ENOINEERINO DATA TRANSMITTAL P.W 1 of 20 627026 · AFT FATHOM, hereafter referred to as FATHOM, was supplied by Applied Flow Technology Corporaoon in Woodlawn Park, Colorado for use

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Val idat ion & Configuration

Control

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R3-86 X

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HO-34 X

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R3-86 X

R3-86 X

L6-13 X

DIMC

DOE/RL Reading Room

SNF Project File W-441

CVD Librarv

H6-15 X

H2-53 X

R3-11 X

R3-86 X

Startup Library

CVD Satellite Library

B2-64 X

X3-25 X

SNF-5332 Rev 0

FATHOM (Version 3) - Commercial Software Validation and Configuration Control

T J h a d Fluor Da&l<anford, Inc RWllsnd,W 99352 U S Department of Enemy Contract DE-AC06-88RL13200

EDTECN 627026 uc 510 Omcode 82600 Chaw Code iosss9/f?A*+ f l M F 5 0 0 ? I

Total Pages 16 r f 4" Code EW04J1110

KsywOrds software validation, configuration control, computer program, flow network, piping,incompressible, FATHOM, applied flow technology

AbStrad FATHOM (Version 3), an incompressible flow piping network modeling and analysis computer program from Applied Flow Technology, was installed for use at the U S Department of Energy Hanford Site near Richland, Washington A series of sample problems were executed to validate the software and confirm proper installation

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Approved For Public Release

SNF-5332, Rev 0

FATHOM (Version 3) - Commercial Software Validation and Configurahon Control

Prepared by

F J Heard Fluor Daniel Hanford. Inc

December 1999

SNF-5332, Rev 0

ABSTRACT

FATHOM (Version 3), an incompressible flow p y ing network anakysw computer code from Applred Flow Technology, was installed for use at the Department of Energv (DOE) Hanford site near Richlmd, Washington A senes of tests were perfkmed to valrdate the software and confirm proper rnstallatwn

SNF-5332 Rev 0

TABLE OF CONTENTS 1 0 INTRODUCTION AND PURPOSE

2 0 DESCRIPTION AND APPLICATION 2 1 OVERVIEW

2 I 1 Input Windows 2 1 2 Ourput Windows

2 2 MODELING CAPABILITIES 2 3 ENGINEERINGASSUMPTIONS

3 0 CONFIGURATION CONTROL 3 1 HARDWARE 3 2 LICENSEKEY 3 3 PROBLEM REPORTINO 3 4 USERMANUAL

4 0 VALIDATION

4 I I Fluids 4 1 2 Losses

4 1 INTERNALDATABASES

4 2 TEST PROBLEMS

5 0 RESULTS 5 1 ACCEPTANCE CRITERIA 5 2 TESTRESULTS

5 2 I Sumple Problem #1 5 2 2 Sample Problem #2 5 2 3 Sample Problems #3 and U3a 5 2 4 Sample Problem #4 5 2 5 Sample Problem #5 5 2 6Sample Problem #6 5 2 7 Sumple Problem #7 5 2 8 Sample Problem #8 5 2 9 Sample Problem #9 5 2 I O Sample Problem U 10 5 2 1 1 SampleProblemUlI 5 2 12 Sample Problem # I 2 5 2 13 Sample Problem #13 5 2 14 Sample Problem #14 5 2 15 Sample Problem #15 5 2 16Sample Problem #I6 5 2 17SampleProblem#17 5 2 18 Sample Problem #18 5219SampleProblem#19 5 2 20 Sample Problem #20 5 2 21 Sample Problem #21 5 2 22 Sample Problem #22

6 0 SUMMARY AND CONCLUSIONS

7 0 REFERENCES

APPENDM A - SAMPLE PROBLEMS INPUT AND OUTPUT

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10 10 11 11 12 14 15 17 17 18 18 19 20 20 21 22 22 23 24 25 28

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TABLES

Table 3-1 Hardware and System Requirements

Table 4-1 Listing of Sample Problems Supplied with FATHOM

Table 5-1 Comparison of Results for Sample Problem #I

Table 5-2 Comparison of Results for Sample Problem #2

Table 5-3 Compmson of Results for Sample Problem #3







Table 5-10 Comparison ofResults for Sample Problem #IO Table 5-1 1 Comparison of Results for Sample Problem #I 1

Table 5-12 Comparison ofResults for Sample Problem #12

Table 5-13 Comparison ofResults for Sample Problem #I3


Table 5-15 Comparison ofResults for Sample Problem #I5

Table 5-16 Comparison of Results for Sample Problem #I6



Table 5-19 Compmson ofResults for Sample Problem #I9




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7

10

10

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1 0 INTRODUCTION AND PURPOSE

The purpose of this report is to document the validation of AFT FATHOM (Version 3) computer code consistent wth the requirements of HNF-PRO-309 (Revision 0) “Computer Software Quality Assurance Requirements” for commercial-off-the-shelf (COTS) software

AFT FATHOM, hereafter referred to as FATHOM, was supplied by Applied Flow Technology Corporaoon in Woodlawn Park, Colorado for use at the Department of Energy’s Hanford site near hchland, Washington “Applied Flow Technology”, “AFT ’, and “AFT Fathom ’ are registered trademarks of the Applied Flow Technology Corporahon

Software validation is the process of evaluatmg a system or component dunng or at the end of the development process to determine whether it sahsfies specified requirements Validation involves running test cases to ensure that the computed output meets specified expectations and requirements, including numerical correctness of the results based on comparisons with alternate calculations (e g , hand calculations, analytical solutions, or acceptance testing)

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2 0 DESCRIPTION AND APPLICATION

FATHOM is an incompressible flow piping network analysis tool FATHOM is intended as an aide for network analyses and not as a replacement for other design and analysis methods, including sound judgement, hand calculations or independent checks FATHOM is supplied by Applied Flow Technology Corporation in Woodlawn Park, Colorado “Applied Flow Technology”, “AFT”, and “AFT Fathom” are registered trademarks of the Applied Flow Technology Corporation

2 1 Overview

FATHOM uses a graphical interface that is based on drag-and-drop operahons inherent to most Windows based applications This allows the user to build a piping network using selections from a palette of components Date is entered or edited for each of the components by double- clicking the component of interest Additional global editing features are avaslable from the menu or tool bars that simplify making large-scale changes to the model

FATHOM has five integrated subordinate windows The five windows can be viewed as an integrated environment for entering, processing, analyzing, and documenting the results of a piping network simulation The user will work from one of the five windows at all times Of the five windows, two are input windows and three are output windows

2 1 1 Input Windows

The two input windows are the Workspace window and the Model Data windows These two windows, one graphical and the other text-based, process the input data for the model

2 1 2 Output Windows

The three output wndows are the Output, the Graph Results, and the Visual Report The Output window is text-based The Graph Results and Visual Report windows are graphical These three windows are essential for reviewing the results of the analysis, spomng analysis errors and preparing the results for documentation

2 2 Modeling Capabilities

FATHOM is an incompressible steady-state one-dimensional Newtonian fluid network flow analysis program and can be used to model a variety of engineering systems including

Open and closed (recirculating) systems Network systems that branch or loop with no limit on the number of loops Pressure and/or gravity feed systems Pumped systems, including multiple pumps in parallel and/or in series Pumps with variable speed, controlled discharge pressure, and viscosity corrections Systems with pressure and/or flow control valves Systems with valves closed or pumps turned off

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Systems with heat exchangers Systems heat transfer from external surfaces Systems with variable density and viscosity

FATHOM also provides hundreds of standard loss models based on well known references such as, Crane (1988), Idelchik (1994), and Miller (1990), but also allows the user to enter there own loss data Vanable or dynamic loss coefficients are supported Vanable loss coefficients may depend on flow, area ratios, and/or flow splits (such as tee’s and wye’s), and the angle of the connectmg piping FATHOM also provides automatic calculation of friction factors using the well-known Colebrook-White correlation Also provided is an extensive database of thermophysical properties for numerous fluids and gases

FATHOM uses a Newton-Raphson method to solve the fundamental equaaons of pipe flow that govern conservation of mass, momentum, and energy Solutions are obtamed by iterative matnx methods that have been optimized for speed and convergence

2 3 Engineering Assumptions

FATHOM is based on the following fundamental fluid mechanics assumptions

Incompressible flow Steady-state conditions One-dimensional flow Newtonian fluid model (fluid viscosity is independent of the fluid dynamics)

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3 0 CONFIGURATION CONTROL

FATHOM was purchased from Applied Flow Technology located in Woodlawn, Colorado FATHOM is currently licensed for a single user on a single personal computer wthin a Windows 9x or NT environment FATHOM is considered commercial-off-the-shelf (COTS) software

3 1 Hardware

FATHOM has been installed on an AST Bravo mth a 200 M H z Pentium processor and 128 MEi of man memory The property tag is WC65744 The operating system is Windows 95 Version 4 00 950B FATHOM was installed by running the automated SETUP program located on the installation disk

The FATHOM installation program is very simple and standard for most Windows based applications SETUP asks you where to unzip the program and where (I e , pathname) to install the program The executable files supplied with FATHOM are complied code No source code is supplied SETUP handles all the file manipulations, short cuts, desktop icons, and registry entries required by Windows FATHOM was installed using the following default pathname C \FATHOM

To install and run AFT FATHOM, the computer must meet the following minimum requirements

Table 3-1 Hardware and System Requirements

Feature IBM - Compatible Processor Hard Disk Space Floppy Drive Monitor Resolution Random Access Memory (RAM) Mouse Math Co-processor

MS-Windows MS-DOS

Required 80286 5Mb 3 % -inch VGA 4Mb Yes No Version 3 1 Version 3 3 1

Recommended 80386 or higher

VGA or higher 8Mb

Yes Version 5 0 or higher Windows 95,98 or NT

3 2 License Key

A hcense key is required to actwate the AFT FATHOM program for use The license key is supplied by the vendor on a separate floppy disk The user must supply the license key when requested dunng setup The license key is copied from the floppy and stored within a hidden and encrypted file somewhere on the system FATHOM will check for the existence and content of the license file each time the program is activated

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The license key contains informauon pertaining to the registered purchaser of the program, authorized number of users, and time remaming for the annual software upgrade mamtenance (SUM) and help agreement if purchased with FATHOM

3 3 Problem Reporting

AFT FATHOM provides an extensive context searchable online help manual and access to additional help, frequently asked questions (FAQ’s), and modeling tips via the internet (www aft com)

Modeling problems, bug reports, and general pleas for assistance can be supplied to AFT via support (support@aft com) A bug report is first verified and then acknowledged usually within two to three business days The response may or may not solve the problem, but may provide a workaround until the problem is fixed If requested, a special version of FATHOM containing the bug fix (when available) can be supplied to the customer If the error@) persist, a special version of FATHOM contaming an extensive set of debugging tools can be supplied for use by the customers in an attempt to resolve the problem

Users are notified via email when an update to FATHOM is aviulable Minor updates are received several times a year Major updates are received approximately once a year Most of the minor revisions address bugs that have been found and corrected The major once-a-year revisions usually deal with major enhancements and new capabilities that have been added Whether or not to update depends on the hme remaining in the annual SUM agreement, current workscope, and the nature of the bug fixes or enhancements

3 4 User Manual

The user manual for AFT FATHOM is a soft cover booklet running about 250 pages The user manual is also available via online help A single copy of the user manual was included with the software and is currently located at 2440 Stevens Center Room 1704 Additional copies can be purchased from Applied Flow Technology

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4 0 VALIDATION

The FATHOM user’s manual contam a detded hscussion of the hndamental concepts and conventions used in processing piping systems and how to interpret the database information imbedded withn FATHOM (see Secuon 2 1) FATHOM assumes that the user has a good general understanding of engineering hydraulics FATHOM is designed for use by persons who possess a level of knowledge consistent with that obtamed from an undergraduate engineering course in the analysis of piping systems and fluid networks

4 1 Internal Databases

Most engineering analyses involve processing very large amounts of information, some of whch is critical, but most of which is of lesser importance The key to accurate and efficient analysis is the proper idenhficahon of critical informahon Two databases embedded within FATHOM manage critical information associated with the fluid properties and pressure loss factors

4 1 1 Fluids

Density and dynamic viscosity are two fluid properties required for all analyses Fluid vapor pressure is optional FATHOM provides a fluid database for numerous common fluids If the worlang fluid is not in the database, the user can enter fluid properties into a custom database for later recall

Spot checks of the properties for ur, helium, hydrogen, oxygen, nitrogen, and water agamst the values summarized in HOLMAN (1990) showed very good agreement

4 1 2 Losses

FATHOM provides hundreds of standard loss models based on well known references such as, Crane (1 988), Idelchik (1 994), and Miller (1 990), but also allows the user to enter there own loss data Vanable or dynamic loss coefficients are supported Vanable loss coefficients may depend on flow, area ratios and/or flow splits (such as tee’s and wye’s) and the angle of the connechng piping FATHOM also provides automatic calculation of friction factors using the well-known Colebrook-White correlation

Spot checks of representative loss coefficients for valves and fittings aganst values summarized within Crane (1988) showed very good agreement

4 2 Test Problems

Twenty-two sample problems (input files) are supplied with FATHOM All twenty-two input files are installed in the SAMPLE sub-directory below the C \FATHOM directory The sample problems model systems that range in size from one pipe to seventy pipes Twenty of the twenty-two sample problems are for systems with solutions avlulable in published literature Sample problems 3 and 4 do not have published solutions, but were run and documented within Appendix A for completeness

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Table 4-1 lists the sample problenls and provides a brief description of each model Appendix A summarizes the model, the reference, and the output test results

Table 4-1 Listing of Sample Problems Supplied with FATHOM

Number 1

2

3

4

5

6

7

8

9

10

11

connected in a single loop and driven by a pump

10 pipes, 10 junctions Model of a system with three pumps supplied by

Model of a branching system fed by two reservoirs

Model of a large branching network Water 1s the

3 pipes, 2 junctions Model of a parallel flow pressure drop Water is the

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Number 12

13

14

15

16

17

18

19

20

21

22

Description 2 pipes, 2 junctions Model of a series flow pressure drop w t h benzene as the worlang fluid 3 pipes, 4 junctions Model of a branching system with component losses included Ethyl alcohol is the workmg fluid 2 pipes, 3 junctions Model of a siphoning system The problem is to determine how high a junction can be rased and continue flowing Water is the worlung fluid 1 pipes 2 junctions Model of the pressure drop through a cylindrical annulus Water is the workmg fluid 8 pipes, 9 junctions Model of a branching system fed by three reservoirs, one of which has a pump One loop is included Water is the workmg fluid 10 pipes, 9 junctions Model of a branching system with a pump and a PRV Two loops are included Water IS the worhng

12 pipes, 10 junctions Model of a branching system fed by two reservoirs and containing two PRV's Several loops are included Water is the worlang fluid 16 pipes, 14 junctions Model of a branching network fed by two reservoirs One reservoir has a pump One PRV is included Water is the workmg fluid 3 1 pipes, 21 junctions Model of a complicated branching network fed by two reservoirs Each reservoir has a pump One other booster pump also is modeled Multiple loops exist Water is the workmg fluid 68 pipes, 44 junctions Model of a complicated branching network fed by six reservoirs Four of the reservoirs have pumps One other booster pump is modeled Multiple loops exist Water IS the worlung fluid 70 pipes, 40 junctions Model of a complicated branching network fed by SIX reservoirs Four of the reservoirs have pumps One other booster pump is modeled Multiple loops exist Water is the workmg fluid

File Name Sample12 fth

Sample13 fth

Sample14 fth

Sample15 fth

Sample16 fth

Sample17 fth

Sample1 8 fth

Sample19 fth

Sample20 fth

Sample21 fth

Sample22 fth

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5 0 RESULTS

Twenty-two sample problems were successhlly executed and inspected The input and output files are attached in Appendix A

5 1 Acceptance Criteria

The following acceptance criteria were used to evaluate the results of the sample runs

1) Each of the sample problems must execute and converge using the default or input supplied convergence criteria

2) Each of the sample problems, with the exception of sample problems #3 and #4 were compared to the published solutions

5 2 Test Results

The pertinent results from each of the sample problems are summarized within the following tables and discussed within the following paragraphs It must be noted that significant differences between FATHOM and the published results were found most notably for a few pipes in sample problems 21 and 22 Most of the differences in flow rates and head losses were due to a combination of items tighter tolerances (both global and individual pipedjunctions), friction factor models, and the rigorous treatment of pump heads (fitted polynomial versus linear interpolation) This is acceptable given that most of the piping lengths in sample problems 21 and 22 are in thousands of feet Even minor differences in the treatment of hction factors and pump heads will have a noticeable affect on the results These differences were judged to reflect the improvements associated with the general state of knowledge now available for use within FATHOM These differences should not reflect adversely given the relatively simple hand calculations and techniques that were used to denve the published solutions

5 2 1 Sample Problem #1

Sample problem # 1 is a model of a water tower fire protection system consisting of two pipes and three junctions from FOX (1985)

A fire protection system is supplied from a water tower and standpipe 80 ft tall The longest pipe in the system is 600 ft long and is made of cast iron The pipe contains one gate valve Other losses may be neglected The pipe diameter is four inches The goal of the analysis is to determine the maximum rate of flow through this pipe, in gallons per minute

The results for sample problem #I are presented in Table 5-1 A simple hand calculation after two iterations gives a volumetnc flow rate of 350 gpm The corresponding FATHOM results are 35 1 755 gpm after three iterations Appendix A contains a listing of the input and output results for sample problem #1

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Fox FATHOM


Volumetric f Flowrate (gpm) Convergence Criteria # of Iterations

(gpm) 0 031 350 0 +o 1 2

0 0306798 351 755 - +o 001 3

Flow Velocity (Ws) Reynolds Number PumpHead (ft) Pump Power (Hp)


Sample problem #2 is model of a pumping system between two reservoirs consisting of six pipes and seven junctions from WHITE (1979) The goal is to determine the required pump horsepower Water is the worlang fluid

The results for sample problem #2 are presented in Table 5-2 A simple hand calculation after gives the pump horsepower at 4 2 Hp The corresponding FATHOM results are 4 1892 Hp Appendix A contans a listing of the input and output results for sample problems #2


White FATHOM 9 17 9 19714

139000 139349 184 0 184 0 4 2 4 1892

5 2 3 Sample Problems #3 and #3a

Sample problem #3 is a classical model of a three reservoir branching system consisting of three pipes and four junctions This particular problem was obtamed from LINDEBURG (1984), but variations can be found in most engineering textbooks about fluid mechanics Water is the working fluid However, since there are no published results for this problem, no comparisons are made

