Design PEL PEW. Reference Guide 3BGB D0012

Transcription

1 IT Design PEL PEW Reference Guide 3BGB D001

2 About this document This document summarises the mathematical theory used by the PEW program. It has been produced to the recommendations of British Standard BS7649 Guide to the design and preparation of documentation for users of application software. Trademarks All trademarks acknowledged. Industrial IT Enabled This product has been certified by ABB Group as Industrial IT Enabled TM Information Level. All product information is supplied in interactive electronic format, based on ABB Aspect Object TM technology. The Industrial IT commitment from ABB ensures that every enterprise building block is equipped with the integral tools necessary to install, operate, and maintain it efficiently throughout the product lifecycle. Associated PEL Support Services Documents PEW User Guide: This guide is designed to assist the user in becoming quickly familiar with the capabilities of PEW, its interface and how the program is used. Contacting PEL Support Services This program is developed, maintained and supported by PEL Support Services, ABB. We run a Hotline telephone and service to answer any queries about PEW. Please let us have any suggestions on how you feel we could improve PEW. You can contact us by any of the following routes: By Telephone: ++44 (0) By Fax: ++44 (0) By pel.support@gb.abb.com By Post: PEL Support Services ABB Ltd. Daresbury Park Daresbury Warrington Cheshire WA4 4BT United kingdom. Owner: M. G. Pass, ABB. Approved By: M. G. Pass, ABB. Document Version / Issue Date: Version 1. / 10 October 00 Last Amended Date: 10 October 00 Last Amended By: M. G. Pass, ABB. ABB 001 No part of this publication may be reproduced, transmitted, transcribed or stored in any retrieval system or translated into any human or computer language without the prior written permission of ABB. Page of 16 PEW Reference Guide

3 Change history This table records the changes made to each new revision of this document. Changes to approved issues are indicated by a double revision bar on the outer margin next to the text. This is an example. Revision Date Description of change Dec. 000 First Approved Issue Mar. 001 Second Approved Issue (ABB logo added) Oct. 00 Third Approved Issue (Industrial IT logo & paragraph added, Eutech removed, Front page modified). PEW Reference Guide Page 3 of 16

4 Contents 1. PEW Reference Guide Introduction Principle features of PEW PEW Calculations Fluid Flow Calculations Incompressible Flow Scope of Incompressible Flow Calculation Source of Theory Assumptions Input Data Title and Pipework Static Head and Fittings Losses Fluid Properties Process Conditions Pipe Fittings Losses - Bends Pipe Fittings Losses - Valves Calculation Method Possible Errors in the Calculation Other Relevant Programs Compressible Flow Scope of Compressible Flow Calculation Source of Theory Assumptions Input Data Title, Calculated Variable and Type of Flow Pipe Details Fluid Properties Process Conditions Pipe Fittings Losses - Bends Pipe Fittings Losses - Valves Other Relevant Programs Gravity Flow Scope of Gravity Flow Calculation Source of Theory Assumptions Input Data Dimensions and Fluid Properties Fluid Properties Pipe Conditions Duct Conditions Calculation Method Possible Errors in the Calculation Manifold and Symmetrical T junctions Scope of Manifold and Symmetrical T junctions Calculations Source of Theory Assumptions Input Data Symmetrical T Junction Flows Fluid Properties Calculation Method for Symmetrical T-junctions Combining Flow Dividing Flow Page 4 of 16 PEW Reference Guide

5 .4.6. Input Data Manifold T Junction Flows Fluid Properties Calculation Method for Manifold T-junctions Dividing Junctions Combining Junctions Possible Errors in the Calculation Other Relevant Programs Pressure Drop through Expansion/Contraction Scope of Expansions and Contractions Calculations Source of Theory Assumptions Input Data Pipe Details, Expansion or Contraction Data Process Conditions Calculation Method Orifice Calculation Scope of Orifice Calculation Source of Theory Input Data General Data Upstream Physical Properties Orifice Details Other Relevant Programs Restrictor Orifice Scope of Restrictor Orifice Calculation Source of Theory Assumptions Input Data Title and Calculated Variable Geometry Orifice Diameter Orifice Plate Thickness Process Conditions Fluid Properties Calculation Method Calculation Method - Liquids Calculation Method - Gases Notes on Use of the Restrictor Orifice Calculation Accuracy Comparison of Orifice and Restrictor Calculations Two Phase Flow Scope of Two Phase Flow Calculation Source of Theory Assumptions and Limitations Input Data Pipe Characteristics Process Fluids Two Phase Flow Calculation Method Flow Patterns Two Phase Frictional Pressure Drop Void Fraction PEW Reference Guide Page 5 of 16

