Fluid Flow Manual.pdf

(1)

CHEVRON RESEARCH AND TECHNOLOGY COMPANY

RICHMOND, CA

March 1997

Manual sponsor: For information or help regarding this manual, contact R.P. (Rob) Hohmann 242-2216

(2)

Fluid Flow Manual

Second Edition January 1990

First Revision October 1992

Second Edition March 1997

The information in this Manual has been jointly developed by Chevron Corporation and its Operating Companies. The Manual has been written to assist Chevron personnel in their work; as such, it may be interpreted and used as seen fit by operating management.

Copyright  1990, 1992, 1997 CHEVRON CORPORATION. All rights reserved. This document contains proprietary information for use by Chevron Corporation, its subsidiaries, and affiliates. All other uses require written permission.

Restricted Material

Technical Memorandum

This material is transmitted subject to the Export Control Laws of the United States Department of Commerce for technical data. Furthermore, you hereby assure us that the material transmitted herewith shall not be exported or re-exported by you in violation of these export controls.

(3)

Fluid Flow Manual

The following list shows publication or revision dates for the contents of this manual. To verify that your manual contains current material, check the sections in question with the list below. If your copy is not current, contact the Technical Standards Team, Chevron Research and Technology Company, Richmond, CA (510) 242-7232.

Section Date

Front Matter March 1997

Table of Contents March 1997

50 March 1997 100 January 1990 200 January 1990 300 October 1992 400 March 1997 500 March 1997 600 January 1990 700 January 1990 800 January 1990 900 January 1990 1000 March 1997 1100 March 1997 Appendix A January 1990 Appendix B January 1990 Appendix C January 1990 Appendix D March 1997 Appendix E October 1992 Appendix F March 1997 Appendix G January 1990 Appendix H January 1990 Appendix I March 1997 Index March 1997

(4)

Fluid Flow Manual

If you have moved or you want to change the distribution of this manual, use the form below. Once you have completed the information, fold, staple, and send by company mail. You can also FAX your change to (510) 242-2157.

❑ Change addressee as shown below. ❑ Replace manual owner with name below. ❑ Remove the name shown below.

Send this completed form to: Document Control, Room 50-4328

Chevron Research and Technology Company 100 Chevron Way (P.O. Box 1627)

Richmond, CA 94802

CRTC Consultants Card

The Chevron Research and Technology Company (CRTC) is a full-service, in-house engineering organi-zation.

CRTC periodically publishes a Consultants Card listing primary contacts in the CRTC specialty divi-sions. To order a Consultants Card, contact Ken Wasilchin of the CRTC Technical Standards Team at (510) 242-7241, or email him at “KWAS.”

Last First M.I.

Current

Owner: Title:

Last First M.I.

Company: Dept/Div:

Street: P.O. Box:

City: State: Zip:

(5)

Fluid Flow Manual

We are very interested in comments and suggestions for improving this manual and keeping it up to date. Please use this form to suggest changes; notify us of errors or inaccuracies; provide information that reflects changing technology; or submit material (drawings, specifications, procedures, etc.) that should be considered for inclusion.

Feel free to include photocopies of page(s) you have comments about. All suggestions will be reviewed as part of the update cycle for the next revision of this manual.

Send your comments to: Document Control, Room 50-4328

Chevron Research and Technology Company 100 Chevron Way (P.O.Box 1627)

Richmond, CA 94802

Page or Section Number Comments

Name Address

(6)

Manual Sponsor: R.P. Hohmann / Phone: (510) 242-2216 / E-mail : [email protected]

List of Current Pages

50 Using This Manual 50-1 100 Introduction 100-1 200 Static Pressure 200-1 300 Acceleration Pressure Drop 300-1 400 Friction Pressure Drop 400-1 500 Fitting Pressure Drop 500-1 600 Noncircular Conduits 600-1 700 Open Channel Flow (Section not developed)

800 Surge Pressure 800-1 900 Pipeline Flow 900-1 1000 Fluid Properties 1000-1 1100 Computer Programs 1100-1 Appendices

Appendix A Conversion Tables Appendix B Properties of Water Appendix C Design Properties of Pipe Appendix D PCFLOW Program Appendix E PIPEFLOW-2 Program Appendix F HOTOIL Program Appendix G HOTOL* Program Appendix H SURGE Program Appendix I PCSURGE Program

This document contains extensive hyperlinks to figures and cross-referenced sections. The pointer will change to a pointing finger when positioned over text which contains a link.

(7)

Abstract

This section summarizes the contents and explains the organization of the Fluid

Flow Manual. This manual is in one volume that includes engineering guidelines

with accompanying appendices. The manual has a table of contents and a complete index to aid you in finding specific subjects.

(8)

Scope and Application

The Fluid Flow Manual provides basic fluid flow theory, calculational methods, and physical data for use in piping design. It is directed both to entry-level personnel and nonspecialists regardless of experience. This manual should not be used as a substitute for sound engineering judgment.

The intent is to provide practical, useful information based on Company experi-ence. Therefore, forms have been included in the front of the manual for your convenience in suggesting changes. Your input and experience are important for improving subsequent printings and keeping this manual up to date.

Organization

This manual comprises Engineering Guidelines and appendices that address such concerns as: (1) designing piping to efficiently carry fluids, (2) determining open channel flow, (3) calculating surge pressures, (4) handling special pipeline prob-lems, (5) fluid and pipe properties, (6) available computer programs.

Tabs

The colored tabs in the manual will help you find information quickly.

• White tabs are for table of contents, introduction, appendices, PC disks, index,

and general purpose topics

• Blue tabs denote Engineering Guidelines

• Red tab marks a place for you to keep documents that are developed at your

(9)

Other Company Manuals

The text sometimes refers to documents in other Company manuals. These docu-ments carry the prefix of that manual. The prefixes are defined here:

Prefix Company Manual

CIV Civil and Structural

CMP Compressor

COM Coatings

CPM Corrosion Prevention

DRI Driver

ELC Electrical

EXH Heat Exchanger and Cooling

Tower

FFM Fluid Flow

FPM Fire Protection

HTR Fired Heater and Waste Heat

Recovery

ICM Instrumentation and Control

IRM Insulation and Refractory

MAC General Machinery

NCM Noise Control in Designs

PIM Piping PMP Pump PPL Pipeline PVM Pressure Vessel TAM Tank UTL Utilities WEM Welding

(10)

Fig. 50-1 Fluid Flow Manual Quick-Reference Guide

Task Fluid Flow Manual Sections

Learning Background Information

• Pressure drop calculations 100, 200, 300, 400, 500

• Pipeline friction heating 900

• Surge 800

• Open channel flow 700

• Computer programs 1100, Appendices D, E, F, G, H, I

Selecting the Best Computer Program

• Selection guide 1100

• Detailed operation Appendices D, E, F, G, H, I

Calculating Flow Rates

• By PCFLOW program 1100, Appendix D

• With flow charts 400

• With sophisticated programs 1100, Appendices D, E, F, G, H, I Finding Engineering Data

• Pipe dimensions Appendix C

• Fluid properties 1000

(11)

Abstract

This section describes the scope of the Fluid Flow Manual and discusses its basic approach to fluid flow problems.