Sample problem #3a is also a classical model of a three reservoir branching system consisting of three pipes and four junctions This particular problem was obtamed from WHITE (1994), Three reservoirs (J1 J2, and J3) are interconnected with a common junction (J4) at an elevation 34 53 meters above some arbitrary reference point The water surface levels for reservoirs J1, J2, and J3 are at elevations of 20, 100, and 40 meters, respectively The pipe from reservoir J 1 to the junction is 100 meters of 8-cm pipe The pipe from reservoir 52 to the Junction is 150 meters of 6-cm pipe The pipe from reservoir J3 to the junction is 80 meters of 4-cm pipe The goal is to determine the flow velocity and direction in each pipe

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uescription

The results for sample problem #3a are presented in Table 5-3 Comparison is made to the published results from WHITE (1994) Appendix A contains a listing of the input and output results for sample problems #3 and #3a


White FATHOM*

* Common junction elevation of 34 53 meters


Sample problem #4 is a model of a circulation system connected in a single loop and driven by a pump The model contains an orifice, seven pipes, and seven junctions Water is the working fluid Given the system as shown, determine the mass and volumetric flow rate in the system, the pressure added by the pump and the total pressure at eachjunction

Table 5-4 was purposely left blank There are no published results for this problem Appendix A contains a listing of the input and output results for sample problem #4


This table was purposely left blank There are no published results for comparison


Sample Problem 5 is a model of a system containing 10 pipes, 10 junctions, and three pumps supplied by three reservoirs Water is the worlung fluid

The supply head for each is given by the equation hp = -10 328Q2 + 2 823Q + 22 289 There IS a defined system outflow of 2 0 cfs at junction 2 Assume all pipes have roughness of 0 012 inch Find the flow and head loss in each pipe, the pump head added for each pump and the pressure at each junction

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Jeppson FATHOM

pibe 2 Pipe 3 Pipe 4 Pipe 5 Pipe 6

Piue 1 0 666 1334 0 573 0 761 0 175

0 841 I 0 8411 0 6664 13336 0 5726 0 7610 0 1747

Pipe 7 0 398 0 3979

Pipe 1 Pipe 2 Pipe 3 Pipe 4

Pipe 6 Pipe 7

Pipe 5

18 456 21 777

3 15 3 1246* 17 63 17 5309 15 46 15 3840 150 14836

11 42 11 3715** 0 674 0 6633 3 24 3 2088***

* PI + P8 See output (Appendix A) ** P5 + P9, See output (Appendix A) *** P7 + P10, See output (Appendix A)


Sample problem #6 is a model of a branching system contaming nine pipes, eight junctions, one pump, one pressure relief valve (PRV), and two loops Water is the worlang fluid

Consider the nine-pipe network shown in Appendix A for Sample Problem #5 A PRV exists 500 feet downstream ofjunction 1 The pump charactenstics are the following Q1 = 1 0 cfs @ HPl = 50 ft, QZ = 1 5 cfs @ Hp2 = 55 ft, Q3 = 2 0 cfs @ H+,3 = 48 fi There are defined system

Pipe 1

12

17 36 17 356 pipe 2 Pipe 3

18 46 21 78

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Jeppson

outflows of 1 0 cfs at junction 2 and 4 Assume all pipes have roughness of 0 02 inches Find the flow and head loss in each pipe the pump head added for each pump and the pressure at each junction

The results for sample problem #6 are presented in Table 5-6 Comparison is made to the published results from JEPPSON (1976) As discussed with Sample Problem #5, FATHOM requires that each pump junction have two connecting pipes an inflow and outflow This is also true for pressure relief valves (PRV) This differs from the problem statement in EPPSON showing a single pipe the pump and PRV The corresponding FATHOM head losses for pipes 1 and 6, as shown in Table 5-6, are the total head loss for two pipes each at the pump and PRV Very good agreement between the published and FATHON results for values of volumetric flow Small differences are noted between the published and FATHOM values for head loss In general very good agreement was found Appendix A contains listing of the input and output results for sample problem #6


FATHOM

Pipe 1 1 03 Pipe 2 0 98 Pipe 3 0 017 Pipe 4 0 97 Pipe 5 0 96 Pipe 6 0 041 Pipe 7 0 003

Pipe 1 Pipe 2 Pipe 3 Pipe 4 Pipe 5 Pipe 6 Pipe 7

102686 0 98435 0 01565 0 97314 0 96007 0 03993 0 00258

23 35 21 43 0 009 4 21

40 92 0 05

23 68

23 32407* 21 44967 0 00632 4 19376 40 82923

0 04598** 21 44336

* P1 + P9, See output (Appendix A) * * P6 + P8 See output (Appendix A)

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Volumetric Flowrate (ft3/s)


Head Loss (ft)

Sample problem #7 is a model of a branching system with 17 pipes and 12 junctions fed by two reservoirs One reservoir has a pump Numerous loops are involved Water is the workmg fluid

11

12

13

Solve for the flow rate in each pipe and the head at each junction of the network shown below The pump characteristic curve is given by hp= -2 505Q2+ 16 707Q + 155 29 (hp is in feet and Q in cfs) There are defined system outflows of 0 5 cfs at junctions 2, 3 and 7 There are additional defined systems outflows of 2 0, 1 0, and 2 0 cfs at junctions 2, 3 and 4, respectively Finally, there is a defined system inflow of 1 5 cfs at junction 4 Assume all pipes have a Hazen- Williams friction factor of 130

The results for sample problem #7 are presented in Table 5-7 Comparison is made to the published results from JEPPSON (1976) As discussed with Sample Problem #5, FATHOM requires that each pump junction have two connecting pipes an inflow and outflow This differs from the problem statement in JEPPSON showing a single pipe for the pump The corresponding FATHOM head loss for Pipe 1, as shown in Table 5-7, is actually the total head loss for two pipes (P1 and P17) adjacent to the pump junction Very good agreement between the published and FATHON results for values of volumetric flow Small differences are noted between the published and FATHOM values for head loss In general, very good agreement was found Appendix A contains a listing of the input and output results for sample problem #7


0 609 0 6101 2 17 2 1681

0 109 0 1101 0 04 0 0381

0 413 0 4133 0 27 0 2750

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Pipe

14

15

16

Volumetric Flowrate (ft3/s) Head Loss (ft)

Jeppson FATHOM Jeppson FATHOM

1587 15867 4 31 4 3049

2 391 2 3910 2 62 2 6285

0 025 0 0233 0 00 0 0003

*PI + P17, see Sample #7 output (Appendix A)

IO

11

12


2 40 2 4019 3 01 2 9964

4 07 4 0661 16 90 16 8501

6 07 6 0661 2 29 2 2741

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16

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Sample problem #9 is a model of a simple network with three pipes in series each with a different diameter Water is the working fluid

The results are presented in Table 5-9 Comparison is made to the published results from WHITE (1979) Very good agreement was found between the published and FATHON results for frlction factor Reynolds numbers flow velocities, and volumetric flows Appendix A contains a listing of the input and output results for sample problem #9


Friction Factor


Sample problem #10 is a model of a simple network with three pipes in parallel with component losses included Water is the working fluid

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Pipe # White FATHOM 1 2 Z

5 2 11 Sample Problem #I 1

Sample problem #11 is a model of a simple series network containing two pipes and three junctions with component losses Water is the workmg fluid

Water at 68 O F leaves an open tank whose surface elevation is 180 ft and enters a 2-inch schedule 40 steel pipe (Pipe 1) via a sharp-edged entrance Pipe 1 is 50 feet in length Pipe 1 contains a 2-inch globe valve Pipe 1 enlarges suddenly to an 8-inch Schedule 40 steel pipe (Pipe 2) Pipe 2 is 100 feet in length and contains two standard 90' elbows and an 8-inch angle valve Pipe 2 discharges below the surface of another open tank whose surface elevation is 100 feet Determine the volumetric flow rate

The results are presented in Table 5-1 1 Comparison is made to the published results from BAUMEISTER (1978) Very good agreement was found between the published and FATHON results for volumetric flows Appendix A contains a listing of the input and output results for sample problem #11


62 5 62 5578 25 9 25 91 19 1 1 4 1 1 4099


Sample problem #12 is a model of a simple parallel network contaming two pipes and two junctions Benzene is the workmg fluid

Benzene at 68 OF flows at a total rate of 0 5 ft3h through two parallel straight, horizontal pipes connecting two pressurized tanks One pipe is 1-inch Schedule 40 The pipe is 2-inch Schedule 40 Both pipes are 100 feet long and have connections that project inwardly in the supply tank

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Friction Factor Pipe 1 Pine 2

Ifthe pressure in the supply tank is maintained are 100 Ibfhn2, what is the pressure in the receiving tank7

The results are presented in Table 5-12 Comparison is made to the published results from BAUMEISTER (1978) Very good agreement was found between the published and FATHON results for volumetnc flows Appendix A contains a listing of the input and output results for sample problem #12

0 02389 0 02392 001981 0 01980

Flow Velocity (ft/s) Pipe 1 Pipe 2

12 50 12 1112 18 23 18 3373

Reynolds Number Pipe 1 Pipe 2

136800 132534 393200 395406

Receiving Tank 73 40


Sample problem #13 is a model of a small branching system with three pipes and four junctions Component losses are included Ethyl alcohol is the working fluid

Ethyl alcohol at 68 OF flows from tank A (Junction I), which is maintained at a constant pressure of 100 psi, through 200 feet of 2-inch Schedule 40 cast-iron pipe (Pipe 1) to a Y branch connection (Junction 2) The flow branches into 100 feet of 2-inch pipe (Pipe 2) to tank B (Junction 3) and 50 feet of 2-inch pipe (Pipe 3) to tank C (Junction 4) Tanks B and C are maintained at 80 psi All tank connections are flush and sharp-edged and are at the same elevation Estimate the flow rate to each tank

The results are presented in Table 5-13 Comparison is made to the published results from BAUMEISTER (1978) Very good agreement was found between the published and FATHON results for volumetnc flows Appendix A contains a listing of the input and output results for sample problem #13

73 5748

19

SNF-5332 Rev 0

Tank A B C

Volumetric Flowrate (ft3/s) Pipe Baumeister FATHOM

1 0 2253 1 0 22520 2 0 09491 0 09484 3 0 13040 0 13036

20

Elevation (ft) of Point B (Junction 3) Above Source

Baumeister FATHOM 16 58 16 69*

SNF-5332, Rev 0

White FATHOMS


Sample problem #16 is a model of a branching system contruning seven pipes and nine junctions The system is fed by three reservoirs, one of which has a pump One loop is included Water is the working fluid

The elevation of all junctions is 80 feet The pump curve is given by hp = -10 33QZ+ 2 823Q + 22 29 There is a defined system outflow of 2 0-cfs junction 2 All pipes have a roughness of 0 012 inches Find the flow and head loss in each pipe, and the head and pressures at each junction

As discussed with Sample Problem #5, FATHOM requires that each pump junction have two connecting pipes an inflow and outflow This differs fiom the problem statement in JEPPSON showing a single pipe (P7) to the pump The corresponding FATHOM head losses for pipe 7 as shown in Table 5-16, are actually the total head loss for pipes 7 and 8

The results are presented in Table 5-16 Comparison is made to the published results fiom JEPPSON (1976) Very good agreement was found between the published and FATHON results for volumetric flow and head loss Appendix A contains a listing of the input and output results for sample problem #16


Reservoir Level (m)

*P7 + P8 See Output for Sample Problem #16 (Appendix A)

3 71 3 71238

21

SNF-5332, Rev 0


Sample problem #17 is a model of a branching system contruning 10 pipes, 9 junctions, a pump and a PRV Two loops are included Water is the working fluid

The ten-pipe network is supplied by two reservoirs with water surfaces at 180 and 200 feet, respectively The PRV is located 450 feet downstream from the upstream junction [J2] and has a pressure setting, which maintains the elevation of the HGL at 50 ft downstream from the valve The pump characteristics are the following Q1 = 1 0 cfs @ hpl= 40 ft, QZ = 1 5 cfs @ hpz= 35 ft Q3 = 2 0 cfs @ hp3 = 26 ft There are define system outflows of 1 0, 2 0, and 2 0 cfs at junctions 6 8 and 9, respectively Assume that pipes 1, 3 and 10 have a CHW = 110 Pipes 2, 4, 5, 6 and 9 have CHW = 120, and pipes 7 and 8 have CHW = 130 Find the flow and head loss in each Pipe

As discussed with Sample Problem #5 , FATHOM requires that each pump junction have two connecting pipes an inflow and outflow This is also true for pressure relief valves (PRV) This differs from the problem statement in JEPPSON (1976) showing a single pipe the pump and PRV The corresponding FATHOM head losses for pipes 1 and 5 as shown in Table 5-6, are the total head loss for two pipes each at the pump and PRV

The results are presented in Table 5-17 Comparison is made to the published results from JEPPSON (1976) Very good agreement was found between the published and FATHON results for volumetric flow and head loss Appendix A contains a listing of the input and output results for sample problem #17


* P1 + P10 See output (Appendix A) ** P5 + P9 See output (Appendix A)


Sample problem #18 IS a model of a branching system containing 12 pipes, 10 junctions two PRVs and fed by two reservoirs Several loops are included The PRVs will act as check valves preventing flow if downstream pressure control is lost

22

SNF-5332 Rev 0

Obtain the volumetric flow rates and head losses in each pipe Water is the worhng fluid (dynamic viscosity = 0 001 13 Kg/m-s and the density = 1000 Kg/m3) Reservoirs A and B are elevations of 300 m and 250 m, respectively

The results are presented in Table 5-18 Comparison is made to the published results from JEPPSON (1976) Downstream pressure control was determined to be lost for both PRVs The corresponding pipe flow (Pipes 7 and 8) was correctly calculated to be zero Very good agreement was found between the published and FATHON results for volumetric flow Some minor differences were noted for head loss, but overall the general agreement was very good Appendix A contams a listing of the input and output results for sample problem #18



Sample problem #19 is a model of a branching network contuning six pipe, 14 junctions and fed by two reservoirs One reservoir has a pump One PRV is included Water is the worhng fluid

In this network the PRV is placed in pipe P5 and has a pressure setting to maintain the HGL downstream from the valve at 350 feet The pump is placed in pipe 1 Solve for the flow rate and the head loss in each pipe The pump characteristics are the following QI = 2 0 cfs @ h,l =

80 ft, Q2 = 3 0 cfs @ h,z = 75 ft Q3 = 4 0 cfs @ hp3 = 68 ft (hp is in feet and Q in cfs) There are defined system outflows

As discussed with Sample Problem #5, FATHOM requires that each pump junction have two connecting pipes an inflow and outflow This is also true for pressure relief valves (PRV) This differs from the problem statement in JEPPSON (1976) showing a single pipe for the pump and PRV The corresponding FATHOM head loss for pipes 4 and 5, as shown in Table 5-6 are actually the total head loss for two pipes each at the pump and PRV Very good agreement is noted between the published and FATHON results for values of volumetric flow Small differences are noted between the published and FATHOM values for head loss Pressure control for the PRV was lost and the flow through pipe 5 is zero In general, very good agreement was found Appendix A contams listing of the input and output results for sample problem #I9

23

SNF-5332 Rev 0

13


0 13 0 1264 0 09 0 0848 14 184 18322 2 21 2 1780

24

Pipe 1 2 3

Volumetric Flowrate (ft3/s) Jeppson FATHOM Jeppson FATHOM

2 94 2 9439 6 41 6 4373 - 1 74 -1 7564 11 85 11 7952 -0 54 -0 5344 n 67 nhlca

Head Loss (ft)

SNF-5332, Rev 0

* P25 f P29 ** P26 + P3 1

***P27+P30


Sample problem #21 is an example of a very large and complicated branching network contuning 63 pipes, 44 junctions, and fed by six reservoirs Four of the reservoirs have pumps One other booster pump is modeled Multiple loops exist The pipe diameters range from 8- to 16-centimeters The piping runs range from 500- to 4300-meters Water IS the working fluid

All pipes have a roughness of 0 026 cm The network is supplied by two reservoirs without pumps and four reservoirs with pumps One booster pump exists between pipe P43 and P68 The water surface elevations are 500, 540 530, 480, 600 and 600 m for reservoirs 546, 547 J48 549, J50 and JS 1 respectively

The results for sample problem #21 are presented in Table 5-21 Comparison is made to the published results from JEPPSON (1976) FATHOM requires that each pump junction have two

25

SNF-5332, Rev 0

connecting pipes an inflow and outflow This differs from the problem statement in JEPPSON showing a single pipe for each pump The corresponding FATHOM head losses for Pipes 1, 20 27,43 and 52, as shown in Table 5-21, are the total head losses for two pipes at each of the three pump junctions A comparison of the volumetric flow rates shows very good agreement However significant differences are noted between the published and FATHOM values for head loss for some of the longer pipes Thls is acceptable given that most of the piping lengths are in thousands of meters Even minor differences in the treatment of friction factors and pump heads will have a noticeable affect on the results These differences were judged to reflect the improvements associated with the general state of knowledge now available for use within FATHOM These differences should not reflect adversely given the relatively simple hand calculations and techniques that were used to derive the published solutions

In general very good agreement was found Appendix A contans a listing of the input and output results for sample problem #21


26

SNF-5332, Rev 0

* P1 + P64 See output (Appendix A) ** P20 + P65 See output (Appendix A) *** P27 + P66, See output (Appendix A)

**** P43 + P68 See output (Appendix A) ***** P52 + P27, See output (Appendix A)

27

SNF-5332. Rev 0


Sample problem #22 is another example of a very large and complicated branching network contiuning 64 pipes 40 junctions, and fed by six reservoirs Four of the reservoirs have pumps One other booster pump is modeled Multiple loops exist The pipe diameters range from 8- to 14-inches The piping runs range from 500- to 4500-feet Water is the working fluid

All pipes have a roughness of 0 0102-inches The network is supplied by two reservoirs without pumps and four reservoirs with pumps One booster pump exists in pipe P55 The water surface elevations are 300, 350 280, 400 150, and 300 feet for reservoirs 541, 542 543 544, 546, and 547, respectively

The results for sample problem #22 are presented in Table 5-22 Comparison IS made to the published results from EPPSON (1976) FATHOM requires that each pump junction have two connecting pipes an inflow and outflow This differs from the problem statement in JEPPSON showing a single pipe for each pump The corresponding FATHOM head losses for Pipes 1, 13 52 5 5 , and 62 as shown in Table 5-22 are the total head losses for two pipes at each of the three pump junctions A comparison of the volumetric flowrates shows very good agreement However, significant differences are noted between the published and FATHOM values for head loss for some of the longer pipes This is acceptable given that most of the piping lengths are in thousands of meters Even minor differences in the treatment of friction factors and pump heads will have a noticeable affect on the results These differences were judged to reflect the improvements associated with the general state of knowledge now available for use within FATHOM These differences should not reflect adversely given the relatively simple hand calculations and techniques that were used to derive the published solutions