6 3. Heat Transfer Calculations Heat Transfer Coefficient Scope of Heat Transfer Coefficient Calculations Source of Theory Assumptions Input Data - Inside Pipe Heat Transfer Coefficient Flowrate Details Pipe Properties System Temperatures Fluid Physical Properties Calculation Method Possible Errors in the Calculation Other Relevant Programs Pipe Heat Loss Scope of Heat Loss/Gain from a Lagged Pipe Source of Theory Assumptions Input Data Lagged Pipe Geometry Process Conditions Heat Transfer Fluid Properties Calculation method Possible Errors in the Calculation Vessel Heat Loss Scope of Vessel Heat Loss Calculation Source of Theory Assumptions Input Data Tank Description Lagging and Emissivities Effects of Solar Radiation Ambient and Ground Conditions Physical Properties of the Tank Liquid Physical Properties of the Tank Vapour Solar Radiation Data Calculation Method Equations used for Vessel Heat Loss Calculation Method Detailed Procedures for Vessel Heat Loss Calculation Method Possible Errors in the Calculation Other Relevant Programs Simple Heat Exchanger Scope of Heat Exchanger Performance Calculation Source of Theory Assumptions Input Data Heat Exchanger Calculation Method Tank Solar Heating Scope of Solar Radiation Calculation and Source of Theory Source of Theory Assumptions and Limitations Input Data Calculation Method Solar Radiation to Storage Tanks Accuracy of Predictions Possible Errors in the Calculation Other Relevant Programs Page 6 of 16 PEW Reference Guide

7 3.6. Finned Tube Heat Transfer Scope of Finned Tubed Heat Transfer Calculations Source of Theory Assumptions and Limitations Input Data Input Data for Tubes Input Data for Fins Input Data for Fluid Calculation Methods Nomenclature Calculation Method - Plain Tubes Calculation Method - High Finned Tubes Calculation method - Low Finned Tubes Calculation Method - Fin Efficiency and Surface Effectiveness Pressure Drop Calculations Methods Accuracy of Predictions Heat Transfer Coefficients Pressure Drop Batch Heating and Cooling Times Scope of Batch Heating and Cooling Times Calculations Source of Theory Assumptions Input data for operating conditions Heat Exchange Type Vessel Data Heat Exchange and Supplementary Data Calculation Method Possible Errors in the Calculation Notes on Use Mixing Calculations Vortex Profile Scope of Vortex Depth Calculation Source of Theory Assumptions Input Data Vortex Profile Details Fixed Vortex Diameter Details Calculation Method Possible Errors in the Calculation Notes on Use Table of Power Numbers Scope Source of Theory Assumptions Calculation Method Speed versus Power Scope of Speed versus Power Calculations Sources of Theory Assumptions Input Data Calculation Type General Agitators Agitator Data Internals/Conditions Calculation Method Other Relevant Programs PEW Reference Guide Page 7 of 16

8 5. Equipment Calculations Vessel Calibration General Data for Inclined Vessels Input Data End Dimensions Calibration Calculation Method Possible Errors in the Calculation Figures Figure 1 Combining Flow...33 Figure Dividing Flow...34 Figure 3 Dividing Junctions...35 Figure 4 Combining Junctions...36 Figure 5 Rounded Contraction...41 Figure 6 Conical Contraction...41 Figure 7 Abrupt Contraction...41 Figure 8 Restrictor Orifice...48 Figure 9 Coils/Jacketed Vessel Figure 10 External Heat Exchanger Figure 11 Vertical Tank with a Dished and Conical End Figure 1 Inclined Vessel Figure 13 Choosing a Fluid Flow Program...14 Appendices Appendix A Choosing a Fluid Flow Program...13 Page 8 of 16 PEW Reference Guide

9 1. PEW Reference Guide 1.1. Introduction The Process Engineers Workbench (PEW) program processes individual process engineering calculations. It also allows the user to build up a collection (or project) of calculations which can then be used to generate summaries and graphs to analyse the results. All the calculations present at any one time, together with any summaries or graphs which have been created, comprise the project. Any combination of the various calculation types can be present in a project and several cases of the same type are allowed. A project can have any number of calculations, graphs and summaries with each having its own sub-window that can be minimised or maximised Principle features of PEW Fluid flow calculations are for single, unbranched pipes of single diameter. Compressible flow calculations are available in isothermal and adiabatic modes and are valid up to approximately 0.3 Ma. Fluids must be single phase gas or liquid. PEW is capable of Design calculations as well as the usual Ratings calculations, that is, data about the piping system such as pipe inner diameter or roughness can be calculated from the fluid flowrate and pressure drop. 1.. PEW Calculations The calculations contained in PEW are for: Fluid Flow Heat Transfer Mixing Equipment. These are described in the following chapters. PEW Reference Guide Page 9 of 16