Contents Page

110 Scope of the Fluid Flow Manual 100-2

120 Basic Elements of Pressure Drop 100-2

130 Importance of the Darcy-Weisbach Equation 100-2

140 Nomenclature 100-3

(12)

110 Scope of the Fluid Flow Manual

The Fluid Flow Manual presents the equations that model basic fluid flow

phenomena. Most of the equations and discussions are oriented toward solving for pressure drop given well defined fluids, flow rates, and geometry in simple hydraulic systems. In general the manual treats isothermal flow. The exception to this is that some of the computer programs referenced in Section 1100 perform heat transfer calculations and appropriately adjust fluid properties and pressure drop along the flow path.

120 Basic Elements of Pressure Drop

The total pressure drop in a fluid flow system can be accurately defined if all of the following components of that pressure drop are found:

• Pressure change due to elevation change • Pressure drop due to acceleration losses • Pressure drop due to frictional losses

The relationship between the three components of pressure drop may be expressed as follows:

∆P_system = ∆P_elevation + ∆P_acceleration + ∆P_friction

(Eq. 100-1)

These components of total system pressure drop are treated in Sections 200, 300, and 400, respectively, for simple cases. Special considerations are treated in the remaining sections. For example, Section 500 presents a method for approximating the combination of both acceleration and friction losses that occurs in valves, fittings, and pipe entrances.

130 Importance of the Darcy-Weisbach Equation

The dominant effect in most fluid flow systems is friction pressure drop. The Darcy-Weisbach equation solves for friction pressure drop for any fluid, in any pipe, over any length for which the fluid properties remain relatively constant. This equation is presented here because of its importance. It is discussed more fully in

Section 410: (Eq. 100-2) where: h = head loss, ft f = friction factor L = pipe length, ft h fL D --- V 2 2g ---⋅ =

(13)

D = pipe internal diameter, ft V = fluid velocity, ft/sec

g = gravitational constant (32.17 ft/sec2)

The Darcy-Weisbach equation defines the friction factor, f. Whenever possible the reader is encouraged to use this equation instead of the flow charts in Section 400. This equation is automated in the “Incompressible Flow” section of the PCFLOW program, which is provided on disk at the end of this manual.

140 Nomenclature

This manual does not contain a master list of nomenclature. Equation variables are defined following each equation.

150 References

The following selection of general references is supplemented by specific refer-ences in the applicable sections of the manual.

1. Fox, R. W., A. T. McDonald. Introduction to Fluid Mechanics. John Wiley & Sons, New York: 1978.

2. Perry, R. H., C. H. Chilton. Chemical Engineers’ Handbook, Section 5. McGraw-Hill, New York: 1973.

3. Streeter, V. L., E. B. Wylie. Fluid Mechanics. McGraw-Hill, New York. 4. Engineering Data Book, Section 17. Gas Processors Association, Tulsa: 1987.

(14)

Abstract

This section discusses the equations for calculating static pressure and head.

210 Definition of Static Pressure 200-2

(15)

210 Definition of Static Pressure

The pressure generated by the height of a column of liquid (see Figure 200-1) is expressed as static pressure, or, alternatively, static head or elevation head. Pres-sures other than static pressure are often expressed in terms of the column of liquid required to generate an equivalent static pressure, such as feet of water or inches of mercury. Similarly head (H), expressed in feet, often describes pressures that are not static. Units of static pressure and head can be converted to one another using the following equations.

220 Equations for Static Pressure and Head

Equation 200-1 expresses the static pressure in psi generated by a column of liquid:

(Eq. 200-1)

where:

P_s = static pressure, psi

h = height of liquid column, ft ρ = fluid density, lb /cu ft Fig. 200-1 Static Pressure

P_s ρh 144 ---=

(16)

Equation 200-2 expresses head, in feet, equivalent to an arbitrary pressure, in psi:

(Eq. 200-2)

where:

H = head, ft P = pressure, psi

ρ = fluid density, lb_m/cu ft

The conversion of head in feet to pressure in pounds per square inch for water at 60°F is as follows:

P_s = 0.433 h

h = 2.31 P_s

(17)

Abstract

This section presents the equations for calculating pressure drop due to fluid accel-eration and discusses the phenomenon in terms of changes in pipe geometry and change of phase.

310 Definition of Acceleration Pressure Drop 300-2

320 Equations for Acceleration Pressure Drop 300-2

(18)

310 Definition of Acceleration Pressure Drop

An increase in velocity (i.e., acceleration) of a fluid is accompanied by a decrease in its static pressure. This decrease is called acceleration pressure drop. It occurs at pipe entrances and reducers, and where a phase change from liquid to gas occurs, to give two common examples. Acceleration pressure drop is usually expressed in pounds per square inch (psi) or in units of velocity head (in feet). One velocity

head is the acceleration head loss of a fluid accelerated from rest in a reservoir to a

specific velocity in a pipe.

320 Equations for Acceleration Pressure Drop

Velocity head is calculated using the following equation:

(Eq. 300-1)

where:

h = velocity head in feet of liquid, ft V = fluid velocity, ft/sec

Acceleration pressure drop across an entrance or reducer, expressed in terms of static pressure drop (in psi), is:

(Eq. 300-2)

where:

∆P = static pressure drop, psi ρ = fluid density, lb_m/cu ft V₁ = upstream fluid velocity, ft/sec V₂ = downstream fluid velocity, ft/sec

Determination of acceleration pressure drop is particularly important when calcu-lating the NPSHA of reciprocating pumps, to avoid cavitation. See Section 100 of the Pump Manual.

330 Discussion

Equations 300-1 and 300-2 describe acceleration loss at pipe entrances and reducers. Frictional losses (see Section 500) must be added to get the total loss for

h V 2 2g ---= ∆P ρ V₂2 –V₁2 ( ) 2g 144⋅ ---=

(19)

this geometry. The fitting loss coefficients given in Section 500 for other types of valves and fittings (besides pipe entrances and reducers) take into account both acceleration and friction effects.