In general very good agreement was found Appendix A contains a listing of the input and output results for sample problem #22


28

SNF-5332, Rev 0

29

SNF-5332 Rev 0

* P1 + P71 See output (Appendix A) ** PI3 + P72, See output (Appendix A) *** P52 + P73, See output (Appendix A)

**** P55 + P75, See output (Appendix A) ***** P52 + P74 See output (Appendix A)

30

SNF-5332 Rev 0

6 0 SUMMARY AND CONCLUSIONS

The FATHOM (Version 3) piping network fluid flow analysis program has been installed and successfully validated for use The FATHOM computer program is judged acceptable for use This is based on the use a license key to assure proper installation and configuration control and comparison of twenty of twenty-two sample problems to published results

The pertinent results from each of the sample problems are summarized within the preceding tables It must be noted that in most cases very good agreement was found However, a few cases of significant differences between FATHOM and the published results were found, most notably for a few pipes in sample problems 21 and 22 Most of the differences in flow rates and head losses were due to a combination of items tighter tolerances (both global and individual pipes/junctions) friction factor models, and the rigorous treatment of pump heads (fitted polynomial versus linear interpolation) This is acceptable given that most of the piping lengths in sample problems 21 and 22 are in thousands of feet Even minor differences in the treatment of friction factors and pump heads will have a noticeable affect on the results

These differences were judged to reflect the improvements associated with the general state of knowledge now automated and available for use within FATHOM These differences should not reflect adversely given the relatively simple hand calculations and techniques that were used to derive the published solutions

31

SNF-5332, Rev 0

7 0 REFERENCES

Flow of Fluids Through Valves, Fittings and Pipe”, Technical Paper Number 410, Crane Company, Chicago, Illinois, 1991

Baumeister, T , Editor, Marks Standard Handbook for Mechanical Engineers” 8th ed , 1978

Fox, R W and A T McDonald “Introduction to Fluid Mechanics”, Third Edition 1985

Holman J P “Heat Transfer , Seventh Edition, McGraw-Hill, Inc , New York New York 1990

Idelchik, I E , “Handbook of Hydraulic Resistance”, Third Edition CRC Press Ann Arbor Michigan, 1994

Jeppson R W ‘ Analysis of Flow in Pipe Networks

Lindeburg, M R , “Mechanical Engineering Review Manual for the P E Exam” 7th Ed 1984, p 3-47, timed problem #1

Miller, D S Services) Cranfield, UK, 1990

White F M “Fluid Mechanics’ , 1979

1976

‘Internal Flow Systems , Second Edition Published by BHRA (Information

32

SNF-5332, Rev 0

APPENDIX A - SAMPLE PROBLEMS INPUT AND OUTPUT

33

SNF-5332, RCV 0

Sample #I

2 pipes 3 junctions Model of a water tower fire protection system

Reference Fox R W and A T McDonald lntroduchon to Fluid Mechanm 3rd Ed 1985 p 376

A fire protection system is supplied from a water tower and standpipe 80 it tall The longest pipe in the system is 600 fl long and is made of cast iron about 20 year old The pipe contains one gate valve other minor losses may be neglected The pipe diameter IS 4 in Determine the maximum rate of flow through this pipe in gallons per minute

JI

34

SNF-5332,Rev 0

Name Object Special Elevation Elevation Initial HGUPressure 7-- - 1: 1 9 0 D e g ~ Bend: ~~~ 7::' ~

01 -F---- _____~ ~

Reservoir Name Object Special Elevation Elevation Initial HGUPressure

feet 80 Reservoir Yes ~ -~

Valve Name1 Obiect SDecial Elevation Elevation Initial HGUPressure

Defined Co- -~ UniE - - ~

~ ~- - ~~ ~ -

AFT Fathom 3 0 Input NUMATEC HANFORD CORPORATION

Initial HGUPressure Connected Pipes UnitsI (+ = in =out)

~~ 1 2 Initial HGUPreSSure Connected Pipes

Units (+ = in =out) feet 1

~

Initial HGUPressure Connected Pipes ,

11/30/19990220PM

I Sample 1 Introduction to Fluid Mechanics p 376 Fox and McDonald 3rd Ed 1985 I

Units (+ = in = out) 1 2

35

SNF-5332, Rev 0

Pipe

1 2

Pipe

AFT Fathom 3 0 Output NUMATEC HANFORD CORPORATION I

Vol Flow Mass Flow Velocity dP Total dP Friction dP Gravity dH Max Pres Min Pres Dyn Pres Igallmin) (Ibm/sec) (feellsec) (p old) (psid) (psid) (feet) (psia) (psia) (psia)

351755 488434 898071 306296 399426 346238 922892 447831 141535 0542465 351755 488434 898071 299569 2995692 00000 6921688 447831 148262 0542465

dPf/dx 1 Resistance 1 f I Reynolds No I N D 1 K I N D + K I

12/01 / I 99:

Jct

1 2 3

I Sample 1 Introduction to Fluid Mechanics p 376 Fox and McDonald 3rd Ed 1985

dP dH Vol Flow Into System Loss Factor (K) EGL Inlet EGL Outlet HGL Inlet HGL Outlet P Stag In

0000000 000000 351 755 0 00000 80 00000 80 0000 80 000000 80 00000 14 6960 0000000 000000 0 000 0 00000 70 77108 70 771 1 69 517691 69 51769 45 3256 0672656 155420 351 755 124000 155420 0 0000 0 300813 1 25339 15 3686

@id) (feet) (aaWmin) (feet) (feet) (feet) (feet) @$la)

Title Sample 1 Introduction lo Flu10 Mecnan cs p 376 Fox and McDonald 3rd Ed 1985 Analysie run on 12/01/1999 2 36 35 PM Input F.le C \FATnOM\SAMPLES\SAMP,El FTrl

Jct

1 2 3

Execution Time= 0 11 seconds Total Number Of Head/Pressure Iterations= 0 Total Number Of Temperature Iterations= 0 Total Number Of Flow Iterations= 2 Number Of Pipes= 2 Number Of Junctions= 3 Pressure Tolerance= 001 psia Volumetric Flow Rate Tolerance= 001 gallmin Relaxation= 1 (None)

P Stag Out P Inlet POutlet (psia) (psia) (psia) 146960 146960 146960 45 3256 44 7831 44 7831 14 6960 14 8262 14 1535

Constant Fluid Property Model Fluid Water at 1 atm Temperature 68 deg F Densiw 62 3229 lbmm3

I S ~ l O ~ ~ ( W 5 ) ’-. ;-, ~ I

r 2 - ’-4 . - 9 9 2 8 x . 112 6928. . 0 0 3 0 3 . 2

- 1 f” 499282. . 1502571 00306798 276-05

SNF-5332, Rev 0

Sample #2

6 pipes 7 junctions Model of a pumping system between two reservoirs Problem is to find the required pump horsepower Water is the working fluid

Reference White F FluidMecbanics 1979 p 359

J5 J6 J7

* p6’

P5>

J1 J2 J3

37

SNF-5332, Rev 0

AFT Fathom 3 0 Input (1)

Sample 2 Frank White Fluid Mechanics 1979 pg 359

NUMATEC HANFORD CORPORATION 11/30/1999 02 20 PL

Title Sample 2 Frank White Fluid Mechanics 1979 pg 359

Number Of Pipes= 6 Number Of Junctions= 7

Head/Pressure Convergence= 001 psia Flow Rate Convergence= 001 fl3/sec Relaxation= 1 Maximum Iterations= 500

Constant Fluid Property Model Fluid Unspecified Densitp 1 94 sIugm3 Viscosity= 0006866 lbmls fl Vapor Pressure= Gravitational Acceleration= 1 g Atmospheric Pressure= 1 atm

Units ~

~ EpslC

None

None

- ~ ~----

Angle I (Degrees)

- -

Bend 1

Custom feet. ~ $5 Custom 90

___- Pump

Units Pump

~ - -~

atm

LOSS LOSS

None feet K Constant 6 9 120 - 2 7

i Model

I

~ - - ~ ~~

Valve

2 ~-

38

SNF-5332, Rev 0

AFT Fathom 3 0 Input (2) 11/30/1999 02 20 PN NUMATEC HANFORD CORPORATION

1 1 Reservoir 1 - 1

Depth 1

1

Valve --

No - ~-~ No

SNF-5332, Rev 0

3 4 5 6

AFT Fathom 3 0 Output (1 )

Sample 2 Frank White Fluid Mechanics 1979 pg 359

NUMATEC HANFORD CORPORATION

900582 125241 919714 368258 368258 00000 849586 8230045 7861787 0569791 900582 125241 9 19714 5439333 11 04774 433456 2548759 7853239 24 13907 0569791 900582 I25241 9 19714 368258 368258 OOOOO 849586 23 59777 1991519 0569791 900582 125241 9 19714 368078 368078 OwOD 849170 1837676 1469598 0569791

11/30/1 999

Tnle Sample 2 Frank White Fluid Mechanics 1979 pg 359 Anaiysisrun on 11/30/19991 3052 PM Input File C \FATHOM\SAMPLES\SAMPLEZ FTH

Executm Time- 0 17 seconds Total Number Of HeaUPressure Iterations= 0 Total Number Of Temperature Iterations= 0 Tdal Number Of Flow Iterations= 3 Number Of Pipes= 6 Number Of Junctions= 7 Pressure Tolerance= 001 psia Volumetnc Flow Rate Tolerance= 001 R3/sec Relaxation= 1 (None)

Constant Fluid Property Model Fluid Unspecified Densty= 1 94 slug/R3 Viscosity= COO6866 lbmis R Vapor Pressure- Gravitational Acceleration= 1 g Atmospheric Pressure= 1 atm

Overall Delta Pressure = 79 7559 psi Overall Frictional Pressure Loss = 36 4103 psi Total Inflow= 0 200650 R3/sec Total Outflow= 0 200650 R3/sec Maximum Pressure is 82 3004 psi at Junction 3 Outlet Minimum Pressure is 2 54457 psi at Junction 3 Inlet

________________________________________------- ............................................... pUMpSUMMARY==============..====...========================~====

Jcf Flow DP DH Speed idealhp NPSHA NPSHR (gaVmin) (psid) (feet) (%) (hp) (feet) (feet)

3 90058 79756 18400 10000 41892 N/A N/A ............................................................................................................. .............................................................................................................

Pipe 1 Vol Flow 1 Mass Flow I Velocity I dP Total I dP Fnction I dP Gravity I dH 1 Max Pres I Min Pres 1 Dyn Pres 1 al/min Ibmlsec) 1 lfeetlsec sid sid std feet sia sia sia

'+9&25241 1 9 197)4i :68:581 '! 68)2581 '0 :OOOi I, 49!2 1!8,'29 1 ,b"15:711 ?569)791i 2 1 9005821 1252411 9197141 368258) 368258) OoooO1 8495861 6227161 2544571 05697911

SNF-5332,Re~ 0

Jct

AFT Fathom 3 0 Output (2) 11/30/1991 NUMATEC HANFORD CORPORATION

dP dH Vol Flow Into System Loss Factor (K) EGL Inlet EGL Outlet HGL Inlet HGL Outlet (psid) (feet)

2 1 393155721 90702601 0 000000 I 6 9OOW 1 10 84687 1 1 77661 1 9 53234 1 0 462082 3 I 7975587461 1840000071 0 m o o o I O W O O O / 6719251 177280751 8033781 175966224 4 1 00854686/ 01971801 0 o m 0 1 01500001 168784901 16858771 1 167470371 167273179

(R3kec) (feet) (feet) (feet) (feet)

I 1 5 1 054130141 12488041

1

0 o o m I 0 950000 I 143 1001 3 I 141 851 33 1 141 78560 I 1 q536795 I

- - baa) (psia) (psia) (psis)

1 1 14695981 14695981 14695981 1469598 2 1 10728501 6796951 10158711 622716

~~

6 I 153843551 35492321 0 ooowo 1 27oooOI 133355461 129806231 132040931 128491702 7 1 056979091 13145301 0 200650 1 1 00000l 120000001 12owoM)l 120000001 12oDooooo

Jct I P Stag In 1 P Staa Out I P Inlet 1 P Outlet I

I 3 1 3114371 82870241 2544571 8230045 79 18766 79 10219 7861787 7853239 24 70887 24 16756 24 13907 23 59777 2048498 1894655 1991519 1837676 I 14 69598 14 69598 14 69598 14 69598

41

SNF-5332, Rev 0

Sample #3

3 pipes 4 junctions Model of a three reservoir branching system Water is the working fluid

Reference Lindeburg M R Mechanical Engmeenng Revfew Manual for the P E Exam 7th Ed 1984 p 3-47 timed problem #1

Three reservoirs (A B C) are interconnected with a common junction at elevation 25 ft above some arbitrary reference point The water surface levels for reservoirs A B and C are at elevations of 50 40 and 22 feet respectively The pipe from reservoir A to the junction is 800 feet of 3 pipe The pipe from reservoir B to the junction is 500 feet of 10 pipe The pipe from reservoir C to the junction 1000 feet of 4 pipe Determine the flow velocity and direction in each pipe Assume f = 0 02 and disregard minor losses and velocity heads

J1

42

SNF-5332, Rev 0

Pipe Initial Flow Junctions Geometry Material Thermal Overall U Units (UpSJown) Boundary

1 mtsec 1, 4 Cvlindrical Pipe Unspecified Adiabatic 0 2 fl3lsec 2, 4 Cylindrical Pipe Unspecified Adiabatic 0 3 ~ t s e c 4, 3 Cvlindrcal Pipe Unspecif i Adiabatic 0

~

AFT Fathom 3 0 Input NUMATECHANFORDCORPORATION

Include Special Internal h Condition

No None No None No None

Sample 3 Mechanical Engineering Review Manual for PE exam 7th Ed page 3-47 timed problem 61

~

t 1 not1 999 01 58 PN

Tnle Sample 3 Mechanical Engineering Review Manual for PE exam 7th Ed page 3 47 timed problem 61


HeadIPressure Convergence= 001 psia Flow Rate Convergence= 001 ft3tsec Relaxation= AFT Fathom Automatic Maximum Iterations. 500

Constant Fluid Property Model Fluid Water at 1 atm Temperature 60 deg F Densty= 62 3721 7 Ibrnlft3 Viscosity= 2 72848 lbrnlhr R Vapor Pressure= 25024 psia Gravitational Acceleration= I g Atmospheric Pressure= 0 atm

Defined

Res Connector B Res Connector C feet 3355 feet

toughness Units Explicit Explicit Explicn

43

AFT Fathom 3 0 Output I NUMATEC HANFORD CORPORATION

Pipe

11/30/199

Vol Flow Mass Flow Velocity dPTotal dP Friction dP Gravlty dH MaxPres Mln Pres Dyn Pres (gal/min) (Ibm/sec) (feeWsec) (p ad) (psid) (pad) (feet) (psia) (psia) (pia)

Pipe

I 7402611 1028711 32118151 2152161 434493921 6497101 1003125741 6414121 4261961 006943755 2 I 10072321 1399711 04098111 2152161 001353881 2165701 003125731 6482431 4330271 000113043 3 I 17474931 2428421 44041051 2152161 778298191 5630821 1796874261 6353001 4200841 013055952

dPf/dx Resistance f Reynolds No WD K fUD+ K (PSl/lW R) (SeC2/ffi)

Jct P Stag Out P Inlet P Outlet (pia) (psia) (psia)

- 1 433140 O W a a o 433140 2 433140 OMXXW) 433140 3 433140 O O W O O 433140 4 648356 643539 643539

~

3 I 0778298191 1185366071 002Waao1

I

44

SNF-5332, Rev 0

Sample #3a

3 pipes, 4 junctions Model of a three reservoir branching system Water is the worhng fluid

Reference White, F M , “Fluid Mechanics”, 3rd Ed , 1994, pp 346-347

Three reservoirs (1 2 and 3) are interconnected with a common junction at elevation 34 53m above some arbitrary reference point The water surface levels for reservoirs 1, 2, and 3 are at elevations of 20 100, and 40 meters, respectively The pipe from reservoir 1 to the common junction is 100 meters of 8-cm pipe (E=O 24mm) The pipe from reservoir 2 to the common junction is 150 meters of 6-cm pipe (E=O 12mm) The pipe from reservoir 3 to the common junction 80 meters of 4-cm pipe (E=O 20mm) Determine the flow velocity and direction in each pipe Assume the fluid is water with a density of 1000 kg/m3 and a dynamic viscosity of 1 02E- 6 m2/s Disregard minor losses and velocity heads

JZ

J3

45

sNF-5332,Rev 0

Plpe

1 2 3

AFT Fathom 3 0 Input NUMATECHANFORDCORPORATION I

Name Object Length Length Hydraulic Hydraulic Roughness Roughness Losses (K) lnltial Flow Denned Unns Diameter Diam Units Unns

ResConnectorA Yes 100 meters 8 cm 24 mm 0 1649 ResConnectorB Yes 150 meters 6 cm 12 mm 0 2244 ResConnsctorC Yes 80 meters 4 cm 2 mm 0 3893

1 2 / 0 7 / 1 ~ 0 4 17 PI

I I I 1 I I I

I 16

AFT Fathom 3 0 Output (1 ) 12K)7/1$3 NUMATEC HANFORD CORPORATION

Sample 3a Three-reservorlunction problem Whlte (1994) Example 6 19 page 346347

Jct

Title Sample 3a Thmreservolrjunction problem White (1994) Example 6 19 page 346347 AnalyslsNnOn 12/07/199941720PM Inpu File C FATHOMEAMPLESEAMPLE3A FTH I

PStag Out Plniet Poutlet (psia) (psia) (psia)

1 I 433527521 O W 0 0 0 0 4335275 2 I 433527521 OOoOWOl 4335275 I t 3 I 433527521 O C C W W [ 4335275

SNF-5332, Rev 0

Sample #4

7 pipes 7 junctions Model of an orificed circulation system connected in a single loop and driven by a pump Water IS the working fluid

Reference Circulation Loop (No reference)

Given the system as shown determine the mass and volumetric flow rate in the system the pressure added by the pump and the total pressure at each junction

J1 52 J3 P I > PZ>

P7" P3v

J6 J5 I

<P6

48


I Boundan I 1 I Cylindrical Pipe 1 Sled I 3 inch I schedula 40 I Adiaballcl 0

Sample 4 Circulallon Loop (No reference)

Internal h I Condition No/ None

11/3011999 02 04 PM

Tnle Sample 4 Circulation Loop (No reference)


HeaWressure Convergence= 00001 (Relative change) Flow Rate Convergence= 00001 (Relative change) Relaxallon= 1 Maximum Iterations= 500

Constant Flud Property Model Fluid Unspecfied Dens+ 62 06239 lbmm3 Viscositp 1 72622 lbmhr fl Vapor pressure= 82151 psia Gravbtional Acceleration= 1 g Atmospheric Pressure= 1 alm

1 Pipe I Geomeln 1 Material 1 Size 1 Twe I Thermal I OverallU 1 Include I Swcial 1

A unns I

I ACME Pump 1 0 3 5 A I Yes 1 None I 01 feet I 1 I , I I I

AFT Fathom 3 0 Input (2) 11/30/19990204PM NUMATEC HANFORD CORPORATION

I I Orifice 1 Restricted Restncted !