10 Page 10 of 16 PEW Reference Guide

11 . Fluid Flow Calculations The calculations used for Fluid Flow are: Incompressible Flow Compressible Flow Gravity Flow Manifold and Symmetrical T junctions Pressure Drop through Expansion/Contraction Orifice Calculation Restrictor Orifice Two phase flow Calculates either pressure drop, flowrate, roughness or diameter, given the other three, for flow of an incompressible fluid along a pipe of circular cross-section. Calculates any of inlet/outlet pressure, mass flowrate, or pipe diameter for adiabatic or isothermal flow of a compressible fluid along a circular cross-section pipe. Calculates either flowrate or depth of liquor in an inclined, partly filled pipe or duct or pipe diameter in an inclined pipe. Gives the pressure drop through various types of T-junction in round pipes. Both manifold flow and symmetrical flow are considered. Calculates both the perceived pressure drop (the static pressure drop) and the frictional pressure loss for various types of expansion and contraction in cylindrical pipes. It displays the number of velocity heads lost in the fitting. This models an orifice or venturi required to measure the flowrate of a gas, liquid or steam. It can calculate any one of orifice diameter, pressure drop and flowrate given the other two. The scope is limited to squareedged orifice plates with one of: Corner pressure tappings D and D/ pressure tappings Flange pressure tappings. This models the flow through restrictor orifices for either liquid or gas flows. It will calculate anyone of flowrate, pressure drop and orifice diameter given the other two. This program is designed to evaluate the two phase flow regime in a pipe as well as the frictional and gravitational pressure drops and the void fraction. It is based on the methods outlined in the HTFS handbook sheets TM1,, 4, 6, 1, 13, 14 and 15. PEW Reference Guide Page 11 of 16

12 .1. Incompressible Flow.1.1. Scope of Incompressible Flow Calculation This program calculates one of pressure drop, flowrate, roughness or diameter (given the other three) for flow of an incompressible fluid along a pipe of circular cross-section. Data for the losses in various bends and fully open valves are included but expansions, contractions and T-junctions are not as these involve change in diameter or flowrate. Programs to calculate expansions, contractions and symmetrical and manifold T-junctions are included within PEW. It is particularly useful in calculating the apparent roughness based on observed pressure drop data but users should be aware that observed data may be affected by air locks..1.. Source of Theory The following publications provided the sources: 1. Estimation of Pressure Drop in Pipe Systems R A Smith 1977, revised ICI Engineering department NE group Design Guide Ref. P/CP/4B. Guide to Calculations in Fluid Flow R A Smith 1978, revised ICI Engineering department NE group Design Guide Ref. V/CP/17B.1.3. Assumptions The following assumptions are made: 1. Circular cross-section pipes only, no change in diameter.. Pipe length must be greater than ten times pipe internal diameter so the end effects can be neglected. 3. Density and viscosity are assumed constant. 4. Single phase incompressible fluid only, that is, not slurries etc Input Data Title and Pipework Title The title is for the user to identify for each calculation. It is not essential but can be helpful. Calculate Select one of flowrate, pressure drop, pipe diameter and pipe roughness. Values for the other three must be supplied. Page 1 of 16 PEW Reference Guide

13 Pipework Enter the pipe dimensions here. The units can be changed in the units box if required. Length: Diameter: Lining thickness: Enter the actual length of the pipe Put in the internal pipe diameter. If there is a lining to the pipe, enter that here. If the lining thickness is greater than zero, the actual internal diameter available for flow are calculated by: ID - * lining thickness Similarly, if diameter is the calculated variable, twice the lining thickness are added to the calculated diameter for flow to obtain the real ID of the pipe. Roughness: The value depends on the material of construction of the pipe. Some typical values for various materials are: Material of construction Roughness (mm) Roughness (inches) Drawn tubing ( plastics ) Commercial steel tube Cast Iron Concrete, scaled pipes Note. Use the Pipe Roughness Calculator on the Tools menu (see the PEW User Guide for more information) to automatically paste the required roughness into the calculation based on the selection of pipe material and surface Static Head and Fittings Losses Static head loss This is the difference in elevation between the point of discharge and the point of entry to the pipe. Thus this number is positive if the pipe runs uphill and negative if it runs downhill. Fittings Loss This is the total K value for the pipe and should take into account pipe entry and exit effects, fittings losses, bends, Tee's etc. The Edit button displays a menu of fittings for which PEW currently has data. Enter the number of each type of fitting and the losses are automatically calculated. A figure can also be entered for miscellaneous losses. Only simple fittings are included involving no change in pipe diameter or branches. The figures for valves assume they are fully open. The help text for the valves supplies factors which can be used to calculate the head loss of a partially open valve which can be entered under miscellaneous losses (see section.1.6 for more information). PEW Reference Guide Page 13 of 16