During changes of phase (evaporation, flashing, and boiling), the velocity of a fluid must increase as the gas phase increases its mass flow rate. The pressure required to produce that acceleration is accurately described by Equations 300-1 and 300-2. The total pressure drop is the sum of the acceleration pressure drop and the flowing friction pressure drop. This friction loss can be difficult to calculate because the flow rates of the two phases are changing and, therefore, the friction pressure drop is changing as the fluid moves downstream.

The static pressure that is converted to kinetic energy through the acceleration of a flowing fluid is theoretically recoverable as static pressure when the flow deceler-ates. However, since even carefully designed diffusers can recover only a fraction of the original static pressure, this recovery is not attempted in normal piping situa-tions. In standard piping systems the kinetic energy of a flowing fluid is dissipated as turbulence at pipe exits and enlargements. Confusion on this point can arise because some authors attribute acceleration pressure loss not to the pipe entrance or reducer, but to the pipe exit or enlargement, where the potentially recoverable energy is finally lost. This gives some readers the false impression that there is a static pressure drop across pipe exits and enlargements. Static pressure drop— produced by acceleration and friction effects—occurs across pipe entrances and reducers, not their exits and enlargements.

(20)

Abstract

This section presents equations for calculating the relationship between flow rate and pressure drop for incompressible flow, two-phase flow, compressible flow, and gas flow at high pressure drop (choked flow).

410 Incompressible Flow 400-3

411 Fitting Loss Coefficients 412 Pipe and Tube Friction Losses 413 Flow Charts

414 Correction Factor for Internal Roughness for Use With Flow Charts

420 Two-phase Flow 400-30

421 Pressure Drop Calculations

422 Friction Pressure Drop Correlations 423 Fitting and Bend Losses

424 Acceleration Pressure Loss 425 Elevation Losses

426 Flow Patterns

427 Accuracy of Friction Pressure Drop Calculation 428 Liquid Holdup Correlation

430 Compressible Flow 400-41

440 Gas Flow At High Pressure Drop (Choked Flow) 400-59

441 Assumptions

442 Use of Design Charts 443 Sonic Flow

444 Choked Flow

(21)

446 Effects of Valves and Fittings 447 Deviation from Assumptions

(22)

410 Incompressible Flow

The Darcy-Weisbach Equation (Equation 400-1) expresses the relationship between flow rate and friction pressure drop for incompressible flow in pipes and tubes. It is accurate for both liquids and gases, and for any length of pipe over which fluid properties are relatively constant.

(Eq. 400-1)

where:

h = head loss, ft

f = Darcy friction factor L = pipe length, ft

D = pipe inside diameter, ft V = fluid velocity, ft/sec

The Darcy-Weisbach Equation can be rewritten in terms of pressure drop in psi, flow rate in pounds per hour, and a constant that combines all the unit conversions, as in Equation 400-2.

(Eq. 400-2)

where:

P = pressure drop, psi W = mass flow rate, lb_m/hr

ρ = fluid density, lb_m/ft3

411 Fitting Loss Coefficients

Fitting loss coefficients (see Section 500) are dimensionally equivalent to the term fL/D and can be added to pipe friction losses using Equation 400-3. Fitting loss coefficients include both friction and acceleration effects.

(Eq. 400-3) h fL D --- V 2 2g ---⋅ = P fL D --- W 2 ρD4(7.4 10⋅ 10) ---⋅ = P K fL D ---+     W2 ρD4(7.4 10⋅ 10) ---⋅ =

(23)

where:

K = fitting loss coefficient (from Section 500)

412 Pipe and Tube Friction Losses

For pipe and tube flow, the friction factor is a function of the Reynolds number and the flow regime. In the turbulent flow regime it is also a function of pipe rough-ness. Reynolds number can be written using units consistent with Equation 400-3, as follows:

(Eq. 400-4)

where:

Re = Reynolds number µ = absolute viscosity, cp

There are no sharp divisions between the laminar, transition, and turbulent flow regimes. For design purposes, the recommended boundary between laminar and transition flow is Re = 1600. The recommended boundary between transition and turbulent flow is Re = 3400. These values provide relatively smooth transitions between regimes for calculated friction factors, and produce conservative results (tend to overpredict pressure drop) around the laminar-to-transition flow boundary. The friction factor for laminar flow (Re < 1600) can be derived analytically (without experimental components) to give:

f = 64/Re

(Eq. 400-5)

The friction factor for transition flow (1600 < Re < 3400) cannot be predicted accu-rately. The following conservative value (overprediction) is recommended for most cases:

f = 0.04

(Eq. 400-6)

The Moody Diagram (Figure 400-1) presents experimentally derived friction factors for turbulent flow (Re ≥ 3400). In turbulent flow the friction factor is a func-tion of pipe roughness as well as the Reynolds number. At high Reynolds numbers the friction factor is a function of only relative roughness (absolute roughness/diam-eter). Figure 400-2 gives the relative roughness for various diameters and types of pipe.

Re 0.526W

Dµ ---=

(24)

(25)

(26)

Many equations have been proposed to approximate the Moody Diagram friction factors. One of these is the Chen Equation (Equation 400-7), which is simple, accu-rate, and stable when used on small computers:

(Eq. 400-7)

where:

ε = absolute pipe roughness, ft D = pipe diameter, ft

= relative roughness

413 Flow Charts

The relationship between pressure drop and flow rate can also be found graphically using the nomographs in Figures 400-4 through 400-13. All of these charts are derived from the Darcy-Weisbach Equation. Be sure to apply the appropriate correc-tions in Figures 400-3 through 400-13.

414 Correction Factor for Internal Roughness for Use With Flow Charts

Figures 400-4 through 400-13 are based on new steel pipe having an absolute roughness of 0.0018 inches. The effect of other values of roughness can be esti-mated by multiplying the pressure drop by a correction factor from Figure 400-3. Typical values of roughness, E, are as follows:

f 2 4 log₁₀ (A1-A2) – ---   2 = A1 ε D ----3.7065 ---= A2 5.0452 Re --- log⋅ ₁₀(A3) = A3 ε D ----   1.1098 2.8257 --- 7.149 Re ---   0.8981 + = ε D

----Pipe Absolute Roughness, ε

Plastic 0.000005 ft

Smooth Steel, New 0.00015 ft

(27)

Correction factors in Figure 400-3 for 1 centistoke (cs) are typical of water or petro-leum products ranging from 0.5 to 2.0 cs viscosity. Correction factors in

Figure 400-3 for 10 centistoke (cs) are typical of crude oils or other liquids in the viscosity range from 5 to 20 cs.