I I Area I Area Units I

2

50

SNF-5335Rev 0

Pipe

AFT Fathom 3 0 Output (1 )

Sample 4 Circulation Loop (No reference)

NUMATECHANFORDCORPORATION

dPf/dx Resistance f ReynoldsNo N D K fL /D+K (ps i / lOO S (secZR5)

11/30/1999

1 2 3 4

164276 8921048 00193406 188422E+05 1512958 0 1512958 164276 8921048 00193406 1@8422E+05 1512958 0 1512958. 1 64276 6 69079 0 0193406 1 88422E+05 1 13472 0 1 13472 1 64274 4460455 00193406 1 8&122E+05 756479 0 756479

. , "

5 1 1 64276 I 44 60524 1 0 0193406 1 1 884ZE+05 1 7 56479 1 0 1 7 56479 6 1 1642761 8921048 001934061 1684ZE+051 15129581 01 1512958 7 1 1642761 6690791 001934061 188422E+05 1134721 01 I13472

Jct 1 dP I dH 1 Vol Flow Into Svstem 1 Loss Factor [K) I EGL Inlet I EGL Outlet 1 HGL Inlet I HGL Outlet I P Stan In I

3 I 01168321 02710781 01 05380001 2031231 2028521 2026191 2023481 9577481 4 1 02336631 05421561 01 1 07600 1 202 260 1 201 738 1 201 776 I 201 234 I 101 8764 I

SNF-5332,ReV 0

JCt

AFT Fathom 3 0 Output NUMATEC hANFORD CORPORATION

dP dH Vol Flow Into System Loss Factor (K) EGL Inlet EGL Outlet HGL Inlet HGL Outlet P Stag In

11/30/19SS

@id) (feet) (gallmin) (feet) (feet) (feet) (feet) (psia) OOMNMO 0

6 I 16042153 37221753 0 0

1 1 10416WI 1040686/ 1039518 2 1 990603/ 10066631 988432 3 1 S 6 W J 955577 954408

0 0000001 1941151 2313361 1936111 2308331 983572 05380001 2237131 2234421 ZBZO~I 2229381 1111139

~~

[ 4 l 101 64271 101 6592) 101 42561

Jct P Stag Out P Inlet P Outlet @la) Lpsia) (pia)

SNF-5332, Rev 0

Sample #5

10 pipes 10junctions Model of a system with three pumps supplied by three reservoirs that connect together One loop exists Water is the working fluid

Reference Jeppson R W Analysrs of Flow m Prpe Networks 1976 p 84

Consider the ten-pipe one loop network supplied by three identical pumps as shown below Each pump supply head according to the equation hp = 10 328Q2 + 2 823Q + 22 289 There IS an outflow of 2 0 cfs leaving the system at junction 2 Assume all pipes have e = 0 012 inch Find the flow and head loss in each pipe the pump head added for each pump and the pressure at each junction

JlO

P P P7A . J9

53

SNF-S33%ROv 0

AFT Fathom 3 0 Input (1) 11/30/19990215PM NUMATEC HANFORD CORPORATION

Sample 5 Roland Jeppson Analysis of Flow In Pipe Networks 1976 p 84

Title Sample 5 Roland Jeppson Analysis of Flow in Pipe Network8 1976 p 84


HeadPressun Convergence= 0001 (Relative change) Flow Rate Convergence= 0001 (Relative change) Relaxation= AFT Fathom Automatic Maximum Iterations= 1000

Constant Fluid Properly Model Fluid Unspecified Dansdy- 62 4 Ibm/ft3 Viscosity= 5 65E 09 Ibf h r m Vapor Pressure= 3 psia Gravitational Acceleration= 1 g Atmosphenc Pressure= 1 atm

Pipe

9 I PlWl Yes1 5001 feet inches I 012 I inches 1 0 1 760992752885893 10 I Pipe/ Yes1 5001 feet/ 61 inches I 012 I inches 1 01 397898251379419

Initial Flow Junctions Geometry Material Thermal Overall U Include Spectal Unlts (Up.Down) Boundary Internal h Condition

3 4

Pump

5

1 - . f l 3 / s e c i 5 ~ d r i c a l Pipe ' UnsDaciW ! Adiabatic., 0 No_--None. 2 -. R3/sec. 1 . 2 . C-1 Pipe.. UntpecMed.. Adiabatic Ti. No. _ . None

~~

Branch Yes None 100 feet 112 084714204485 feet $4.5 Branch Yes None 100 fwt 113 586290626129 feet 4 6 7

Name object Special €levalion Elan(nn Inltlal HGWressun lnltial HGUPressure Connected Pipes Defined Condition Units Units (+=in. =out).

Pump Yes None 100 feet 98 4376689086968 feet & l

~- - .- Rflec! . 7 . 4 ! Cylindrical Pipe, UnrpeclfbdI Adiabatb . -' None

;V: e-.. fl3/sec-. 8.5 Cyll_nddcal Pipe UnrpecMed . Adlabatlc None . - 9 f13/s.ec_ I L l ~ i n d n q l ~ ~ n r p e w f i s d 0 , None

10.- R3/rec. B.CCylindricalPlpe Uns@fied Adiabatic 0 . ..* None]

Branch 1 Name I Object i Special I Elevation i Elevation 1 Initial HGLPressun 1 lnltial HGSressure 1 Connededpes 1 I 1 Defined) Condltionl I Units I I units 1 (+ = i n c o u t )

1 1 Branch1 Yes1 None1 100 I fwtl 1142316275479821 feet I 1. 2 4 2 1 Branch1 Yes1 None1 100 I feet I OB 7006888750291 I feet I 2.3

6 I Pump 1 Yea I None 1 1001 feet I 99 3141452735089 1 feet I 9.5 7 Pump I YES I None I 1001 feet I 93 3954509453878 1 feet I 10, 7

I I 1

w

sNp5uzRov 0

AFT Fathom 3 0 Input (2) 111301199902 15 PM NUMATEC HANFORD CORPORATION

ReSeNOir

8 9 10

Branch

1 2 3

Name Object Special Elevation Elevation Initial HGUPressure lntital HGLlPressure Connected Pipes Defined Condition Units - ~ -_- ___ Units (+=in, =out)

Reservoir Yes NIA 100 feet ~- 100 feet -8 Reservoir Yes N/A 95 feet _ _ - 95 feet 10 ReseNolr Yes NIA 105 feet ~~~ 105 feet 9

- Boundaty Flow Boundaty Flow (+ = In1 =out) Units

0 flwsec 2 fl31sec 0 fl3lsec

- -. -

Pump

5 6 7

Independent Ind Variable Dependent Dep Variable LOSS LOSS LOSS LOSS

Variable Units Variable Units G e n t a Constant b Constant c Constant d Vol Flow fl31sec Head feet -22-289 2 823 10 328 0 Vol Flow flwsec Head feet 22289 2 823 10 328 0 Vol Flow fl31sec Head feet 22289 2 823 10 328 0

Branch 1 I I I

R088NOlr

8 9 10

Surfaca Surface Depth Depth Density Density Temperature Temperature Pressure Pressure Units Units Units Units

1 atm 0 feet 1 a h 0 feet 1 atm 0 feet

SNF43S&Rav 0


Sample 5 Roland Jeppson Analysis of Flow in Pipe Networks 1976 p 64

Tdle Sample 5 Roland Jeppson Analysis of Flow in Pipe Networks 1976 p 84 4nalysis run on 12/01/1999 3 12 31 PM Input File C FATHOMSAMPLESSAMPLE5 FTH

Execution The= 0 17 seconds Total Number Of HeadPressure Iterations= 2 Total Number Of Temperature Iterations= 0 Total Number 01 Flow Iterations= 2 Number Of Plpaa= 10 Number Of Junctions= 10 Head Toleran-= 0001 relative change Wolumetric Flow Rate ToIeranm= 0001 relative change Relaxation= 2

Constant Fluid Property Model Fluid Unspeclfled Densii-p 62 4 1bmm3 V l s c o s ~ 5 65E-09 Ibf hrKU Vapor Pressure= 3 psia Gravltltlonal Acceleration.; 1 g Atmospheric Pressure= 1 atm

~ o t a i Inflow 2 00007 n3sm

Maximum Pressure Is 22 2954 psia at Junction 6 Outlet Minimum Pressure is 11 6064 psia at Junction 7 Inlet

rota1 o u m w 2 00007 n m c

===_ ___________ ____--__ ----=..==pUMpSUMMARY==============================================

Jct Flow DP DH Speed idealhp NPSHA NPSHR

5 084114 75211 17356 10000 16561 31659 N/A 6 076099 79977 16456 10000 15932 32536 N/A 7 039769 94368 21 777 10000 098292 26617 N/A __ ____________________------------__ ___-__-_II=Elll.ll===IEIII=====.lllllll.===

(n3kec) (psid) (feet) (%) (hp) (feet) (feet)

1 Pipe 1 dFi/dx I Resistance \ f

SNF-5332.R~ 0

Jd

AFT Fathom 3 0 Output NUMATEC HANFORD CORPORATION

PStag Out Plnlet Poutlet (psia) (psia) Ipsla)

12Mlll999

1 Jd I dP I dH I Vol Flow Into System I Loss Factor (K) I EGL Inlet I EGL Outlet I HGL Inlet I HGL Outlst I P Stag In I

4 5 1 2154001 1397991 2150091

9 1 1469601 146960/ 146960 10 I 1469601 1469601 146960

>q F-5332, Rev 0

Sample #6

9 pipes 8 junctions Model of a branching system with a pump a PRV and two loops Water is the working fluid

Reference Jeppson R W Analysis ofNow in Pipe Networks 1976 p 86

Consider the nine-pipe network shown below A pressure reducing valve exists 500 feet downstream of junction 1 The pump characteristics are the following 0 1 = 1 0 cfs @ Hpl = 50 ft Q2 = 1 5 cfs @ Hp2 = 55 ft Q3 = 2 0 cfs @ Hp3 = 48 ft There are outflows of 1 0 cfs leaving the system at both junction 2 and 4 Assume all pipes have e = 0 02 inch Find the flow and head loss in each pipe the pump head added for each pump and the pressure at each junction

JB rn P4V

JZ A

J7

P9w

58

sm;-s332#thr Z 0


11/30/1999 02 23 PM (1)

Sample 6 Roland Jeppson Analysis of Flow in Pipe Networks 1976 p 86

Title Sample 6 Roland Jeppson Analysis of Flow In Pipe Nelwoilu 1976 p 88

Number O+ Pipes= 9 Number Of Junctions= 8

Headffresrure Convergence= 0001 (Relative change) Flow Rate Convergence= 0001 (Relative change) Relaxation- AFT Fathom Automatic Maximum Iterations- 1000

Constant Flud Properly Model Fluid UnspecMed Density- 62 4 l b M 3 Vircoslp 0006558 Ibm/s fl Vapor Pressure= 3 psla Gravltallonal Acceleration= 1 g Atmospheric Pressure= 1 atm

I Pioe I Name 1 Obiect I Lenath 1 Lenath 1 Hvdraullc I Hvdraulic 1 Roughness 1 Roughness 1 LOSSeS (K) 1 J u n c t a

inches 1 02 1 inches I 01 1.21

SNF-5332,R.v 0

Reservoir Name Objed Special Elevation Elevation Initial HGLlPressure Defined Condition Unib

7 Reservoir Yes N/A 90 feet 90 8 RBSBNDL~ Yes MA 100 feet 100


- Initial HGUPresrure Connected Pipes

Units (+=in, -out) feet 9 feet -4

11/30/1999 02 23 PM

Branch Boundary Flow Boundary Flow (+ = in/ =out) Units

I I I I I I I

Branch 1 I I 1 2 I I 1


Sample 6 Roland Jeppson Anaiyds of Flow In Pipe Networks 1976 p 86 I 11/30/199~

Tltb Sample 6 Roland Jeppson Analysis of Flow in Pipe Network$ 1976 p 86 Analyris run on 11i3011999 2 26 14 PM Input Fib C FATHOMEAMPLESSAMPLE6 FTH

ExecuUon Time= 0 83 seconds Total Number Of HeadPressure iterations= 117 Total Number of Temperatun Iterations. 0 Total Number Of Flow Iterations= 70 Number Of Pipes= 9 Number Of Junctions= 8 Head Toleranm= 0001 relattve chanm Volumetric FIOW Rate Tolerance= 0061 reiattve change Relaxation= 2

sn-u3;r,m# 0


0000 ~ 000000 -448 831 0 00000

0 000 000000 -448831 ~ 000000

I PIW I Dvn pres I dWIdx I Resistance 1 f I RevnoldsNo I RID 1 K I W D i K 1

(feel) (feet) (feet) (feel) (psia) 1172496 11724960 1171338 11713377 4383747 95 7999 95 79993 95 7998 95 79993 34 54261 958062 9580624 957012 9570120 3454535 549770 724960 549764 724960 2985268

(psla) 1 (DsUIOOR) 1 ( seczm5) - 1 6 1 00002784580/ 00019924271 14421091 003577611 967430Ei031 3577611 01 357761

Jct

1 2 3

I 7 _00015118860 009292120_, 3,210,74679410 00512172, 375706Ei03, 6146@15.,,, 0,,,6146C61.5,

8 [ 0 0002784580 0 001992476 . 14 42144! 0 0357763. 967330Ei03 35 7761, 0. 35 7761, 9 0 1841841935' 1010723877 _. - . 11 06001 , 0 0274379. 2P_8809E+05 1 27 4379, 0 . 27 4379

PStag Out P Inlet P Outlet (psia) (psla) (psia) 4383747 4378728 4378728 3454261 3454257 3454261 3454535 3449983 3449983

I J d 1 dP 1 dH 1 Vol Flow Into System 1 Loss Factor (K) I EGL Inlet 1 EGL Outlet I HGL Inlet j HGL Outlet 1 P Stag In I

[ 5 1 21 91531 50 5737 I 00001 ~ 0000001 7833781 12891147/ 7791281 128486431 9642351 6 1 2696491 6222661 0 000 1 96.83641 1172266 5500000I 1172260/ 54999361 4166084 7 I 000001 0000ol 460 888 1 0000001 9OOOOOI 900000OI 90000OI 9000OOOI 1469598 8 1 oowo/ 000001 435 774 I 0000001 1000000~ 10000000~ 1000000~ 10000000/ 1469598

2 88782 29 85241 2 88782 31 55762 945818 31 37343 1469598 4166056 1469570 1469598 1469598 1469598

1 8 1 14695981 14695981 14695981

SNF-5332, Rev 0

Sample #7

17 pipes 12 junctions Model of a branching system fed by two reservoirs One reservoir has a pump Numerous loops are involved Water is the working fluid

Reference Jeppson R W Analysis ofFlow in Rpe Networks 1976 p 135

Solve for the flow rate in each pipe and the head at each junction of the network shown below The pump characteristic curve is given by hp = -2 505Q2 + 16 707Q + 155 29 (hp is in feet and Qp in cfs) There are outflows of 0 5 cfs leaving the system at junctions 2 3 and 7 There are additional outflows of 2 0 1 0 and 2 0 cfs at junctions 2 3 and 4 respectively Finally there is an inflow of 1 5 cfs entering the system at junction 4 Assume all pipes Hazen Williams factor of 130

5

63

~~ ~~

AFT Fathom 3 0 Input (1) 11/30/1999 02 39 PM NUMATEC HANFORD CORPORATION

Sample 7 Roland Jeppson Analyrls of Flow in Pipe Networks 1976 p 135

Tale Sample 7 Roland Jeppson Analysts of Flow in Pipe Nehwrks 1978 p 135

Number Of Pipes.; 17 Number Of Jundions= 12

HeadlPressure Convergence= 0001 (Relallve change) Flow Rate Convergence= 0001 (Relattve change) Relnxollon- AFT Fathom Automatic Maximum Iterations= 500

Constant Fluid Propem Model Fluid UnspecMed Dens+ 62 29329 lbmm3 Viscositr 2 47554 lbmhr R Vapor Prassure= Gravitational Acceleration= 1 g Atmospheric Pressure= 1 atm


8 I I I 9

I I I

sNF-nn,%k 0


11/30/1999 02 39 PM

66

AFT Fathom 3 0 Oulpul NUMATEC HANFORD CORPORATION

SamDle 7 Roland JeDDson Anabis of Flow in Pipe Networks 1976 p 135

11/30/1999

T I e Sample 7 Roland Jeppson Analysis of Flow in Pipe Networks 1976 p 135 Analysis run on 11/30/1999 2 35 30 PM Input File C FATHOMSAMPLESEAMPLE7 FTH

Exewtlon Time= 0 99 seconds Total Number Of HeadiPressure Iterations= 129 Total Number Of Temperature iterations= 0 Total Number Of Flow Iterations= 58 Number Of Pipes= 17 Number Of Junctions- 12 Head Tolerance= 0001 reiatwe change Volumetric Flow Rats Tolerance= 0001 relative change Relaxation= 2

Constant Fluid Propedy Model Fluid Unspeclfied DensHy= 62 29329 I b M 3 V!~mity- 2 47554 lbmlhr fl Vapor Pressure- Gravlationai Acceleration= 1 g Atmospheric Pressure- 1 atm

Tolsl Inflows 6 50000 fl3eec Tots1 O U M w 6 50000 fl3sac Maximum Pressure is 86 2804 psia at Junction 12 Outlet Minimum Pressure is 11 9742 psia at Junction 12 Inlet