14 Fluid Properties Density The actual density of the fluid at operating conditions is needed. Viscosity The actual viscosity of the fluid at operating conditions is needed. As an example, the viscosity of water varies between 0.3 and 1.8 cp Process Conditions Pressure Drop The measured or estimated pressure drop down the pipe is needed. The program does not cater for reverse flow conditions so the pressure drop must not be less than the static head loss. If this data is real, there may be plant data errors (static head errors), instrument errors or gas entrainment. Mass Flowrate The flowrate down the pipe Pipe Fittings Losses - Bends A circular bend is a quite smooth bend that turns through a right angle. A cut mitre has two elbows in it of 45 each. A 3 cut mitre has three elbows in it of 30 each. In each case, for a 45 bend multiply the figure by 0.7, for 180 bends by 1.4. Enter the figure under Miscellaneous losses. Radius/Diameter This is the ratio of the radius of curvature of the bend to the internal diameter of the pipe. Note. The radius of curvature is taken to the centre line of the pipe. The values given for the bends and elbows below are for turbulent flow in rough round pipes (Ref. R A Smith Estimation of pressure drop in pipe systems P/CP/4B ICI Engineering Dept. Design Code - for more details). Elbows A 30 elbow is a sharp turn through 30. A 45 elbow is a sharp turn through 45. A 60 elbow is a sharp turn through 60. A 90 elbow is a sharp turn through 90. Dead Leg of T A T-junction with one leg blanked off with only one entry and one exit of the same diameter (there is very little loss for flow past a blanked off branch). Flow into leg The flow is towards the blanked off part. Flow out of leg The flow is across the blanked off end. Page 14 of 16 PEW Reference Guide

15 .1.6. Pipe Fittings Losses - Valves Plug Valves - Rectangular Port Plug Valves The size of the port relative to the pipe area is shown in the prompt. Plug Valves - Circular Port Plug Valves For this data, the port size is the same as the pipe area. The values given for the following valves are all for turbulent flow through a fully open valve. Ref. R A Smith - Estimation of pressure drop in pipe systems P/CP/4B ICI Engineering Dept. Design Code - for more details. The adjustment factors for partly closed valves (from above ref.) are given for each valve type. To account for a partly open valve, multiply the heads lost by the factor and include the result in miscellaneous losses. Globe Valves There is no data for forged globe valves larger than two inches nominal diameter. % open Factor (approx.) Gate Valves Here the seat area is assumed to be the same as the pipe area (There is no data for valves smaller than four inches nominal diameter). % open Factor (approx.) Diaphragm Valves % open Factor (approx.) Butterfly Valves The thickness of the valve is shown in the prompt. % open Factor (approx.) Miscellaneous Losses This can be used to give any losses not specifically listed on the form. PEW Reference Guide Page 15 of 16

16 .1.7. Calculation Method Nomenclature Symbol Definition L Length of pipe T l Lining thickness H Static head loss K Fittings loss as velocity heads ρ Density of the liquid µ Viscosity of the liquid D Internal diameter of pipe itself, that is, with no allowance for any lining M Mass flow through the pipe r Roughness of the pipe wall P Pressure drop along the pipe v Velocity R Relative roughness of the pipe wall. Basic Theory The pressure drop is calculated from the standard relationship: Pressure Drop = Frictional loss + Static head loss + Velocity head loss, that is, ρυ Ρ = Κ + ρg Η + 0 where: 4M = πd ρ ν The velocity head term is zero as there is no change in diameter or density (r) along the pipe. The change in static head ( H) is supplied. The only complication is the calculation of the frictional loss, represented in the above equation by the term ΣK. ΣK is the number of velocity heads (that is, number of ½.ϑ.v ) lost due to the straight parts of the pipe and the various fittings such as bends, valves, blanked off T-junctions etc. K can be summed from the contributions made by these various items. While the straight pipe K is calculated using various equations, the fittings K is usually simply looked up in a table of empirical values. This gives the pressure drop given all other data. Where the pressure drop is known, and the diameter, flowrate or roughness need to be calculated, the same equations are used but the required variable is guessed and the program iterates to match the calculated pressure drops for two successive guesses. Page 16 of 16 PEW Reference Guide