Correction factors are applicable for turbulent flow. No correction is required for laminar flow. The uncertainties in the transition range increase with roughness. The correction factors are the ratio f_c / f_o

where:

f_c = friction factor from the Colebrook formula (Equation 400-12) f_o = friction factor on which Figures 400-4 to 400-13 are based

Where accurate performance data are required, pressure losses should be deter-mined by test. If test measurements are not possible, the friction factor can be found with the Moody Diagram or calculated with the Chen Equation (Equation 400-7).

Cast Iron, Asphalted 0.00042 ft

Transite 0.00042 ft

Cast Iron, Uncoated, New 0.00083 ft

Steel, Concrete Lined 0.00083 ft

Concrete 0.0083 ft

Riveted Steel 0.025 ft

Pipe Absolute Roughness, ε

Fig. 400-3 Correction Factors for Internal Roughness (1 of 2)

Use for Viscosity = 1 Centistoke and Turbulent flow. No correction for laminar flow. Absolute Roughness, in.

ID, in. Velocity, ft/sec 0.0010 0.0018 0.0050 0.0100 0.0300 0.1000 0.3000

2 3 0.95 0.99 1.15 1.34 1.85 5 0.98 1.05 1.24 1.47 2.06 10 1.01 1.10 1.35 1.62 2.30 5 3 0.99 1.04 1.17 1.33 1.76 2.62 5 1.03 1.09 1.27 1.47 1.96 2.94 10 1.02 1.10 1.31 1.54 2.08 3.14 10 3 1.06 1.10 1.22 1.38 1.77 2.52 3.78 5 1.11 1.16 1.33 1.51 1.97 2.82 4.25 10 1.02 1.09 1.29 1.49 1.96 2.83 4.26

(28)

Use for Viscosity = 1 Centistoke and Turbulent flow. No correction for laminar flow (cont.). Absolute Roughness, in.

20 3 1.08 1.12 1.23 1.37 1.72 2.37 3.39 5 1.11 1.16 1.31 1.48 1.88 2.60 3.73 10 1.03 1.09 1.27 1.45 1.86 2.59 3.72 50 3 1.13 1.16 1.27 1.39 1.70 2.25 3.08 5 1.11 1.16 1.29 1.43 1.77 2.36 3.23 10 1.03 1.09 1.25 1.41 1.76 2.36 3.23

Use for Viscosity = 10 centistoke and turbulent flow. Absolute Roughness, in.

2 3 0.97 0.98 1.02 1.08 1.30 1.91 5 0.93 0.94 1.00 1.08 1.34 2.04 10 0.92 0.94 1.03 1.14 1.50 2.35 5 3 0.95 0.96 0.99 1.03 1.20 1.63 2.52 5 0.94 0.95 1.00 1.06 1.28 1.79 2.81 10 0.95 0.97 1.04 1.13 1.42 2.07 3.27 10 3 0.98 0.99 1.01 1.06 1.20 1.57 2.27 5 0.98 0.99 1.03 1.09 1.28 1.72 2.53 10 1.00 1.01 1.08 1.17 1.43 1.98 2.95 20 3 0.97 0.98 1.01 1.04 1.16 1.47 2.04 5 0.98 0.99 1.03 1.08 1.24 1.62 2.27 10 1.01 1.03 1.08 1.16 1.39 1.86 2.64 50 3 0.99 .99 1.01 1.04 1.15 1.40 1.85 5 1.01 1.01 1.04 1.09 1.22 1.54 2.06 10 1.04 1.06 1.11 1.17 1.37 1.77 2.40

(29)

Fig. 400-4 1-Inch Pipe—Schedule 40 (1 of 2)

Correction Factor Table for 1 in. Pipe of Various Thicknesses Schedule

Inside

Diameter, in. Transition & Turbulent Flow Laminar Flow

5S 1.185 0.56 1.39 0.61 1.63 10S 1.097 0.81 1.13 0.84 1.20 F_p F_q F_p F_q 40 1.049 1.00 1.00 1.00 1.00 80 0.957 1.55 0.78 1.44 0.69 160 0.815 3.33 0.51 2.74 0.36

F_p = Pressure loss correction factor F_q = Flow rate correction factor

NOTES:

1. Multiply pressure loss from flow chart by F_pfor pressure loss with pipe walls other than Schedule 40. 2. Multiply flow rate from flow chart by F_q to obtain flow rate with pipe walls other than Schedule 40.

3. For SG≠1.0, multiply pressure loss at SG 1.0 by actual SG to obtain pressure loss. For known pressure loss, divide by SG, then enter chart at SG 1.0 to determine flow rate.

4. In laminar range, pressure loss is directly proportional to viscosity. To determine pressure losses for viscosi-ties not shown, the ratio of a known viscosity to pressure loss at desired flow rate is applied to the actual viscosity.

EXAMPLE 1:

Given: Flow rate = 5 BPH; viscosity = 20 cs; specific gravity = 0.9; line size = 1 in. schedule 10S (ID = 1.097 in.)

Determine: Pressure loss (psi/1000 ft)

Solution: Enter flow chart at 5 BPH. Move across to viscosity of 20 cs. Move vertically to SG 0.9. Move diagonally to pressure loss of 14.3 psi/1000 ft. for 1.049-in. ID pipe. From correction table, for 1.097-in. ID pipe and laminar flow, F_p = 0.84

Pressure loss = (14.3) (0.84) = 12 psi/1000 feet

EXAMPLE 2:

Given: Pressure loss = 16.0 psi/1000 ft; viscosity = 2 cs; specific gravity = 0.9; line size = 1 in. schedule 80 (ID = 0.957 in.)

Determine: Flow rate (BPH)

Solution: Enter flow chart at 16 psi/1000 feet. Move diagonally to SG 0.9. Move vertically to viscosity of 2.0 cs in turbulent range. Move horizontally to flow rate of 10 BPH for 1.049-in. ID pipe. From correction table, for 0.957-in. ID pipe and turbulent flow, F_q = 0.78.

(30)

(31)

Fig. 400-5 1-1/2-Inch Pipe—Schedule 40 (1 of 2)

Correction Factor Table for 1-1/2 in. Pipe of Various Thicknesses Schedule

Inside

F_p F_q F_p F_q 5S 1.770 0.64 1.29 0.68 1.46 10S 1.682 0.81 1.13 0.84 1.19 40 1.610 1.00 1.00 1.00 1.00 80 1.500 1.40 0.83 1.33 0.75 160 1.337 2.43 0.61 2.10 0.48

NOTES:

EXAMPLE 1:

Given: Flow rate 12 BPH; viscosity = 20 cs; specific gravity = 0.9; line size = 1-1/2 in. schedule 10S (ID = 1.682 in.)