J d Flow DP DH Speed idealhp NPSHA NPSHR

I P im 1 Vol Flow 1 MaruFlow 1 Velocitv I dPTotal I dPFriction I dPGravlty I dH

67

sNF-sa* 0 AFT Fathom 3 0 Output (2) 11/30/1999 NUMATEC HANFORD CORPORATION

I Plpe I DYn Pres I dPf/dx 1 Resistance 1 f

SNF-5332, Rev 0

Sample #8

48 pipes 32 junctions Model of a large branching network Water is the working fluid

Reference Jeppson R W Analysrs of Flow in Prpe Networks 1976 p 138

Solve for the flow rate in each pipe and the head at each junction of the network shown below Note that there are outflows at each junction as described in the problem except at junction 15 which has an inflow of 20 428 cfs Assume all pipes have e = 0 012 inch

69

SNF-5332,Rav 0


Sample 8 Roland Jeppson Anabls of Flow in Pipe Networks 1976 p 138

Title Sample 8 Roland Jeppson Analysis of Flow in Plpe Networks 1976 p 138

Number Of Pipes- 48 Number Of Junctions= 32

Head/Pmssura Convergences 0001 feet Flow Rate Convergence= 0001 fl3Isec Relaxations AFT Fathom Automatic Maximum Iterations= 5000

Constant Flu@ Property Model FluM Unspecified Densip 62 4 I b m 3 Viscosily- 0006558 Ibm/s fl Vapor Pressure= Gravitational Acceleration= 1 g Atmospheric Pressure= 1 atm

29 I Plpel Yes1 20001 feel 181 012 1 inches I 01 24827761 fl3lrec Inch& ~ 012 I inches I 01 B 9 2 l fl3/sec 30 1 Pipe/ yes1 ~ O O O I feet1 181 ~

w

SNF-5332 Rev 0


~

11/30/19990243PN

~~ ~

1 Pipe 1 Name I Obied 1 Length 1 Length I Hvdraulic I Hvdraulic t Roughness t Roughness 1 Lasses IK) I initial Floq InaTFlow 1 ~-

19 I 23, 31 1 Cyllndrical Pipe I Unspecifiedl Adiabatic 1 20 I 31,25 1 Cylindncal Pipe 1 Unspecified j Adiabatic

71

AFT Fathom 3 0 Input NUMATEC W F O R D CORPORATION

~

32 Branch -Yes ~ None 100 feet ~ 1874156 feet 22 , 23

ReseNoir Name Object Special Elevation Elevation Initial HGWressure Initial HGVPressure Connected Pipes Defined Condition Units Units (+=in, = out1

1 ReseNOlr Yes N/A 100 leet 100 feet 4 3 . 4 -

~

___

~~

_______________ Branch Boundaly Flow Boundaly Flow

2 3 fl3lsec 3 2 fl3/sec 4 2 fl3/sec 5 3 fl3kec

(+ = in/ =out) Units ~

(3) 11/30/1999 02 43 PM

I - 4 8 - 13, a C y l i n m c a l P b . Unspcif ed . Adlabats. 0. - N o L None,

r4&.! -14. ld Cylina!cal P ! e . Unrpecifed pdlaba!& . 0. - No - Non9 47 - K 2 0 m n d M P i p e , Unspecified. Adxbatic . - . 0- -No. -hone.

____ 1 Branch 1 Neme 1 Object 1 S&cra/rEleva(lon/ Elevation I Initial HGUPressure I Initial HGUPressure 1 Connected Plpeq I I Units + = i n =out 1 Defined 1 Condition 1 units 1

2 1 Branch Yes/ None] 1001 feet I 3 1 Branch) Yes1 None1 100 I feet 1 82 28107 1 -42 -43 45

74538261 ~ -1 35 36 -45

Branch1 Yes1 None1 19 36394 1 feet I 7, 8. I O . 13 27 I Branch Yes1 None/ 35 49176 I feet I 8.9, 12

~ ~

28 I Branch/ Yes] None $ 21 16367521 ~ feet I 10. 11, 15 29 1 Branch Yes1 None 33 21765 1 feet I 11.12

feet 1 16.17 feet I 19,20

30 I Branch1 Yes] None/ 31 1 Branch Yes1 ~ None1 _____

SNP-5332,RCv 0

Re sew o i r

1

AFT Fathom 3 0 Input (4) 11i30/1999 02 43 PM NUMATEC HANFORD CORPORATION

SUIface Surlace Deplh Depth Balance Pressure Pressure Units4 Units Energy

1 a h - 0 feet No I 1 I I I 1

n

SNF-5332, Rev 0

AFT Fathom 3 0 Output NUMATEC "FORD CORPORATION

(1) 12/02/1999

Sample 8 Roland Jeppson Analysls of Flow in Pipe Networks 1976 p 138

Tab Sample 8 Roland Jappson Analysis of Flow in Pipe Networks 1976 p 138 Analytls run on 12102/1989 10 57 30 AM Input File C FATHOMSAMPLESSAMPLE8 FTH

Execution Time= 0 44 seconds (Iteration History vas ON)

Tote1 Number Of Hesd/Pre6sure Iterations= 3 Total Number Of Temperatun iterations= 0 Total Number Of Flow Iterations= 2 Number Of Pipes- 48 Number Of Junctions= 32 Held Tolerance= 0001 feet Volumetnc Flow Rate Tolerance= 0001 Wsec Relaxation= 1 (None)

Constant Fluid Pmpriy Model Fluld UnspscMed DsnrMp 62 4 lbrnm3 Wsmntllp 0006558 lbmls fl Vapor Pressure- Gravitatlonal Acceleration= 1 g Abnospherlc Pressure= 1 aim

rota1 Innowl76 74 n m c TOMI ournow= 76 74 n3.w Maxlmum Pressure is 14 70 psia at Junction 1 Outlet Minimum Pressure In 23 27 psia at Junction 30 Outlet

74

SNF-5332, Rev 0 ~ ~ ~~~~~


~~

12/02/1999

n

SNF-5332 Rev 0

I 48 I 00567471 0027581 0017521 5903E+05/ 175171 01 175171

I I Jct I dP 1 dH I Vol Flow Into Svstem 1 Loss Factor (K) I EGL Inlet 1 EGL OutleI I HGL Inlet 1 HGL Oullet I P Stag In t


. . - I (Dsld) I (feet) I (paUmin) I (feet) I I feet) I I feet) 1 ( feet) I (p sia) I i 1 I 01 01 25,274 6 1 00001 10000/ 100001 10000/ 100001 146960

(3)

Jet

12/02/1995

PStap Out P InleI POutleI

36 0001333 011436 002298 5130E+04 22979 0 22979 37 0172373 009176 001844 6513E+05 18439 0 18439. 38 0M)llW 002053 001739 7087E+05 13041 0 13041

(osia) (psis) (psia) 1 1 146960) 14895961 1469598 2 1 366261 3553631 355363 3 1 701781 670910~ 670910

4FT Fathom 3 0 Output (4) 12/02/1999 UUMATEC HANFORD CORPORATION

n

SNF-5332, Rev 0

Sample #9

3 pipes 4 junctions Model of a simple series flow pressure drop Water is the working fluid

Reference White F FlwdMechanics 1979 p 362

J3 J4 J1 52

SNF-5332,Re~ 0

Assigned Pressure

AFT Fathom 3 0 Input (1) NUMATEC HANFORD CORPORATION

Sample 9 Fluid Mechanics Frank White 1979 p 362

Name Object Special Elevation Elevation Initial HGWressure Initial HGI&&re Defined Condition Uniis Unlts

11/30/1999 02 49 Ph

Branch

2 3

Title Sample 9 Fluld Mechanics Frank White 1979 p 362


HeWressure Convergence= 001 meters Flow Rate Convergence= 0001 m3sec RelaxaUon= AFT Fathom Automatic Maximum iterations- 500

Constant Fluid Propew Model Fluid Unspecified Density= 1000 kghn3 ViSWSlW 00102 kghec-rn Vapor Pressure= Gravitational Acceleration= 1 g Atmospherlc Pressure= 1 atm

_ _ -

Name Objed Special Elevation Elevation Initial HGWressure lnilial HGWressure Defined Co>dfion.- Unlts Units

Branch Yes None ~ 5 meters Branch Yes None 5 meters

Pipe Name Object Length Length Defined Units

PI e Yes 150 meters Pi e Yes 80 meters

Hydraulic Diarn Units

VI VI VI

Unils

005

1 I Asslgned Pressure I Yes 1 N/A 1 51 meterr1 200000 1 Pascals 4 1 h m n e d Pressure 1 Yes 1 - N/AI ~ 0 1 meters1 50000 1 Pascals

79

SNF-5332, Rev 0

AFT Fathom 3 0 Output (1) 11/30/199I NUMATEC HANFORD CORPORATION

Sample 9 Fiuld Mechanics Frank White 1979 p 362 - Till9 Sample 9 Fluid Mechanics Frank White 1979 p 382 Analysis run on 11/30/1999 2 48 12 PM input File C FATHOMSAMPLESSAMPLE9 FTH

1 2 . 3

1 Pipe 1 dPfldx 1 Resistance 1 f I ReynoidrNo 1 I1/D 1 K I m + K 1 (psJ100 fl) (secZm5)

0254956 191 594 00288728 443395E104 360908 0 360908 0970572 1094046 00260829 591193E+04 852072 0 652072 8859934 5326437 00313882 886790E+04 627764 0 627764

I 1 J d I P Stao Out 1 P inlet 1 POutiet 1 1 ~ 1 ( p i a l 1 (psia) 1 (psis) 1 29 007% 28 98436 28 96436 28 17107 28 14789 28 09782 23 38463 23 32138 23 02380 725188 688108 688106

SNF-5332, Rev 0

Sample # I O

3 pipes 2 junctions Model of a simple parallel flow pressure drop Water is the working fluid

Reference White F FluidA4echanic.s 1979 p 363

81

SNF-5332,Rev 0

Assigned Name Objed Spadal Elevation Elevation Initial HGWressure PIeaSUre Defined conditm Units

1 Assianed Pressure Yes N/A o meters 249000~ 2 AssignedPressure Yes N/A 0 meters 50000


(1) 1 li30/1999 02 54 PM

lnlttal HGLlPressure Units

Pascals Pascals

Sample 10 Fluid Mechanics Frank Whde 1979 p 363

Title Sample 10 Fluid Mechanics Frank White 1979 p 363


HendPressure Convergence= 001 meters Flow Rate Convergence= 001 m3hr Relaxntion- AFT Fathom Automatic Maximum Iterations= 5M)

Constant Fluid Property Model

Densip 1000 kg/m3 Vimstly= 00102 kg/serm Vapor Pressure= Gravilational Acceleration= 1 g ALmosphenc Pressure= 1 atm

Fluld UMpeclfmd

Assigned Pressure

1 2

Connected Pipes Pressure Pressure Balance f+=in, -out) Units Enernv

1, 2, 3 249000 Pascals No 1.23 50000 Pascals No

SNF-5332, Rev 0

I (psld) 1 fleet) 1 (gaWmin)


1 (feet) 1 ( feet) 1 ( feet) I ( feet) I IP sia)

11/30/1999

sia) 1 (p sia) -


(psis)

Title Sainpte 10 Fluld Mechanlca Frank White 1979 p 363 Analyak run on 11/30/1999 2 53 21 PM Input File C \FATHOMEAMPLESSAMPLEI0 FTH

ExewIion Time= 0 11 seconds (Iteratron History was ON)

Total Number Of HesdPrersure Iterations= 0 ToIal Number Of Temperature Iterations= 0 Total Number Of Flow Iterations= 4 Number OfPipes= 3 Number Of Jundions. 2 Head Tolerance- 001 meters Volumetnc Flow Rate Tolerance= 001 myhr Relaxation= 1 (None)

Constant Fluld Properly Model Fluid Unspecified DenayL 1 WO kg/m3 Viawsitp 00102 kg/sec-m Vapor Prerauw Gravitatlonal Amleratlon= 1 g Ahorphenc herrum- I aIm

Total Inflow 99 8796 myhr Total OUmow= 99 8796 m3/hr Maxhum Pressure ia 35 5288 psia at Junction 1 Inlet Mlnlmum Pressure is 6 66830 psia at Junction 2 Inlet

1 Pipe 1 Vol Flow 1 Mass Flow 1 Velocity 1 dP Total 1 dP Friction 1 dP Gravity 1 dH 1 Max Pres 1 Min Pres I Dyn Pres I I (m3/hr) I (Ibmlsec) 1 (feevsec) 1 (poid) i (p sid) 1 ( fee9 I (p sia) 1 (p sia) 1 (p ria)

1 1 6255781 38310101 1 01 6657591 3524771 6385181 0866702 2 I 2591191 15868321 01 6657591 3564441 6781931 0469959

1 3 1 1140991 6987391 8274761 2886251 2886251 01 6657591 3565311 6790581 04613101

1 Pipe 1 dPlldx 1 Resistance 1 f 1 ReynoldsNo 1 f l lD 1 K 1 fLiD+K 1 I a I w i o o n ) I (se~2lff5) I 1 ~ 1 1 I 1 JCI 1 dP I dH I v01 FIOW Into System I LOSS Factor (K) r EGL Inlet 1 EGL Outlet I HGL Inlet I HGL outlet I P Stag In I

879729 178787 00266412 271143E+05 333015 0 333015 588486 1030419 00245660 149746E+05 614150 0 614150

1099661 5314301 00312832 989078E+04 625664 0 625664

~~

1 2 I 01 01 -439 757 I 000000~ 171710~ 171710] 1852171 1852171 7251881

J d 1 PStao Out 1 P Inlet 1 Poutlet 1

SNF-5332, Rev 0

Sample #I 1

2 pipes 3 junctions Model of a simple series flow pressure drop with component losses included Water is the working fluid

Reference Marks Standard Handbook for Mechanical Engineers 8th ed 1978 T Baumeister editor p 3 58

Water at 680F leaves an open tank whose surface elevation is 180 ft and enters a 2-in schedule 40 steel pipe via a sharp edged entrance After 50 ft of straight 2 in pipe that contains a 2-111 globe valve the line enlarges suddenly to an 8 in schedule 40 steel pipe which consists of 100 ft of straight 80 in pipe two standard 900 elbows and one 8 in angle valve The 8 in line discharges below the surface of another open tank whose surface elevation is 100 fl Determine the volumetric flow rate

J1 52

84

SNF4332,RN 0

P i p Name Object Length Length Hydraulic Hydraulic Denned Units Diameter Diam Units

1 PIP0 Yes 50 feet 2067 inches 2 PIP+ Yes 100 feet I981 inches

~. , Pips Geometry Material Sire Type Thermal Boundary

2 c v lindrical Plpe Steel 8 inch schedule 40 Adla&& 1 Cviindrlcal PIDO Steel 2 inch schedule 40 Adiabatic


Roughness Roughness Losses (K) Junctions ~ units (Up.Down) ~ 00015 feet 9 04 1.2

00015 feet 4 016 2,3 ~

Overall U Include SP%Cial Internal h Condition

0 No None 0 No None

-

Samole 1 1 Marks Standard Handbook for Mechanical Engineers 8th ed 1978 p 3 58

lnltial HGLlPressure lnltial HGUPressure Units Units

ReseNolr Initlal HGUPressure Initial HGLiPressure

11/30/1999 02 58 PM

Connected Pipes (+ = in, =out)

1, 2

Connected Pipes Units 1 Units 1 (+ = in. =out) 1 1 Defied Condltionl - _.

3 I RsseNoir 1 Yes 1 N/A 1 100 I feet 1 100 I feet1 - ~~

(1) 12/01/1999 AFT Fathom 3 0 Output NUMATEC HANFORD CORPORATION

Sample 11 Marks Standard Handbook for Mechanical Engineers 8th ed 1978 p 3 58

Title SBmPle 11 Marks Standard Handbook for Mechanical Engineen 8th ed 1978 p 3 58 Analysis run on 12/01/1999 2 26 00 PM Input FIIe C \FATHOM\SAMPLES\SAMPLEI 1 FTH

Execution Time- 0 11 seconds Total Number Of Headpressure Iterations= 0 Total Number OfTernperatura Iterations= 0 Total Number Of Flow Iterations- 3 Number Of Pipes- 2 Number Of Junctions- 3 Head Tolerance= 001 feet Volumetnc Flow Rate Tolerance- 001 fl3/sec Relaxatlon- 1 (None)

Constant Fluid Property Model Fluld Unspecihd DanrHp 62 4 l b M 3 vllau&= 2 092E-05 Ibf r/Rz Vapor Pressure. Gravltatlonal Acceleration- 1 g Umoapherlc Pressure- 1 atm

Xerall Dens Head = 80 0000 feet rotai Inflows o 414394 flwsec rotai OMMF o 414394 RWSEC dulmum Pressure 1s 58 0293 psia at Junction 1 Outlet dlnlmum Pmssure Is 20 1704 psia at Junction 2 Inlet

Pipe

1 2

Pipe

1 2

VOl Flow MBM Flow V9lOCiiy dPTotal dP Friction dP Gravlty dH Max Pres Min Pres Dyn Pres sid) @id) (psid) (feet) Ipsia) (psia) (psia) (fl3lsec) (Ibmlsec) (feetlaec) (P

0414384 258582 1778298 750054 31 6720295 433333 73089303 548349 201704 2 12959146 0 414394 25 8582 1 19281 77 9325 0 0675128 78 0000 0 155799 58 0293 19 9032 0 00958140

dWdx Resistance f ReynoldsNo fLD K W O + K

63 3440590 425 825779 0 0200924 2 83976E+05 5 83235 9 04000 14 87235 00675128 0907273 00201711 735470E+04 303287 401600 704887

(PSVIOO n) i ~ ~ m 5 )

JCt

1 2 3

JCt

1 2 3

dP dH VOl Flow Into SWtem Loss Factor (K) EGL Inlet EGL Outlet HGL Inlet HGL Outlet (psw (feet) (gal/min) (feet) (feet) (feet) (feet)

106479573 24572211 185 993 0 500000 180 000 180 000 180 OW0 180 000 185274470 42755649 0 000 0870000 104453 100178 995390 100156 000958140 00221109 185 993 100000 100000 100000 1000000 100000

PStag In PStag Out P Inlet Poutlet (psla) (psia) @sip) (psia) 146960 580293 146960 580293 180408 198936 201704 199032 148980 580293 146960 580293

SNF-5332, Rev 0

Sample #I 2

2 pipes 2 junctions Model of a simple series flow pressure drop with benzene as the working fluid

Reference Marks Standard Handbook for Mechamcal Engmeers 8th ed 1978 T Baumelster edltor p 3 58

Benzene at 680F flows at a rate of 0 5 ft3/s through two parallel straight horizontal pipes connecting two pressurized tanks The pipes are both schedule 40 steel one being 1 in the other 2 in They both are 100 ft long and have connections that project inwardly in the supply tank I f the pressure in the supply tank IS maintained are 100 Ibf/in2 what pressure should be maintained on the receiving tank?

a7

SNF-5332,Rev 0

(1) 11/30/199903 51 Pk AFT Fathom 3 0 Input NUMATEC HANFORD CORPORATION


Tile Sample 12 Mark8 Standard Handbook for Mechanical Engineers 8th sd 1978 p 3 58

Number Of Pipes= 2 Number Of Junctiona- 2

HeadPressure Convergence= 001 (Relative change) Flow Rats Convergence= 001 (Relative change) Relaxation- AFT Fathom Automatic Maximum iterations- 500

Constant Fluld Pmpelly Model Fluid Unspsclfied Density= 1 705 alugnt3 VlSCOSHy= 1 362E-05 Ibf s/fl2 Vapor Pressure- GravHationai Acceleration= 1 g Atmoapheric Pressure= 1 atm

Pipe

1 2

I 1 Pipe 1 Name 1 object I Length I Length 1 Hydraulic 1 Hydraulic I Roughness 1 Roughness 1 Losses (K) 1 Junctions I

Geometry Material Ske Type Thermal OverallU Include Special Boundaw Internal h Condition.

