the average pressure. These two averages are used in calculating the compressibility factor. For the two calculations, a calculated friction factor of 0.
For the Weymouth and Panhandle A calculations, the form of equation that had eliminated the friction factor by including it in the II.