Pressure loss = (6.1) (0.84) = 5.1 psi/1000 feet

EXAMPLE 2:

Given: Pressure loss = 15.7 psi/1000 ft; viscosity = 5 cs; specific gravity = 0.9; line size = 1-1/2 in. schedule 80 (ID = 1.500 in.)

Solution: Enter flow chart at 15.7 psi/1000 feet. Move diagonally to SG 0.9. Move vertically to viscosity of 5.0 cs in turbulent range. Move horizontally to flow rate of 28 BPH for 1.610-in. ID pipe. From correction table, for 1.500-in. ID pipe and turbulent flow, F_q = 0.83.

(32)

(33)

Inside

F_p F_q F_p F_q 5S 2.245 0.67 1.25 0.72 1.39 10S 2.157 0.82 1.12 0.84 1.19 40 2.067 1.00 1.00 1.00 1.00 80 1.939 1.36 0.84 1.29 0.77 160 1.689 2.62 0.58 2.24 0.45

NOTES:

EXAMPLE 1:

EXAMPLE 2:

Given: Pressure loss = 12.4 psi/1000 ft; viscosity = 5 cs; specific gravity = 0.9; line size = 2 in. Schedule 80 (ID = 1.939 in.)

Solution: Enter flow chart at 12.4 psi/1000 feet. Move diagonally to SG 0.9. Move vertically to viscosity of 5.0 cs in turbulent range. Move horizontally to flow rate of 48 BPH for 2.067-in. ID pipe. From correction table, for 1.939-in. ID pipe and turbulent flow, F_q = 0.84.

(34)

(35)

Fig. 400-7 2-1/2-Inch Pipe—Schedule 40 (1 of 2)

Correction Factor Table for 2-1/2 in. Pipe of Various Thicknesses Schedule

Inside

F_p F_q F_p F_q 5S 2.709 0.64 1.28 0.69 1.45 10S 2.635 0.73 1.19 0.77 1.30 40 2.469 1.00 1.00 1.00 1.00 80 2.323 1.34 0.85 1.29 0.78 160 2.125 2.05 0.67 1.82 0.55

F_p = Pressure loss correction factor F_q= Flow rate correction factor

NOTES:

EXAMPLE 1:

Given: Flow rate = 40 BPH; viscosity = 60 cs; specific gravity = 0.9; line size = 2-1/2 in. schedule 10S (ID = 2.635 in.)

EXAMPLE 2:

Given: Pressure loss = 12.8 psi/1000 ft; viscosity = 10 cs; specific gravity = 0.9; line size = 2-1/2 in. schedule 80 (ID = 2.323 in.)

Solution: Enter flow chart at 12.8 psi/1000 feet. Move diagonally to SG 0.9. Move vertically to viscosity of 10 cs in turbulent range. Move horizontally to flow rate of 74 BPH for 2.469-in. ID pipe. From correction table, for 2.323-in. ID pipe and turbulent flow, F_q = 0.85.

(36)

(37)

Inside

F_p F_q F_p F_q 5S 3.334 0.67 1.25 0.72 1.39 10S 3.260 0.75 1.18 0.78 1.27 40 3.068 1.00 1.00 1.00 1.00 80 2.900 1.31 0.86 1.25 0.80 160 2.624 2.11 0.66 1.87 0.54

NOTES:

EXAMPLE 1:

EXAMPLE 2:

(38)

(39)

Inside

F_p F_q F_p F_q 5S 4.334 0.70 1.22 0.74 1.34 10S 4.260 0.76 1.16 0.80 1.25 40 4.026 1.00 1.00 1.00 1.00 80 3.826 1.28 0.87 1.23 0.82 120 3.624 1.65 0.75 1.52 0.66 160 3.438 2.12 0.65 1.88 0.53

NOTES:

EXAMPLE 1:

EXAMPLE 2:

(40)

(41)

Fig. 400-10 6-Inch Pipe—1/4-Inch Wall (1 of 2)

Inside

F_p F_q F_p F_q 5S 6.407 .81 1.13 .84 1.20 10S 6.357 .84 1.11 .86 1.16 1/4 in. wall 6.125 1.00 1.00 1.00 1.00 40 6.065 1.05 .97 1.04 .96 80 5.761 1.34 .85 1.28 .78 120 5.501 1.67 .75 1.54 .65 160 5.189 2.21 .64 1.94 .52

NOTES:

1. Multiply pressure loss from flow chart by F_pfor pressure loss with pipe walls other than 1/4-inch. 2. Multiply flow rate from flow chart by F_q to obtain flow rate with pipe walls other than 1/4-inch.

EXAMPLE 1:

Given: Flow rate = 400 BPH; viscosity = 150 cs; specific gravity = 0.9; line size = 6 in. schedule 40 (ID = 6.065 in.)

EXAMPLE 2:

(42)

(43)

Inside

F_p F_q F_p F_q 10S 8.329 0.89 1.07 0.91 1.10 20 8.125 1.00 1.00 1.00 1.00 40 7.981 1.09 0.95 1.07 0.93 60 7.813 1.21 0.90 1.17 0.86 80 7.625 1.35 0.84 1.29 0.78 120 7.189 1.79 0.72 1.63 0.61 160 6.813 2.32 0.62 2.02 0.49

NOTES:

EXAMPLE 1:

EXAMPLE 2:

(44)

(45)

Inside

F_p F_q F_p F_q 10S 10.420 0.92 1.05 0.94 1.07 20S 10.250 1.00 1.00 1.00 1.00 40 10.020 1.11 0.94 1.10 0.91 60 9.750 1.27 0.87 1.22 0.82 80 9.564 1.39 0.83 1.32 0.76 120 9.064 1.80 0.72 1.64 0.61 160 8.500 2.44 0.60 2.11 0.47

NOTES:

1. Multiply pressure loss from flow chart by F_pfor pressure loss with pipe walls other than Schedule 20S. 2. Multiply flow rate from flow chart by F_q to obtain flow rate with pipe walls other than Schedule 20S. 3. For SG≠1.0, multiply pressure loss at SG 1.0 by actual SG to obtain pressure loss. For known pressure loss,

divide by SG, then enter chart at SG 1.0 to determine flow rate.