Cylindrical Pipe Steel 1 inch schedule 40 Adiabatic 0 No None 0 No None Cviindrical Pipe Steel 2 inch schedule 40 Adlabatic

I Defined 1 1 Unns I Diameter I Diam Units 1 1 Units I 1 (Up.Down) Yes/ io01 feet/ 10491 inches I 00015 1 feet I 01 1.2 Yes/ 1001 fee l 20671 inches I 00015 I feet I 01 1,2

SNF-5332,Rcv 0

Pipe


__ . Vol Flow Mass Flow Veloctty dP Total dP Friction dP Gravity dH Max Pres Min Pres Cyn Pres

11/30/199s

(Mlrec) (IbnVsec) (feevsec) (psid) (poid) (psid) (feet)


(psia) (psia) Lpsia)

TIM Sample 12 Marks Standard Handbook for Mechanical Englneers 8th ed 1978 p 3 58 Analysis run on 11/30/1999 3 51 03 PM Input File C \FATHOMEAMPLESSAMPLEI2 FTH

Pipe

1 2

Execution Time- 0 11 seconds Total Number Of Hesd/Pressure Iterations= 8 Total Number Of Temperature Iterations= 0 Total Number Of Flow lbratIons= 3 Number Of Pipes= 2 Number Of Junctions- 2 Head Tolerance= 001 relative change Volumetric Flow Rate Tolerance. 001 relative change Relaxatlon- 1 (None)

Constant Fluid Properiy Model Fluid UnspecHied Dana* I 705 slugM3 Vlrcositr 1 362E 05 Ibf s/RZ Vapor Preuun= Gmvl(st1onal Acceleration= 1 g Atmospheric Pressure= 1 atm

Total Inflow 0 500000 fl3/sec Total O u M w 0 500000 fl3/sec Maximum Presaure is 100 000 psia at Junction 1 Inlet Minimum Pressure Is 73 5748 psia at Junction 2 Inlet

Junction 1 Loss Results Pipe 1 1 77800 feet 0 677329 psid K= 0 780000 Pipe 2 4 07598 feet 1 55274 psid K= 0 780000

__ dPT/dx Resistance f ReynoldsNo L/D K W D + K

23 7572 11,803 151 0 0239163 1 32534E+05 27 3589 0 27 3589 228818 328952 00197990 395406E+05 114943 0- 114943

(paV100 ft) (secZM6)

J d

1 2

6236311 9845431 7469711 0868371 600651 I 9645661 7357481 1990698

1 I 007268831 3987451 121112~ 2375721 2375721 _ I 1 2 I 042731171 23440931 1833731 2288181 2288181

PStag In PStag Out Plnlet Poutlet (pala) (psia) (psia) (psia)

1000000 1000000 1000000 980093 755655 740127 735748 740127

1 (P sid) 1 ( feet) I (fl3/sec) - 1 1 (feet) I ( feet) I ( feet) 1 ( feet) 1 1 See General I See General I 0 500000 t See General I 223 925 1 223 925 1 223 925 1 218 699 2 1 01 01 0 500000 I 000000~ 1597841 1557081 1545581 155708

89

SNF-5332, Rev 0

Sample #I 3

3 pipes 4 junctions Model of a branching system with component losses included Ethyl alcohol is the working fluid

Reference Marks Standard Handbook for Mechanical Engfneers 8th ed 1978 T Baumeister editor p 3 59

Ethyl alcohol at 680F flows from tank A which is maintained at a constant pressure of 100 psi through 200 ft of 2 in cast iron schedule 40 pipe to a Y branch connection (K = 0 5) where 100 ft of 2-in pipe goes to tank B which is maintained at 80 psi and 50 fl of 2 in pipe to tank C which IS also maintained at 80 psi All tank connections are flush and sharp edged and are at the same elevation Estimate the flow rate to each tank

J3

SNP4332,W 0

AFT Fathom 3 0 Input NUMAEC HANFORD CORPORATION

Sample 13 "Marks Standard Handbook for Mechanical Engineers 8th ed 1978 p 3 59

11130/1999 04 07 PM

Tllle Sample 13 "Marks Standard Handbook for Mechanical Engineers 8th ed 1978 p 3 59

Number 01 Pipes= 3 Number 01 Junctions= 4

Head/Pressum Convergence= 001 psla Flow Rate Convergence= 001 ff3hlec Relaxation- AFT Fathom Automatic Maximum Iterations- 500

Constant Flud Properly Model Fluld Unspecified Density= 1 532 slug&? Viscositr: 2 506E 05 Ibf SMZ vapor Pressure= GraYllahonaIACC(IIemtlon= 1 g Atmospheric Pressure= 1 atm

2067 __ inches 00085

91

AFT Fnlhom 3 0 Outpul (1) 11/30/1999 NUMATEC HANFORD CORPORATION

Sample 13 Marks Standard Handbook for Mechanical Engineam 8lh ed 1978 p 3 59

Tub Snrnple 13 Marks Stnndard Hnndbook for Mechnnlcsi Enginears 8th ed 1978 p 3 59 Anstyskrunon 11/30/199940822 PM Input File C FATHOMiSAMPLESiSAMPLE13 FTH

Execution Time- 0 11 seconda Totnl Number Of HeadPressure Iterations- 8 Totnl Number Of Tempernlura Itarnlians= 0 Totnl Number Of Flow Iterations- 3 Number Of Pipes= 3 Number 01 Jumttons- 4 Pressure Tolerance= 001 pria Volumelric Flow Rate Tolerance= 001 fl3/sec Rnl&bn= 1 (None)

Constan1 FluM Properly Model FIuM U n w e c i M DenrHy- I 532 riug/fn WrnHy- 2 506E-05 Ibf sM2 Vapor Prsuure- Gravilatlonal Accelernbon- 1 g Almospherlc Pressure= 1 alm

rota1 i n f l w o 225202 n3-C rotai OUMOW o 225202 ~ W W C Maximum Pra8surn is 99 5032 psi at Jundm 1 Inlet Minimum Pressure is 79 8335 pal at Junction 4 inlet

Pipa Vol Flow (Wwc)

1 02252023 2 00948423 3 01303801

P i p dPlldx (P.IIIOO n)

1 910728

Jundlon 2 LOSS Results Pips 2 0 128713 feet 0 0440579 psld K= 0 500000 Pipe 3 0 243169 feel 0 0832356 psM K= 0 500000

MassFlow Velocity dPTotnl dP Fnctlon dPGravity dH MaxPres Min Pres Eyn Pres (Ibm/sec) (fwt/sec) (p sad) (paid) (psld) (feet) (psia) (psla) @sa) 111W36 986417 1821457 1821457 0 5321291 995032 81 2886 04968164

406999 467483 174137 174137 0 508733 816533 799119 00881158 ~ 642553 559418 170220 170220 0 497288 81 5357 798335 0 1664713

Rarlstance f Reynolds No fl/D K U D + K

10492311 00311452~ 101766Et051 38162751 050W001 366628 ( s e c ~ ~ 5 )

2 2 3 4

2 1 74137 565 570 I 0 0323188 4 28579E+M 18 78272' 1 OWOW 192627 - _ _ -- 3 I 3 4 0 4 3 z 2 9 2 8 3 0 0 0 3 1 7 8 d 5 8%6%E+& 9 22519 1 000000 10_2252.

(Paid) (feet) (gaVmln) (feat) (feet) (feet) (feet) 0 0 101 0778 OMXMO 249211 249211 247760 247760

See Oeneral See General 0 OW0 See General 195 998 195 998 195 353 195 353 0 0 -42 5681 OWOOO 190782 190782 190525 190525 0 0 58 50% O O O W O 190782 190782 190296 190296

Jct 1 dP I dH 1 Vol Flow Into System 1 Loaa Fndor (K) 1 EGL Inlet I EGL Outlet I HGL Inlet I HGL Outlet 1

I (P ais) I (p sla) I (p ala) I (P ala) 1 I 1OOOWOI 10OOwM1 995032/ 995032 2 I 81 78541 81 78541 81 - 1 81 5846 3 1 800OW~ 8OOOOOl 7991191 799119 4 1 8OoooOl 8OowOl 7983351 798335

LOSMS

92

SNF-5332, Rev 0

Sample #I4

2 pipes 3 junctions Model of a siphoning system The problem is to determine how high a junction can be raised and still continue flowing Water is the working fluid

Reference Marks Standard Handbook for Mechanical Engineers 8th ed 1978 T Baumeister editor p 3-60

The siphon shown in [sample problem] is composed of 2000 ft of 6-in schedule 40 cast iron pipe Reservoir J1 is at elevation 800 ft and J2 at 600 ft Estimate the maximum height ofjunction J3 if the water temperature may reach 1040F The amount of straight pipe from A to B is 100 ft For the first bend UD = 25 and the second UD = 50 Atmospheric pressure IS 14 7 psia

J3

93


1 Pipe Name Object Length Length Hydraulic Hydraulic Roughness Roughness Losses (K) Junctions Defined Units Diameter Diam Units Unils (UpDown)

2 PlDB Yes 100 feet 6065 inches 00085 I feet 1 5 1.3 1 PIP2 k a 1900 feat 6065 inches 00085 1 feat 2 1 3.2

Pipe Geometry Material Thermal Overall U Include Special Boundary Internal h Condition

1 Cvlindrical PiDe Cast Iron Adiabatic 0 No None 2 Cviindncal Piw Cast imn Adiabatic 0 No None

12/01/1999 09 30 AM


Title Sample 14 Marks Standard Handbook for Machanical Engineen 8th ed 1978 p 3-60

Number Of Pipes- 2 Number Of Junctions= 3

HeaWretsure Convergence= 001 feet Flow Rate Convergence= 001 ft3sec Relaxation- AFT Fathom Automatic Maximum Iterations- 500

Constant Fluid Property Model Fluid Unspecfied Dens@ 1 925 SlUp/fl3 VlscOSltr 1 361E 05 Ibf sM2 Vapor Pressure= I 07 psia Graviiationai Amleration= 1 g Atmosphenc Pressure= I atm

94

SNF-5332,Rev 0

Pipe Vol Flow MarsFloW Velocity dPTotai dPFrldion dPGravw dH MaxPres MinPres Dyn Pres

. 1 105898 146131 117602 126997 8049958 9319930 1871629 137716 107183 0924424

. 2 105698 146131 117602 126997 552128 717844 128371 137716 107183 0924424

(flaVmin) (lbm/sec) (feeVsec) (MI id) (Paid) (psld) (feet) (psia) (psia) (Psla)

- Pipe dWldx Reeistanca f Reynolds No ND K f V D + K

(Psl/loO fl) (SeC2m5) 1 4 23882 33 62091 0 0226058 8 40696E+05 84 98075 2 10000 87 08075 2 552126 230598 00228058 640696€+05 447267 15woo 597267


Jct

(1) 12/01/1995

dP dH Val Flow Into Syatem Loss Factor (K) EGL inlet EGLOutlet HGL inlet HGL Outlet P Stag in (psidl (feat) (gal/min) (feet) (feet) (feet) (feet) (psia)

1 1 01 01 1058 98 1 OOooOO~ 800000/ 6000001 8000001 8000001 1469598 2 1 01 01 1058 98 I OoooW( goOOO0~ 8M)oWl 8ooOO0~ 8ooOO01 1469598 3 1 01 01 0001 0000001 7871631 7871631 7850141 7850141 199626

sia) I (p sia) I (P ria) I I 14695981 14695981 1469598 2 1 14895981 1469598\ 1469598

1 3 1 1996281 1071831 1071831

SNF-5332 Rev 0

Sample #I 5

1 pipes 2 junctions Model of the pressure drop through an cylindrical annulus Water IS the working fluid

Reference White F F/u/dMechanrcs 1979 p 349

96

Sh’F-5332,Rc~ 0

Pipe Name Object Length Length Hydraulic Hydraulic Roughness Roughness Losses (K) Defined Unit8 Diameter Diam Units Units

AFT Flthom 3 0 Input (1)

Sample 15 Fluid Mechanics Frank While 1979 p 349

NUMATEC “FORD CORPORATION

Junctions (UD.DOVM)

1

pipe

9

Pipe inner Pipe OD Special Condition

PIDO I Yes I 301 meters 41 em 046 I mm I I I 1, 3

Geometry Matenai Thermal Overall U include Outer Pipe ID Outer Pipe ID Inner Pipe 00

Cvlindncel Annulus 1 Unmufifd 1 Adiababc I 01 No 101 cm I 6 BOundaN Internal h Units

Asslgned Flow

1

REIENOb

3

97

Loss Factor

0

Depth Balanca Unib EnemL

metera No

SNF-5332, Rev 0

Pipe

1

Pipe

1


Vol Flow Mass Flow Velocity dPTotal dPFnction dPGravity dH MaxPres MinPres Dyn Pres

001WOW 220462 6527021 5280241 5280241 0 3712381 1968921 1440901 0287020 (m3/wc) (Ibmhec) (feeVsec) (pad) (DSld) (psid) (meters) (Dola) (pria) (DSia)

f ReynoldsNo IUD K I U D + K

536472 978623 002319571 780171E+041 1739681 lOOOW/ 183968

dPfIdx Resistance (DSt'lw fi) (Mczlff5)


12M1/19E

Tkle Sample 15 Fluid Mechmiu Frank Whne 1979 p 349 Analysis run on 12/01/1999 10 05 30 AM input File C FATHOMWAMPLESbSAMPLE15 FTH

Exscution The- 0 11 seconds Total Number Of HeadiPmrsura Iterations= 0 Total Number Of Temperature Iterations= 0 Total Number Of Flow Iterations= 2 Number Of Pipes- 1 Number Of JunctiQns= 2 Head Tolerance= 001 meters Volumetrlc Flow Rate Tolerance- 0001 m3/sec Relaxation= 1 (None)

Constant Fluld Property Model FiuM Unspecified DenrHp 1000 k g h 3

Vapor P n u u r s l GrnvltPtional Acceleration- 1 g Atmospheric Pressure= 1 atm

Overall Dolts Head = 12 1797 feet Total Inflow- o 353147 fwsec

Maximum Pressure is 0 135752 MPa at Junction 1 Inlet Minimum Pressure is 0 101325 MPa at Junction 3 Outlet

Vhcolltr 00102 kghec-m

T O ~ I ournow= o 353147 rwsec

Jd I dP 1 dH I Vol Flow Into System I Loss Factor (K) I EGL Inlet I EGL Outlet I HGL Inlet 1 HGL Outlet 1 P Stan In I I ---- ... ~ ~~~~~~~ . .

I (Wd) I (bd) I I (feel) I feat) I ( feet) I ( feet) I (p sia) I I 01 01 158 503 I 000000 1217971 1217971 1151771 1151771 199762 3 1 01 01 158 503 I 0000001 000001 000001 oooool 0 0000 I 14 6960

J d I P stag out I P Inlet I P Outlet I I I 19 9762 I 19 6892 I 19 6892 3 1 1469601 146960I 146960

Losses

SNF-5332, Rev 0

Sample #I 6

8 pipes 9 junctions Model of a branching system fed by three reservoirs one of which has a pump One loop IS included Water IS the workng fluid

Reference Jeppson R W Analysis of Flow 11) Pips Networks 1976 p 94

Water supply comes from one pump and two reservoirs as shown below The elevation of all junctions is 80 feet The pump characteristic curve is given by hp = -10 33Q2 + 2 823Q + 22 29 There IS an outflow of 2 0 cfs leaving the system at junction 2 Assume all pipes have e = 0 012 inch Find the flow and head loss in each pipe and the head and pressures at each junction

p7* 1 J7

99

AFT Fathom 3 0 Input NUMATEC HANFORD CORPORATION I

Sample 16 Analysis of Flow in Pipe Networks Roland Jeppson 1976 p 94

Title Sample 16 Analysis of Flow In Pipe Networks Roland Jeppson 1976 p 94


Head/Pressure Convergence= 0001 feet Flow Rate Convergence= 0001 flzsec Relaxation- 1 Maximum lteretlons= 500

Constant Fluid Property Mcdel Fluid Unspecifmd Densip 62 4 l b m 3 V i s c o s ~ 0006558 lbmh R Vapor Pressure Gravltatlonal Acceleration= 1 g Atmospheric Pressure- I atm

I

100

SNF4332,Rev 0

Branch

1 2

AFT Fathom 3 0 Input (2) 12/01/1999 1040AM NUMATEC HANFORD CORPORATION

Boundary Flow Boundary Flow (+ = in/ = out) Unlts

900 saVmin

Pump

8

3 I I I I I I I I 4

I I I I I I I I

Independent Ind Variable Dependent Dep Variable LOSS LOSS LOSS LOSS Vanable Units Variable Units Constant a Constant b Constant c Constant d

Vol Flow ~3/sec Head feet 22 29 2 823 10 33 0

5 8 7

I I I 1 I 1 I I Reservoir I Surface I surface I Depth I Depth I Density/ Density I Temperature I Temperature

Pressure Pressure Units Units Units Units 1 atm 0 feet 1 atm 0 feet 1 atm 0 feet

Branch I I I 1 I 2 I I 3 I I I 4

I I I

'im 1 Datailed InDut D& Name Pipe Geometry Cylindncal Pipe Matenal Unspecified Inner Diameter= 8 inches Length= 1000 feet Absolute Roughness= 012 inches Addltionai Losses= 0

'Ice 2 Detailed lnout Dat@ Name Pipe Geometry Cylindrical Pipe Matenal Unspecifmd inner Diameter= 6 inches Length= 2000 feet Absolute Roughness= 012 inches Additional Losses= 0

Detailed lmut Data Name Pipe Geometry Cylindncal Pipe Material Unspeufied Inner Diameter- 8 inches

SNF-5332,Rev 0

AFT Fathom 3 0 Input (3) 12/01/1999 1040AM NUMATEC HANFORD CORPORATION


&& Detal led lnwt Data (co nt 1 Length= 2000 feet Absolute Roughness= 012 inches Addhmal Losseas 0 - Name Pipe Geometry Cylindrical Pipe Material Unspecffled Inner Diameter= 8 inches Length- 1000 feet Absolute Roughness= 012 Inches Addtranai Losse.s= 0

lnout Data Name Pipe Geormy CylMnCal P I p Matensi UnspecMed Inner Diameter= 6 inches Length- 1000 f w t Absolute Roughness= 012 inches Additional Loasas= 0

Ploe 8 D a t a i l ~ Name Pipe Geometry Cylindrical Pipe Material Unspeclfmd Inner Diameter- 8 inches Length- 1000 feet Absolute Roughness- 012 Inches Additional Losses= 0 - Name Pipe Geometry Cylindrical Pipe Material UnspecMed Inner Diameter= 6 inches Length= 500 feet Absolute Roughness= 012 inches Addllional Lesser= 0

ploe 8 Detailed ln~ut Data Name Pipe Geometry Cylindrical Pipe Materlal Unspecifmd Inner Diameter= 6 inches Length= 500 feet Absolute Roughness= 012 inches Additional Losses= 0

102

AFT Fathom 3 0 Output (1) NUMATEC HANFORD CORPORATION


1210111999

Tme Sample 16 Analysis of Flow in Pipe Networks Roland Jeppson 1976 p 94 Analyrls tun on 1210111999 10 39 23 AM Input File C FATHOMEAMPLESSAMPLE16 FTH

Execution Time= 0 27 seconds Total Number Of Headffressure Iterations= 21 Total Number Of Temperature Iterallonr= 0 Tots1 Number Of Flow ltarations= 7 Number Of Pipes- 6 Number Of Junctions= 8 Head Tolerance- 0001 feet Volumetric Flow Rate Tolerance= 0001 n31sec Relaxation= 1 (None)

Constant Fluid Property Model Fluid Unspecfmd Denally= 62 4 Ibm/ft3 ViscMlly= 0006558 Ibm/s fl Vapor Pressure= Gravilattonal Acceleration= 1 g Atmospheric Pressure= 1 alm

Total Inflow 2 00521 n31sec Total O u M w 2 00521 nYsec Maximum Pressure 1s 25 7554 psia at Junchon 8 Outlet Minimum Pressure is 14 6960 psta at Junction 5 Outlet


8 082916 75958 17529 10000 16487 NIA N1A (fl31aeC) (psM) (feet) (96) (hp) (feet) (feet)

7 1 0 629163 1 51 73976 1 4 222892 1 2 916030 1 2 916030 I 0 00000 1 6 729301 I 25 7554 1 22 8393 1 0 12009005 8 1 08291631 51 739761 42228921 35836841 29163161 -6500001 67299591 1815%1 1457591 012009005

I Pipe I dPf1dx I Resistance 1 f 1 ReynoldsNo 1 fllD 1 K 1 WD+K I I (DSUIOOII) I ~ s e c ~ 1 5 ) I I I I 1

I 1 005843231 4547711 00237716/ 972458E+041 3565741 01 356574 2 1 037673241 39488751 002449111 160782E+051 9796431 01 979643

7 I 058320601 9787921 00242844 2 0 0 9 0 3 242844 0. I 8 I 05832631 I 9788871 002428441 2 0 0 9 0 6 E + 0 5 ~ 8 4 ~ 242844

_ _ Vol Flow Into System Loss Fanor (K) Inlet EGL Outlet ’ HGL Inlet HGL Outlet I P Slag In’

(feet) , (feet

103

SNF4332,Rev 0

7 I ow00o I ooooo1 372 154 1 0 00000 I 95 0000 1 95 0000 I 95 0000 I 95 0000 1 14 6960 . 8 1 7595791 1752871 0 000 I 0000001 8827001 10579881 8799291 10552161 182797

JCI I P Stao out I P Inlet I P 0utie1 I


12/01/1999

1 JCt 1 dP 1 dH 1 Vot Flow into System 1 Lass Factor (K) [ EGL inlet 1 EGL Outlet 1 HGL inlet 1 HGL Outlet I P Stag In 1 4 I 00000oI 00000I 0 000 I 0 00000 1 99 0695 I 99 0695 I 98 9876 I 98 9876 I 22 9594 5 I 00000oI 000001 240 181 I 0000001 1000000~ 1OOOOOOI 1OOOOOOI 1000000~ 146960 8 I 0000001 000001 287 665 1 0000001 1050000~ 1050000I 1050000I 1050000) 148960

- (Dsia) I (psla) I (P sia)

1 1 22 7983 I 22 7751 1 22 7751 1 2 1 152637) 151642) 152637)

220096 21 9474 21 9474 229594 229240 229240 148960 146960 146960

L 6 I 14 8960 I 14 6980 I 14 6960 I 7 1 1489601 1469601 146960 e l 25 8755 1 18 1596 I 25 7554 - Name Pipe Geomelry Cylindrical Ptpe Material UnspeMed Inner Diameter= 8 inches Length= 1000 feet Ablolulm Roughness- 012 inches Additional Losses- 0

inout Data Name Pipe Geometry Cylindncal Pipe Material UnspecMed inner Diameter= 6 inches Length- 2000 feet Absolute Roughness= 012 inches Adddionai Losses- 0

Pi- 3 D m d lnout Data Name Pim Geometry Cylindncai Pipe Material UnspacMed Inner Diameter- 8 inches Length- 2000 feet Abrolute Roughness= 012 inches Additional Losses= 0

&g 4 Deta iled h D u t Name Ppa Geometry Cylindncai Pipe Material UnrpecMsd Inner Diameter= 8 inches Length- IO00 fwt Absolute Roughness= 012 inches Additional Losses. 0

Plos 5 Dehl le- Name Pipe Geometry Cylindrical Pipe Material Unspeufied

104

AFT Falhom 3 0 Oulput (3) 12DlH 999 NUMATEC HANFORD CORPORATION


Data lcont I Inner Diameter= 6 inches Length= 1000 feet Absolute Roughness. 012 inches Additional Losses= 0

P i w 6 D e w InDut Datp Name P l w . . .. GeomeIG Cylindrical Pipe Material Unspecified Inner Diamder= 6 inches Length= 1000 feel Absolute Roughness= 012 inches Additional Losses= 0

I Inout Datp Name Plpe Geometly Cylindrlcal Plpe Materlsl Unspecified Inner Diameter- 6 inches

Absoiute Roughness= 012 Inches Addltional Losses- 0

Lenm= 500 f N t - Name Pipe Geometly Cylindrical Pipe Material UnspecHied Inner DIameterP 6 inches Length= 500 feet Absolute Roughness= 012 inches Additional Losses= 0

105

SNF-5332, Rev 0

Sample #I7

10 pipes 9 junctions Model of a branching system with a pump and a PRV Two loops are included Water is the working fluid

Reference Jsppson R W Ana/ys/s ofNow in Pipe Networks 1976 p 110

Solve the ten pipe network shown in the accompanying sketch which is supplied by two reservoirs with water surfaces at 180 and 200 feet respectively The PRV is located 450 feet downstream from the upstreamjunction [JZ] and has a pressure setting which maintains the elevation of the HGL at 50 fl downstream from the valve The pump characteristics are the following Q l = 1 0 cfs @ Hpl = 40 ft Q2 = 1 5 cfs @ Hp2 = 35 ft Q3 = 2 0 cfs @ Hp3 = 26 fl There are outflows of 1 0 2 0 and 2 0 cfs at junctions 6 8 and 9 respectively Assume pipes 1 3 and 10 have CHW = 110 pipes 2 4 5 6 and 9 have CHW = 120 and pipes 7 and 8 have CHW = 130 Find the flow and head loss in each pipe the pump head added for each pump and the pressure at each junction

57 J1 J9

P4"

J8 . P3>

105


Pipe

12/01/1999 10 56 AM

Geometry Matenal Thermal Overall U Include Special Boundary Internal h Condition

Semple 17 Analysis of Flow in Pipe Networks Roland Jeppson 1976 p 110

Pump

Title Sample 17 Analysis of Flow in Plpe Networks Roland Jeppoon 1976 p 110


HeadPreaaure Convergence= 0001 (Relative change) Flow Rate Convergence= 0001 (Relative change) Relaxation= 1 Maxlmum Iterations- 500

Constant Fluid Property Model Fluid Water at 1 atm Temperature 70deg F Density. 62 30842 IbmM3 Viacosltyc 2 36004 Ibm/hr R Vapor Preasum= 36157 psia Gravitabonal Acceleratm= 1 g Atmospheric Pressure= 1 atm

Name Object Spectal Elevation Elevation Initial HGLPressure Initial HGLlPressure Defimd Conditon Units units

I 1 l c v l lndrical Pipe I Unspecfied I Adiabatic ' I 2 I Cvllndrlcal Pipe I Unspscified I Adiabatic I

Junctions (Up.Down)

1. 5 2,; 4, 2 4. 1 2, f 3, ! 7, 1 8.4 6. E 9. i

SNF4332,Rev 0

1 I

107

SNF-5332, Rev 0

9

ReseNOir

7 8

AFT Fathom 3 0 Input (2) izmi/i999 1 0 5 6 ~ ~ NUMATEC HANFORD CORPORATION

Pump Yes None 100 fee1

Name Object Special Elevation Elevalion Initial HGUPressure Initial HGUPreasure Defined Condition Units Units

ReseNOIr Yes N/A 180 feet 180 feel Reservoir Yes N/A 200 feel 200 feel

Branch I I I I I .I

2 3 4 I .,

Control Valve

7 I I I I

I I I I 8 No I

108

I Pipe I Vol Flow I Mars Flow I Velocity I dP Total [ dP Fridion 1 dP Gravity I dH I Max Pres I Min Pres I Oyn Pres I 1 (ft3/aec) I (Ibm/sec) I (feevsec) 1 (P sid) I (P sid) I [P sid) 1 ( feet) I (P sia) I (p sia) I (P sia)

1 I 2 532886 I 157 8201 I 12 69988 I 70 88551 I 27 61578 1 43 2697 I 63 82239 1 88 7576 I 17 8721 I 1 1189760 2 I -03758031 2341571 1913951 110244/ 1102441 000001 2547831 4091721 3981481 00246326

I I I I 1 1 55231561 9948141 002467951 613036E+051 2467951 01 246795 2 I -01378051 1804061\ 00279722\ 909557E+04\ 4475551 01 447555 3 I 52608281 1997491 I 002477711 597121E+051 495541 I 01 495541 4 I 04591871 1636320/ 002537131 174335E+051 4059411 01 405941

I H19

AFT Fathwn 3 0 Output NUMATEC HANFORD CORPORATION

6 0990397; 19218211 00238384' 284135E+05! 4767671 0 4767671 . 7 05409771 190289' 001989101 329026E1051 149182' 0 149182

8 1 537067 I 1 74822 1 0 0182762 ' 5 78592E105 I 13 7071 I 0 13 7071 , 9 07057321 14815081 002450241 219926€+051 367536 0 367536'

(2) 1210111998

5 I 07057291 8869021 002450241 219926E+051 220522) 01 220522

I 10 1 55231761 9948171 00246795) 613036E+051 2467951 01 2467951

110

SNF-5332, Rev 0

Sample #I 8

12 pipes 10 junctions Model of a branching system fed by two reservoirs and containing two PRVs Several loops are included Water is the working fluid

Reference Jeppson R W Analyss of Flow 11) Rpe Networks 1976 p 11 1

Obtain the flow rates in each pipe and the pressure at each junction of the network in the accompanying sketch Water is flowing (in SI units the kinematic viscosity v = 1 13e-6 N2h = 0 0133 Stokes and the specific weighty = 9800 Nlrn3) Reservoir A and B are elevations of 300 rn and 250 rn respectively

J9

111

SNF-5332, Rev 0

A m Fathom 3 0 Input NUMATEC HANFORD CORPORATION

Sample 18 Analysis of Flow in Pipe Networks Roland Jeppson 1976 p 11 1

12/01/1999 11 07AM

Tltle Sample 18 Anaiysis of Flow in Pipe Networks Roland Jeppson 1976 p 111

Number Of Pipas= 12 Number Of Junctions= 10

HeadiPreuure Convergence= 001 meters Flow Rate Convergence= 00001 m 3 h c Relaxation- AFT Fathom Automatic Mwmum Iterations= 500

Constant Fluid Properly Model Fluid Unspecified Dens ip 1000 k g h 3 Vlscosily= 001 13 kg/sec-m Vapor Pressure= Gravltational Acceleration= 1 g Atmospheric Pressure= 1 atm

112

SNF-5332, Rev 0

RESENOlr

8 9

AFT Fathom 3 0 Input (2) 12/01/1999 11 07AM NUMATEC HANFORD CORPORATION

COllnEded PIPS Surlace Surface Depth Depth Density Balance (+=in. =out) Pressure Pressure Units Units Energy

1 1 atm 0 meters No 10 1 atm 0 meters No

113


9 10 11 12

Sample 18 Anaiyais of Flow In Pipe Networks Roland Jeppson 1976 p 1 I 1

Titla Sample 18 Analysis of Flow In Pipe Networks Roland Jeppson 1976 p 111 Analyrla run on 12/01/1999 11 09 0.5 AM Input File C FATHOMLSAMPLESLSAMPLE18 FTH

Execution Time- 0 71 seconds Total Number Of HeadiPressure Iterations= 11 1 Total Number Of Temperature Iterations- 0 Total Number Of Flow Iterations= 16 Number Of Pipes- 12 Number Of Junctions= 10 Head Tolerance= 001 meters

01200000 264555 1253189 -618573 7917432 8534005 5566505 1533221 1471564 02014074 444027 5256% 7411293 2 M 2 1 71 11671 210655 886226 145097 00000000 0000 000000 1422334 Ow000 1422334 000000 1543802 1401568 00000000 0000 000000 711167 OOoooO 711167 000000 I543802 1472685

Volumetric Flow Rate Tolemnce= 00001 m3/sec Relaxation= 1 (None)

I (P sin) I (p a i / I ~ f i ) I ( r e m ) I I Pipe I Cyn Prea I dFf/dx I Resistance I f 1 ReynoldrNo I RID I K I W D + K I

2 ' 115848301 13573741 051597051 001153231 106111E+M 1922051 000001 192205] 3 I 06371878 08525071 093170711 001229061 734493€+05I 2633701 000001 283370 4 1 009883721 0 1444051 064339451 001438031 309940E+O51 2396721 000001 2396721

I 5 I 118478721 21039801 123886571 001164881 100155E+06 2495741 I O O O O O I 3495741 6 I 0 9173864 1 7 I 000000001 00000001 OOOWOWI 00000000l O00000E+WI 00000~ 000001 00000

1 096573 I 0 5283928 i 0 0117653 I 9 U253E+05 I 19 6087 I 0 0000 19 6087 I 8 I000000001 0000ooo1 000000001 oow00001 00QOOOE+WI 000001 000001 000001


(2) 12/01/1999

~

3,192 371 1 owoool 8202101 8202101 25OwOI 250wO\ 146960 I O 1 4012601 9255711 ooool 0 00000 I 874 078 I 781 521 I 266 419 1 238 208 1 187 3945

9

115

SNF-5332, Rev 0

Sample #I 9

16 pipes 14junctions Model of a branching network fed by two reservoirs One reservoir has a pump One PRV is included Water is the working fluid

Reference Jeppson R W Analysis of Flow in Pipe Networks 1976 p 88

As an example of a network in which a PRV acts as a check valve consider the 16 pipe network in the sketch below In this network the PRV is placed between pipes P5 and PI5 and has a pressure setting which results in the elevation of the HGL downstream from the valve being 350 ft Solve for the flow rate in each pipe and the head at each junction The pump characteristics are the following (11 = 2 0 cfs @I Hpl = 80 ft Q2 = 3 0 cfs @ Hp2 = 75 ft Q3 = 4 0 cfs @I Hp3 = 68 ft (hp is in feet and Qp in cfs) There are outflow leaving the system as defined

J12

Iml J l A J2

P13'

116


Sample 19 Analysis of Flow in Pipe NeWorks Roland Jeppson 1977 p 88

Tdle Sample 19 Analysis of Flow in Pipe NeWorks Roland Jeppson 1977 p 88

Number 01 Pipes= 16 Number of Jundions= 14

Head/Presrure Convergenca- OOW1 feel Flow Rate Convergence= 00001 fl3/sec Relaxplton- AFT Fathom Automatic Maximum Ilerations= 500

Constant Fluid Properly Model Fluid UnspscMed Dens@= 62 4 I b M 3 V l s c o s ~ OM16558 Ibmls-fl Vapor Pressure- Gravitational Acceleralion= 1 g Almosphenc Pressure= 1 alm

Condiiion

None

117

SNF-5332, RW 0

Amgned Connected Pipa T W Flow Flow Flow (+=in. =out) Unb

1 1 OUtfloW 5 n m c

Branch Connected Pipes Boundary Flow Boundav Flow (+ = in, =out) (+=in/ = out) Unb


LOSS

Factor 0

12/01/1999 12 04 PM

3 I 2.3, 11 I II RYSOC I I I I I

118

SNF-5332, Rev 0

AFT Fathom 3 0 input NUMATEC HANFORD CORPORATION

(3) 12/01/1999 12 04 PM

4 I 3.4. 5.6 I 01 ft3/sec 1 I I I 5 6. 7 , 8 1 51 fl3/sec I

Assigned Flow

I I I I

Branch I I 1 1 I 2

I I I I I

6 I I I 1 I

10 1 I I I I

Control Valve

13

Pump LOSS LOSS Loss Speed% Viscosity Constant c Constant d Constant e Correction

14 1 0 0 100 No

ReSeNOlr Temperature Temperature Balance units Energy

11 No 12 No

119

AFT Fathom 3 0 Output (1) 1 zmi / i 999 NUMATEC HANFORD CORPORATION

Sample I 9 Analysis of Flow in Pipe Networks Roland Jeppson 1977 p 88

Title Sample 19 Analysis of Flow in Pipe Networks Roland Jeppson 1977 p 88 Analyak run on 12/01/1999 12 00 15 PM Input File C FATHOMSAMPLESSAMPLE19 FTH