EXAMPLE 1:

EXAMPLE 2:

(46)

(47)

Inside

F_p F_q F_p F_q 10S 12.390 0.95 1.03 0.96 1.05 20S 12.250 1.00 1.00 1.00 1.00 40 11.938 1.13 0.93 1.11 0.90 80 11.376 1.42 0.82 1.34 0.74 120 10.750 1.86 0.70 1.69 0.59 160 10.126 2.48 0.60 2.14 0.47

NOTES:

1. Multiply pressure loss from flow chart by F_pfor pressure loss with pipe walls other than Schedule 20S. 2. Multiply flow rate from flow chart by F_q to obtain flow rate with pipe walls other than Schedule 20S. 3. For SG≠1.0, multiply pressure loss at SG 1.0 by actual SG to obtain pressure loss. For known pressure loss,

divide by SG, then enter chart at SG 1.0 to determine flow rate.

EXAMPLE 1:

EXAMPLE 2:

(48)

(49)

420 Two-phase Flow

This section presents a method for calculating gas-liquid two-phase flow pressure drop. Lines carrying flashing mixtures, solid-liquid mixtures, or gas-solid mixtures must be analyzed more thoroughly than this method allows. The special cases of (1) mixture flow in column and furnace transfer lines, and (2) flashing water are covered in the Fired Heater and Waste Heat Recovery Manual and Utilities

Manual, respectively.

Limitations

The method described here applies to isothermal gas-liquid flow, not to situations in which a phase change occurs; that is, constant gas-liquid ratios (by weight) are assumed.

This method has not been verified for very long vertical piping (such as in oil wells) nor has the accuracy been established for horizontal piping more than 5-1/2 inches in diameter. In these cases the method should be used with caution, for vertical piping, PIPEFLOW-2 will yield better results. In addition, the limited exper-imental data available indicate that when the mixture velocity is less than 3 ft/sec the accuracy of the friction pressure drop calculations is very poor.

This method is not fully applicable to flow of water-oil-gas (WOG) mixtures (so-called three-phase flow). This case requires the more powerful calculation methods of PIPEFLOW-2.

General References

Reference 1 (see Section 450) contains a more detailed discussion of two-phase flow. Reference 2 contains an extensive bibliography of two-phase literature.

421 Pressure Drop Calculations

As in single-phase flow, pressure drop in two-phase flow consists of several compo-nents, as shown in Equation 400-8.

∆P_total = ∆P_friction + ∆P_fittings + ∆P_acceleration + ∆P_elevation

(Eq. 400-8)

The components of this equation, ∆P_friction, ∆P_fittings, ∆P_acceleration, and ∆P_elevation are discussed in the following sections. The total pressure drop is calculated by eval-uating each component individually and summing.

422 Friction Pressure Drop Correlations

More than 25 correlations for two-phase friction pressure drop have appeared in print. Because these correlations contain empirical factors obtained from limited experimental data, they cannot be applied with confidence beyond their particular experimental bases.

(50)

The five most widely used correlations are compared in Reference 3 using experi-mental data from a number of investigators. The data were carefully screened to eliminate unreliable measurements. The screened data, about 2600 points in all, cover pipe diameters from 1 to 5-1/2 inches and liquid viscosities from 1 to 20 centipoise. Of the five the most reliable correlation over this range of experimental conditions was the Lockhart-Martinelli correlation (see Reference 4).

Another somewhat better correlation with the screened experimental data was achieved using similarity analysis (see Reference 5). This method is based on calcu-lating a two-phase density, ρ_tp, and viscosity, µ_tp,evaluated at the pipe entrance pressure and temperature and assumed constant for the friction and fitting pressure drop calculation, as follows:

ρ_tp = ρ_l (λ) + ρ_g (1.0 - λ) (Eq. 400-9) µ_tp = µ_l (λ) + µ_g (1.0 - λ) (Eq. 400-10) where: ρ = fluid density, lb_m/ft3 µ = absolute viscosity, cp tp = two-phase l = liquid phase g = gas phase

λ = liquid volume fraction at pipe entrance

Equations 400-9 and 400-10 assume that both phases flow at the same velocity. The two-phase Reynolds number Re_tp is expressed as follows:

(Eq. 400-11)

where:

V_m = velocity of mixture, ft/sec

D = pipe inside diameter, ft

W_t = mass flow rate of total fluid, lb_m/hr

For new steel pipe, two-phase Reynolds numbers should be used with the Moody diagram (Figure 400-1) to determine the friction factor f. If different pipe condi-tions exist or a more accurate determination is desired, the Colebrook formula (Equation 400-12) may be used.

Re_tp V_mDρ_tp µ_tp 1490 ---    ---0.527W_t Dµ_tp ---= =

(51)

(Eq. 400-12)

where:

ε = absolute pipe wall roughness, ft

The need to proceed by trial and error is an inconvenience when using this equation for hand calculation, but a computer or Moody chart eliminates this problem. The equation reduces to the smooth tube equation when the wall roughness (left term in bracket) approaches zero or to Nikuradse’s Formula at high Reynolds numbers (when the right term in bracket approaches zero). The same absolute wall rough-ness, ε, should be used for both single-phase and two-phase flow calculations. The pressure drop due to friction may then be calculated as follows:

(Eq. 400-13)

where:

∆P = pressure drop, psi f = friction factor L = pipe length, ft

g_o = gravitational constant (32.174 lb_m ft/lb_f sec2) W_l = flow rate of liquid, lb_m/hr

W_g = flow rate of gas, lb_m/hr W_t = W_l + W_g

This method of calculating friction pressure drop has the following characteristics: • It reduces to the single-phase flow equations if the flow rate of either phase is

zero.

• Except for the assumptions concerning two-phase density and viscosity (Equa-tions 400-9 and 400-10), no empirical factors from two-phase flow data have been used.

• It is reasonably accurate for all flow patterns (see Section 427). 1 f --- 2 log₁₀ ε 3.7D --- 2.51 Re_tp f ---+       – = ∆P_friction fL D ----ρtp 144 ---V_m2 2g_o ---⋅ = 1.35 10–11f L D5 ---W2_t ρ_tp ---⋅ =

(52)

423 Fitting and Bend Losses

For two-phase flow, as for single-phase flow, pressure drop due to bends and fittings can be expressed in terms of velocity head loss. However, for two-phase flow, the velocity head is based on the pipe inlet mixture density, rtp, from Equation 400-9, as follows:

(Eq. 400-14)

where:

K = single phase velocity head loss

424 Acceleration Pressure Loss

Acceleration losses also contribute to the total pressure drop. In most cases this loss is relatively small, and may be neglected if only a rough estimate is required. However, when the total pressure drop along the line is large, the acceleration losses can be significant and should be calculated. In this case, the gas expands and the mixture occupies a larger volume at a lower pressure. This causes the mixture to be accelerated to a higher velocity in order to maintain the same mass flow. The expression for acceleration pressure drop, as given in Reference 5, is as follows:

(Eq. 400-15)

where:

Z = compressibility factor T = temperature, °R R = gas constant

P₁ = upstream pressure, psi

P₂ = downstream pressure, psi D = pipe inside diameter, ft

425 Elevation Losses

The calculation of two-phase density using Equation 400-9 is an approximation that assumes the velocities of the liquid and gas phases are equal. However, the actual density of the gas-liquid mixture is needed to calculate the elevation pressure drop for upwards flow. One cannot assume that the velocities of the two phases are equal.

∆P_fittings Kρtp 144 --- Vm 2 2g_o ---⋅ 1.35 10–11 KWt 2 D4ρ_tp ---⋅ ⋅ = = ∆P_acceleration 1.87 10⋅ –13W_tW_gZRT D4P₁P₂ ---⋅∆P_tp =

(53)

The actual flow density depends on how the liquid and gas are distributed in the pipe. The flow density in a short section of pipe of length L is given by

Equation 400-16:

(Eq. 400-16)

where:

ρ´ = actual density in pipe section A_g = area gas

A_l = area liquid

R_g = gas volume fraction

R_l = liquid holdup

R_g is the fractional volume of the pipe filled with gas and R_l is the fractional volume of the pipe filled with liquid. R_l is called liquid holdup (see

Equation 400-22). Because of the difference in velocity of the two phases, liquid holdup is greater downstream than at the entrance. Therefore, to calculate the actual flow density, the liquid holdup R_l has to be known along the pipe. The available correlations for liquid holdup were checked against experimental data from Refer-ence 3. The correlation developed by Hughmark (see ReferRefer-ence 7, and below in this section, “Liquid Holdup Correlation”) was the best.

The effects of bends and fittings on liquid holdup and, therefore, the flow density cannot be predicted at this time. Therefore, it is assumed that the same holdup corre-lation can be used even if the pipe contains bends and fittings.

In two-phase flow, as in single-phase flow, the elevation head loss is expressed as follows:

(Eq. 400-17)

where:

h = static elevation, ft

The flow density is calculated using Equation 400-16, where the gas density is eval-uated at the average pressure. The elevation pressure drop term is included only in vertical upward flow.

A conservative evaluation of acceleration pressure loss for vertical downward flow cannot take credit for the elevation pressure component in the downward section. Therefore, sections where the flow is downward should be treated as horizontal piping. No provisions have been made to handle inclined piping.

ρ′_tp LAgρg+LA1ρ1 LA --- R_gρ_g+R₁ρ₁ = = ∆P_elevation ρ′tp 144 --- h⋅ =

(54)

426 Flow Patterns

Horizontal Flow. When gas and liquid fluids flow in a pipe together, the two

phases can be distributed in a number of ways. The distribution is described according to visually observed flow patterns, which depend on the gas and liquid mass velocity as well as on the physical properties of the fluids. Figure 400-14 is a flow map devised by Baker (Reference 8), to predict flow patterns and indicate the physical appearance of the flow. A detailed description of the flow patterns is given in the review of two-phase flow in Reference 1.

The pressure drop calculation method presented in this section does not depend on flow patterns. However, the comparison of calculated pressure drop with experi-mental data has been grouped according to flow patterns (see the next section below, “Accuracy of Friction Pressure Drop Calculation,” and Figure 400-16). Figure 400-14 can help in predicting the calculated pressure drop. The boundaries separating the flow regimes in Figure 400-14 are not distinct, but represent regions of transition. A band of ± 20% of the ordinate as shown by the dashed lines was chosen to represent the region of uncertainty.

Vertical Flow. Figure 400-15 is a flow pattern map for vertical upwards flow (see

Reference 9). The slug flow region of the map was determined by plotting points where slug flow has been observed experimentally. The boundaries between the flow patterns are transition regions, represented by a band ± 20% wide.

427 Accuracy of Friction Pressure Drop Calculation

The friction pressure drop calculation was checked against carefully screened exper-imental data from a number of investigators. Partial results of the comparison are shown in Figure 400-16. A more extensive discussion of the calculations and a statistical analysis of the errors are available in References 3 and 5.

The values shown in Figure 400-16 represent the percent deviation between the calculated pressure drop and experimental data, as shown in Equation 400-18.

(Eq. 400-18)

Figure 400-17 can be used to estimate the accuracy of a calculated friction pressure drop for any flow regime. For example, the calculated friction pressure drop for horizontal slug flow is within -18.0 to +12.0 percent of the actual value.

Equation 400-18 may be restated as follows:

(Eq. 400-19) %dev ∆ P_calc–∆P_exp ∆P_exp --- 100⋅ = ∆P_exp ∆ P_calc 1 % dev 100 ---+ ---=

(55)

(56)

Fig. 400-15 Flow Pattern Map for Vertical Two-Phase Flow From Two Phase Slug Flow by Griffith & Wallis. Journal of Heat Transfer, Transactions of ASME Series C83 (Aug., 1961). Courtesy of ASME

(57)

Based on the range of deviation for horizontal slug flow, the actual value of a calcu-lated pressure drop of 10 psi would be (approximately) between the following values:

(Eq. 400-20)

and

(Eq. 400-21)

A comparison between calculated and experimental friction pressure drop for vertical flow is not available.

428 Liquid Holdup Correlation

The density of two-phase mixtures at any section in the pipe may be calculated if the liquid holdup–the fractional volume of the pipe occupied by the liquid–is known. Correlations have been developed to predict the holdup as it changes along the pipe. That developed by Hughmark (Reference 7) is the most accurate. This correlation relates the flow parameter Y to the variable X as shown in

Figure 400-17.

The relationship between the flow parameter Y and the gas volume fraction Rg assumes that Rg is distributed radially across the pipe, with the largest value at the center. The relationship is expressed in terms of the gas volume fraction Rg and liquid holdup Rl, as follows:

Fig. 400-16 Calculated vs. Experimental Frictional Pressure Drop—Horizontal Flow Flow Regime Range of Deviation (%)

Plug -22.3 to -2.3 Stratified -25.3 to +24.7 Wave -21.0 to +39.0 Slug -17.9 to +12.1 Annular -59.2 to +15.8 Dispersed -24.4 to +30.6

Bubble not given

∆P 10 1+(–0.18) --- 12.2 psi = = ∆P 10 1+0.12 --- 8.9 psi = =

(58)

(Eq. 400-22)

The variable X in Equation 400-22 is defined as follows:

(Eq. 400-23)

where:

Fr = Froude number = V2/Dg

λ = liquid volume fraction at pipe entrance

Fig. 400-17 Correlation for the Flow Pattern Y From “Holdup in Gas-Liquid Flow” by G.A. Hughmark, Chemical Engi-neering Progress, Vol. 58, April, 1962, p. 62

R_g 1–R₁ _ρ Y g ρ₁ --- 1 X ----–1    ₊₁ ---= = X Re 1 6 ---Fr 1 8 ---⋅ λ 1 4 --- ---=

(59)

D = diameter, ft

The dimensionless numbers used in the variable X are shown in Equations 400-24 and 400-25.