Execution Time= 2 20 seconds Total Number Of HeadlPressure Iterations= 399 Total Number Of Temperature Iterations= 0 Total Number Of Flow Iterations= 11 1 Number Of Pipes= 16 Number Of Junctions= 14 Head Tolerance- 00001 feet Volumetric Flow Rate Tolerancs= 00001 fl3/sec Relaxation= 2

Constant Fluld Properly Model Fluid Unspewfied Dens* 62 4 IbmM3 Viscosity= 0006558 IbWs fl Vapor Pressure= Gravitational Acceleration= 1 g Atmospheric Pressure= 1 atm

Total Inflow 5 WOO4 M/sec Total Outflow= 5 00004 fl3/aec Maximum Pressure is 84 5537 psia at Junction 5 Inlet Minimum Pressure is 13 0875 psia at Junction 14 Inlet

=I I IPI I I====I=C======~~.~=.~~TE~~~~~~~~~======~U~~SVMMARYII===E=I I I I I I======~====~~=============

J d Flow DP DH Speed idealhp NPSHA NPSHR

14 31678 32051 73965 10000 26579 N/A N/A (fl3sec) (pod) (feel) (96) (hp) (feet) (feet)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


(2) 12/01/1999

JCI I P stag out I P Inlet I P OU~M I

10 I 57 0655 1 57 0608 I 57 0608 I

121

Sample #20

31 pipes 21 junctions Model of a complicated branching network fed by two reservoirs Each reservoir has a pump One other booster pump also is modeled Multiple loops exist Water is the working fluid

Reference Jeppson R W Ana/ysis of f low in Pipe Networks 1976 p 96

Determine the flow and head loss in each pipe the pump head added for each pump and the pressure at each junction for the network described below

Pipe Dia (in) Length (fI) CHW Pipe Dia (in) Length (ft) CHW 1 12 1500 130 16 6 1800 120 2 8 1000 130 17 10 1200 130 3 10 1200 120 18 6 1800 120 4 10 2000 120 I 9 6 1300 120 5 8 2800 120 20 8 1000 130

6 8 7 8 8 8 9 8 10 6

11 6 12 6 13 6 14 6 15 6

1100 1000 2500 61 1 1300

1000 1100 1000 1800 1100

120 120 120 100 100

100 130 130 120 120

21 8 22 8 23 8 24 6 25 12

26 20 27 20 28 12 29 12 30 20 31 20

1200 1100 1100 1800 750

250 250 2500 750 250 250

120 120 120 120 130

110 110 120 130 110 110

PumpJ17 hp=-O417Q2+517Q+4403 Pump J16 hp = 0 378Q2 5 09Q + 298 2 Pump J19 hp = -2 51Q2 + 16 7Q + 155 3

122

SNF-5332,&/ 0

123



12/01/1999 12 14 PM

Tllle Sample 20 Analysis of Flow in Pipe Networks Roland Jeppson 1976 p 96

Number of Pipes= 31 Number Of Jundions= 21

HeadiPressure Convergence= 0001 (Relative change) Flow Rate Convergence= 00001 (Relative change) Relaxation= 1 Maximum Iterations= 1000

Constant FluKl Property Model Fluid Unspecnied Density= 62 4 IbmR3 Viscosity= 2 7 Ibmhr R Vapor Pressure= Gravitational Acceleration= 1 g Atmospheric Pressure= 1 atm

AFT Fathom 3 0 input NUMATEC HANFORD CORPORATION

12/01/1999 12 14 PM

29 I Cvlindricai Pipe I Unswcified I Adiabatic I 01 None 30 I Cviindncal Pipe I Unspeufied 1 Adiabatic j 01 No I None 31 I Cvlindricai Pipe I Unspecified I Adiabalicl 01 No I None

sNF4332, Rav 0

AFT Fathom 3 0 Input (3) iz/oi/i999 12 14 PM NUMATEC HANFORD CORPORATION

20 I Reservoir I Yes I N/A I 9101 feet I 31 I 11 atm 21 I Reservoir1 Yes I N/A I 10801 feet 1 30 I I I atm

I 1

S~4334R8V 0

AFT Fathom 3 0 Output (1) 12/01/1999 NUMAEC HANFORD CORPORATION

Sample 20 Analysis of Flow in Plpe Networks Roland Jeppson 1976 p 96

Title Sample 20 Analysis of Flow in Pipe Networks Roland Jeppson 1976 p 96 Analyris run on 12/01/1999 12 10 58 PM Input File C FATHOMEAMPLESEAMPLEZO FTH

Execution Time= 3 57 seconds I Total Number Of HeadiPressure Iteretions= 608 Total Number Of Temperature Iterations= 0 Total Number Of Flow iterations= 16 Number Of Pipes= 31 Number Of Junctions= 21 Head Tolerance= 0001 relatlve change Volumetnc Flow Rate Tolerance= 00001 relative change Relaxation= 1 (None)

Constant Fluid Property Model Fluid Unspeclnad Densltye 62 4 I b M 3 Viscosityi 2 7 lbmihr fl Vapor Pressure- Gravltstbnal Acceleration= 1 g Atmospheric Pressure= 1 elm

Tdsl Inflow= 9 35764 fl3/rec Tdsl Outflow- 9 35764 fl3/rec Maximum Pressure is 212 102 psia at Junction 17 Oullel Minimum Pressure is 14 4454 psia at Junction 17 Inlet

I =III=L=====.;=======================-==========PUMPSUMMARYII=========I====II=I-IIIISIIEIISE=============

Jet Flow DP DH Speed idealhp NPSHA NPSHR

17 60150 19766 45613 10000 31122 N/A N/A 18 33427 12002 27696 10000 10502 N/A N/A I 9 66499 65832 15192 10000 11805 N/A N/A

(fl3lsec) (psid) (feet) (%) (hp) (feel) (feel)

EP11..13===SI=II.IIIlllllllllllllllEllll==~===~=~=========~================================================

I I

07

9 1 000001 00001 600 000 I 0000001 1321 5141 1321 5141 13209991 13209991 1596521 10 I 000001 00001 0 000 I 0000001 13293371 13293371 13290241 13290241 1509086

I

128


- (Dsla)

(3) 12/01/1999

h a ) (Dsla)

1 JCt 1 dP I dH I Vol Flow Into Svstem 1 Loss Factor IK1 I EGL Inlet I EGL Outlet I HGL Inlet I HGL Outlet I P Stao In 1

J C ~ I ~ s t a o out I P Inlet I P outlet I

10 1 1509088) 15077291 1507729) ii 1 14865571 l r 5 6 7 4 1 14856741 1431010 1430721 1430721 141 1900 140 7166 1407166 1314693 1 13788 1313788

129

SNF-5332, Rev 0

Sample #21

68 pipes 44 junctions Model of a complicated branching network fed by six reservoirs Four of the reservoirs have pumps One other booster pump is modeled Multiple loops exist Water is the working fluid

Reference Jeppson R W Analysis ofNowm P/pe Networks 1976 p 107

Determine the flow rates and head losses of each of the 68 pipes of the network shown below The diameter of each pipe is given in centimeters and the length in meters All pipes have a roughness of 0 026 cm The network is supplied by two reservoirs without pumps and 4 pumps obtaining their water from the reservoirs as shown in the sketch A booster pump exists between pipe P43 and P68 The water surface elevations are 500 540 530 480 600 and 600 rn for reservoirs J46 J47 J48 J49 J50 and J51 respectively

The pump characteristics are the following (hp is in meters and Qp in 11731s) Pump J41 Q1 = 0 03 @ Hpl = 84 Q2 = 0 045 @ Hp2 = 70 Q3 = 0 06 @ Hp3 = 52 Pump J42 Q1 = 0 06 @ Hpl =45 Q2 = 0 105 @ Hp2 = 39 Q3 = 0 15 @ Hp3 = 31 Pump J43 Q1 = 0 06 @ Hpl = 45 Q2 = 0 105 @ Hp2 = 39 Q3 = 0 15 @ Hp3 = 31 Pump J44 (11 = 0 06 @ Hpl = 45 Q2 = 0 105 @ Hp2 = 39 Q3 = 0 15 @ Hp3 = 31 Pump J45 Q1= 0 03 @ Hpl = 9 0 Q2 =0045@ Hp2 = 7 5 Q3 = 0 06 @ Hp3 = 5 5

130

sNF-5332.Ibv 0

Hydraulic Diameter

16 12 12 12 12 16 16 16

14 12 14 12 14 12 8 8 8

12 16 12 8 8

12 12 16 16 16 12 16 16 12 16 16 16 1 14 16 16 16

16


Hydraulic Diam Units

cn cn CIT

UT

cn cn cn cn CIT

CIT

CIT

CIT

UT

cm CIT

CIT

UT

Cll.

cm cm

cm cm cm cm

cm cm cm

m

cm

cm M cm cm cm cm cm cm cm cm


Roughness Unis

ern cm cm cm cm cm M cm cm cm cm cm cm cm cm an cm cm cm cm un cm cm cm em M cm cm cm cm cm cm cm cm cm M cm cm cm

Tile Sample 21 Analysis of Flow in Pipe NetworYs Roland Jeppson 1976 p 107


HeadPressure Convergence= 0001 (Relatne change) Flow Raie Convergence= 0001 (Relative change) Relaxallon= 1 Maximum Iterations- 1000

Constant Fluid Properly Model Fluid Water at 1 atm Temperature 22 deg C Density= 62 29624 I b m m Viscosity= 2 30822 I b M r fl Vapor Pressure- 38264 psia Gravitational Acceleration= 1 g Atmospheric PldllSurB' 1 atm

Losses (K)

(

(

(

(

(

(

(

( c (

(

(

(

C (

(

(

c C C C C C C C C C C

. c C C a a a a

a a

C C

Roughness

026 026 026 026 026 026 026 026 026 026 026 - 026 026 026 026 - 026 026 026 026 026 026 026 026 026 026 026 026 026 026 026 026 026 026 028 026 026 026 026 026

Junctions 1Up.Down)

41. ' 1.: 1.1 4, i 3. : 1. ! 1, c 4. f 5, f 7, t 7, f 8, f 7, s

I O . s 8. I( 9.11

12.11 12, s

12, 1c 42, li 12.1: 14.1: 14. I C 13, 31 14,31 15, 14 43.15

15. € 8, 1E 6. I 5

15, l e 6, 17

17,16 18.17 16.21 18,21 50. I€ 4.18

19.18

131

SNF-5332.R~ 0

AFT Fathom 3 0 Input NUMATEC HANFORD CORWRATION

12/01/1999 12 34 PM

AFT Fathom 3 0 InpuI (3) 12/01/1999 12 SI PM NUMATEC HANFORD CORPORATION

1 Piw 1 Geornetw 1 Material 1 Thermal 1 Overall U 1 Include 1 SDecial t I Boundaly 1 1 Internal h 1 Conddon

24 1 CVllndrical Pmej Unspecified 1 Adiabatic1 01 No I None

133

SNF-5332, Rev 0


12/01/1999 12 34 PM (4)

Branch 1 2 3 4

6 I I 1 1 1 1 1 1 1 7

134

SNF-5332,ROv 0


12/01/1999 12 34 PN

135

SNF-5332,Rev 0

14 15 16 17

AFT Fathom 3 0 Output (1) NUMATEC HANFORD CORPORATION


00188611521 41493991 40198260 I09462852 316337509 4258004 222877561 352654 00259801164 57 155508 7 5365700 I08049927 116 9350128 12774001 82 3872912 348509 0 0109524056 24 094977 7 1486605 18 4761658 117 8294678 99 35330 83 0174850 35 0305 0 01 15475960 25 404379 7 5371427 4 7048340 222 3884735 227 09331 156 6851833 16 5160

12/02/1999

Tllle Sample 21 Analysis of Flow in Pipe Nehvorks Roland Jeppson 1976 p 107 Analysis run on 12/02/1999 3 29 51 PM Input File C \FATHOM!SAMPLES\SAMPLEZI FTH

Execution Time= 1 43 seconds Total Number Of HeadlPressure Iterations= 62 Total Number Cf Temperature Iterations= 0 Total Number Of Flow iterations= 11 Number Of Pipes= 68 Number Of Junctions= 44 Head Tolerance= 0001 relahve change Volumetric Flow Rate Tolerance= 0001 relative change Relaxation= 1 (None)

Constant Fluld Property Model Fluid Water at 1 atm Temperature 2 2 d q C QanaUp 62 29624 lbmm3 ViscosHy= 2 30822 Ibm/hr fl Vapor Pressure= 38264 psia Gravitational Acceleration= 1 g Atmospheric Pressure= 1 atm

Total Inflow 22 9389 Wsec Total ournow= 22 9389 flwsec Maximum Pressure is 866 296 psia at Junction 50 Outlel Minimum Pressure is 11 7080 psia at Junction 12 Inlet

111==1.11==.11-1=111========================== PUMPSUMMARY====s=========================================


41 0087215 12957 29950 10000 10447 35798 NIA 42 0078664 60683 14027 10000 44129 15691 NIA 43 0080810 60285 13935 10000 45036 44442 NIA 44 0054920 64653 14945 10000 32825 35733 NIA 45 0045000 10645 24606 10000 44284 11931 N/A

(mWsec) (psid) (feet) (%) (hp) (feet) (feet)

ill==llll=llli==IIIP=IEIIPI=IIIEIIIII=II===~======~=====================~=============~====================

18 I 00072505929; 19 1 00251176379) 122347183 3 9 2 5 2 4 7 2 8515997 513799368 240708

231810074' 1045589981( 12774001 1 7366769301 3522351

- 20 ' 0 0786637581 I 173 058002 12 8360043 116 7527924 ' - 3 7 5 2 5 0 00000 82 25890661 127 8381

136

SNF-5332 ,W 0


12/02/1999

SNF-5332, Rcv 0

AFT Fathom 3 0 Output (3) 1 2 ~ 2 ~ 9 9 9 NUMATEC HANFORD CORPORATION

SNF-5332,Rev 0

(mie) I M a )


( p s m o n) 1 ( SSCZZIR~) I I PiDe I Min Pres I Dvn Pres I dPf/dx I Resistance I f I RevnoldsNo 1 fL/D I K 1 N D + K I

L 60 I 20 5228 I 0 1470760852 1 1 557145443 1 1843 6 3 9 I 0 02778831 1 19275€+051 347 354 I 0 I 347 354 I

1 64 1538858 13616344929 582432923? 3492181 00224538 725839Ei051 105252 01 1-2. ' 65 67 1555 I 1 1077046394 I 4 744831075 I 34 9710 0 0224855 I 6 54669E+05 I 105 401 1 0 I 105 401 I 191 4742 ' 1 1689734459 -370835 58 2628 I 0 0224769' 6 72531Ei05 175 601 ' 0 175 601

67 , 10 4 8 4 0 8 a 105 6570' 0 0241887 6 0 9 4 1 5 E + 0 5 ! T i 0 4 68 23 6704 0 3624930084 1 569078358 35 3392 I 0 0227222 ' 3 74507E-05 I -0 0 106 510-

9 I oooool 000001 356 6322 1 000000~ 11304751 11304751 1130.1591 1130159~ 353741 10 I 000001 00000l 475 5096 I 0 WOO0 1 1203 598 1 1203 598 1 1202 5€4 1 1202 964 I 24 4278 I 1 I 000001 0000ol 356 6322 1 000000~ 8581081 5581081 857Z51 8581081 168979

139

SNF-5332, Rev 0

Sample #22

70 pipes 40 junctions Model of a complicated branching network fed by six reservoirs Four of the reservoirs have pumps One other booster pump is modeled Multiple loops exist Water is the wqrking fluid

Reference Jeppson R W Analysis of Flow in Ppe Nefworks 1976 p 103

Solve the 70-pipe network below for the flow rates in all pipes the head losses in all pipes the elevation of the HGL at all junctions and the pressure at all junctions All pipes have e = 0 0102 inch

The pump characteristics are the following (hp IS in feet and Qp in cfs) Pump J31 Q1 = 8 0 @ Hpl = Z O O Q2 = 11 0 @ Hp2 = 180 0 3 = 16 0 @ Hp3= 80 Pump J32 Q1 = 5 0 @ Hpl = 180 Q2 = 7 5 @ Hp2 = 150 Q3 = 100 @ Hp3 = 50 Pump J33 Q1 = 4 0 @ Hpl = 200 Q2 = 6 0 @ Hp2 = 180 Q3 = 10 0 @ Hp3 = 80 Pump J34 Q1 = 4 0 @ Hpl =250 Q2 = 6 0 @ Hp2 =210 Q3 = 8 0 @ Hp3 = 150 PumpJ35 Q l = 2 O @ H p l = 5 0 Q2=4O@Hp2=40 Q3=6O@Hp3=20

141

SNF-5332, Rev 0

m o m h h h tjjf

G o 6

T E C v u u E C E - - -

w r - m h N h m

0 4 0

I n I n u ) m m m c c c 0 0 0 C E E

N N N 0 0 0

0 0 0 _r.-

m w m m w m c z . c 0 0 0 E C E

2 S Z

I.-- m a l m 2.22

0 0 0 0 0 0

N 0 ° F

m I n m * m m m

/

m m m L i h h

N m 4 r _ -

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r

C 0 In

m -J u C m

a a

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lT

m a

B

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E" ;

c 0 In

m

N N m -

m 'E I-

>I>

142

143

SNF-5332,ReV 0

144

6NF-5332 Rev 0

145

SNF-5332, Rev 0

SNF-5332,Rev 0

E n

r f

a E C i

I

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3 a

E e

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e z

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E ii i

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$

i

p

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r

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f

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:

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2

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I :

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1

,

SNF-5332, Rev 0

1 I

1 L

1 1

C P . < I < '

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U C

f 6

U c

SNF-5332,Rcv 0

149

SNF-5332. RCV 0

S W S 3 3 2 , Rev 0

t51

m 0

a W h

- z E 0 VI a a m 7

z m 0

LT -

152

153

SNF4332,Rev 0

m v )

m N

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g : ! 2

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L D L D v )

0 0 0

( 0 r . m w o o 0 v ) m m m m

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m w t c m m o )

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t c m , % N z z Zp?.

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w r . m w m z

m m - r t c m

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m - t - w o r n

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8 z g w z w

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m m m ~ * m r . r . m - b o

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154

h - m m 0 - h - r m *

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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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