(Eq. 400-24)

where:

G_m = ρ_tpV_m

= mass velocity _mixture (lbm/ft2-sec) Re ≠ Re_tp (from Equation 400-11)

(Eq. 400-25)

(Eq. 400-26)

where:

υ = specific volume

The calculation procedure is to evaluate Re, Fr, and λ using Equations 400-24, 400-25, and 400-26. The variable X is then evaluated using Equation 400-23, and the flow parameter Y is determined from Figure 400-16. Using the flow parameter Y, the liquid holdup is found from Equation 400-22. An iterative calculation is required since the gas density used in Equation 400-22 is evaluated at the average pressure. The gas volume flow rate Qg used in Equations 400-25 and 400-26 is the inlet value evaluated using the inlet density.

The actual flow density calculated using Equation 400-16 is then used to determine the elevation pressure drop in upwards vertical flow.

The deviation between the calculated (Figure 400-17) and experimental (Reference 3) values of the liquid holdup varies by ± 25%. For vertical flow not as much experi-mental data are available. For the available data the deviation between experiexperi-mental and calculated liquid holdup does not exceed ± 10 percent (see Section 450, Refer-ence 7). Re D G⋅ _m R₁µ₁+R_gµ_g ( ) ---1490 ---= F_r V_m2 gD ---Q₁+Q_g ( )⁄A ( )2 gD ---= = λ W1υ1 W₁υ₁+W_gυ_g ---Q₁ Q₁+Q_g ---= =

(60)

430 Compressible Flow

Pressure drop in gas transmission lines can be calculated in five ways, as follows: • Using the PIPEFLOW-2 program, discussed in Section 1100

• Using the gas flow charts, Figures 400-18 through Figure 400-25. These give reasonable engineering accuracy.

• Applying the widely used Weymouth and Panhandle fundamental flow equa-tions (see Figure 400-26 on page 400-58)

• Using the PCFLOW program, discussed in Section 1100

• Using COMFLOW, a computer program developed for Chevron Pipeline Company by CRTC. COMFLOW solves for pressure drop in branched gas pipeline systems. See Section 1100 for further discussion.

Of these options only COMFLOW and PIPEFLOW-2 consider heat transfer, and only PIPEFLOW-2 considers condensation. Condensation due to heat transfer is common in hot gas transmission and can significantly affect the friction pressure drop. Section 420 discusses two-phase flow pressure drop.

Weymouth and Panhandle Equations

The general formula for compressible flow has the following form:

(Eq. 400-27)

where:

Q = flow rate, SCFD

T_o = standard absolute temperature, °R P_o = standard pressure, psia

D = pipe ID, in.

P₁ = upstream pressure, psia

P₂ = downstream pressure, psia S = fluid specific gravity (air = 1) T = fluid absolute temperature, °R L = length of pipeline, miles

(61)

ti on Pr es sur e Dr op Flui d Fl ow Ma nual 1 997 400-42 Ch evron Co rp orat io n Nomenclature:

M Mass flow rate, lb/hr P Average line pressure, psia P₁ & P₂ Initial and final pressure, psia P′ Rate of pressure drop, psi/1000 ft T Absolute temperature, °F + 460

µ Viscosity, cp

V Specific volume of fluid, cu ft/sec

G Specific gravity of gas referred to dry air at standard conditions L Line length, thousands of feet

Examples:

1. Fluid, carbon dioxide gas; flow rate = 2500 lb/hr; temperature = 70°F; viscosity = 0.015 cp; inlet pressure 15 psig; pipe size = 3 in. sch 40 = 3.068 in. ID. Assume average line pressure = 12 psig. Determine pressure loss.

2. Fluid, carbon dioxide gas; temperature = 70°F; viscosity = 0.015 cp; inlet pressure = 25 psig; outlet pressure = 20 psig; line length = 600 ft; line size = 2 in. sch 40 = 2.067 in. ID. Average flowing pressure = 22.5 psig.

Miscellaneous Data:

Specific volume of a perfect gas, V = 10.72 T / P(MOL. WT)

1 cubic foot per minute of gas at standard conditions = 4.58G pounds per hour

1 inch of water = 0.0361 pounds per square inch

Notes:

1. The chart, strictly speaking, gives rate of pressure drop at a point in the pipe, but for a perfect gas will give the average rate of pressure drop if the specific volume at the average pressure is used.

(62)

Flow Man ual 400 Fr ic tion P re ssur e D rporat io n 400-43 March 19

(63)

ti on Pr es sur e Dr op Flui d Fl ow Ma nual 1 997 400-44 Ch evron Co rp orat io n Nomenclature:

M Mass flow rate, lb/hr P Average line pressure, psia P₁ & P₂ Initial and final pressure, psia P′ Rate of pressure drop, psi/1000 ft T Absolute temperature, °F + 460

µ Viscosity, cp

V Specific volume of fluid, cu ft/sec

G Specific gravity of gas referred to dry air at standard conditions L Line length, thousands of feet

Examples:

1. Fluid, carbon dioxide gas; flow rate = 50 lb/hr; temperature = 70°F; viscosity = 0.015 cp; inlet pressure 15 psig; pipe size = 3/4 in. sch 40 = 0.824 in. ID. Assume average line pressure = 12 psig. Determine pressure loss.

2. Fluid, carbon dioxide gas; temperature = 70°F; viscosity = 0.015 cp; inlet pressure = 25 psig; outlet pressure = 20 psig; line length = 600 ft; line size = 2 in. sch 40 = 2.067 in. ID. Average flowing pressure = 22.5 psig.

Miscellaneous Data:

Specific volume of a perfect gas, V = 10.72 T / P(MOL. WT)

1 cubic foot per minute of gas at standard conditions = 4.58G pounds per hour

1 inch of water = 0.0361 pounds per square inch

Notes:

1. The chart, strictly speaking, gives rate of pressure drop at a point in the pipe, but for a perfect gas will give the average rate of pressure drop if the specific volume at the average pressure is used.

(64)

Flow Man ual 400 Fr ic tion P re ssur e D rporat io n 400-45 March 19