17 Pipe Frictional Loss This is calculated from the relationship: K = FL D T l using the above terminology. The friction factor (F) is in turn calculated from various correlations depending on the flow regime (laminar, transitional or turbulent) and the roughness of the pipe. In the laminar flow region (R e <000) F is calculated from: F = where: R e = 64 R e 4M π( D - T )µ l In the turbulent region (R e >4000) wall roughness becomes important and the Colebrook-White equation is used: 1 F = log 10 R R F e where: R = r D T l In the transition region (000< R e <4000) F is calculated at R e =000 and R e =4000 using the appropriate equations above. A cubic function is fitted such that it (and its first derivative) are continuous at these two points (that is, so that the function smoothly runs into both laminar and turbulent regions). F is then calculated from this function. This method is also used by the PEL program FLONET. It is important to note that there are several friction factors in general use. They can easily be distinguished by the expression used to calculate them in the laminar flow region - there are friction factors calculated as 3/ R e, 16/ R e and even 8/ R e, rather than 64/ R e as in PEW. It does not matter which is used, as long as it is used consistently, but be aware of this when comparing the PEW friction factors with values from other sources. PEW Reference Guide Page 17 of 16

18 .1.8. Possible Errors in the Calculation Failure to converge This is normally due to an estimate of the calculated variable being of the wrong magnitude. Try adjusting the estimate to your estimate of the answer. If that fails, call the Hotline (see page for contact numbers). This error is very rare. If the flowrate is too small for the pressure drop (or the pressure drop too large for the flow) the implied frictional loss may be greater than that which can be provided by roughness alone. In such a case, the program will find the calculated roughness or diameter is such that the roughness would meet in the middle of the pipe (that is, R>½). In this case, check the flow and pressure drop. Static head loss less than pressure drop The pressure drop is assumed to include the static head loss, so specifying a head loss greater than the pressure drop is inconsistent. Check these two data items. Friction factor or roughness calculated as a negative number This implies the flow is too large for the given pressure drop so one of these is probably incorrect. Remember the losses form part of the pressure drop. Flow laminar Roughness cannot be calculated. Flowrate in the laminar regime is independent of roughness so there is no way of deducing it from the data that implies laminar flow. Page 18 of 16 PEW Reference Guide

19 .1.9. Other Relevant Programs See the Compressible Flow calculation in PEW for an approximate calculation of the flow of compressible fluids in a pipe (see section. for more information). The following PEL programs also give more detailed models and should be used if the relevant assumptions are invalid for your problem or for critical applications: VISFLO This program: Calculates incompressible flow and heat transfer coefficients for very viscous flow. Includes non-newtonian flow models. Calculates flow or pressure drop. FLONET This program: Calculates incompressible or isothermal compressible flow in a network of pipes. Does not handle sonic flow. ADRIAN This program: Can perform relief calculations. Calculates adiabatic or isothermal compressible flow in limited pipe networks. Handles sonic flow and calculates all pressure discontinuities. PIPER This program: Calculates the pressure changes with flow of a liquid and two-phase mixture of gas through an unbranched piping system. Makes allowance for heat transfer through the pipe wall and change of phase for any point in the system. Variations of phase composition and physical properties with temperature and pressure are accounted for during the calculation. Handles sonic flow. See Appendix A for an overview of choosing a fluid flow program. PEW Reference Guide Page 19 of 16

20 .. Compressible Flow..1. Scope of Compressible Flow Calculation This program calculates any of inlet/outlet pressure, mass flowrate or pipe diameter for adiabatic or isothermal flow of a compressible fluid along a circular cross-section pipe. Data for the losses in various bends and fully open valves are included, but expansions, contractions and T-junctions are not as these involve change in diameter or flowrate. It should not be used for Mach numbers much above Source of Theory This program is based on the Mond program MCH0 that used to run on the DEC-10. Source: MCH0 user guide, version 1, September Reference: ICI Fluid Flow Brochure (1950)...3. Assumptions 1. The calculations are limited to flow in circular cross-section pipes of a single diameter.. The Mach number must be significantly less than The pipe length must be greater than ten times the internal diameter so that end effects can be neglected. 4. Only single phase fluids can be considered. 5. The fluid is assumed to behave like an ideal gas. For real gases the biggest error is the variation of Gamma with temperature and pressure so as good an average as possible should be used. 6. The friction factor is assumed constant. This is a safe assumption as long as the viscosity does not vary much along the pipe...4. Input Data Title, Calculated Variable and Type of Flow Title This is only used to identify each calculation. It is not essential. Calculated Variable The program calculates compressible flow along a cylindrical pipe. It will calculate any one of the following, given the other three: Flowrate Pipe internal diameter Inlet pressure Outlet pressure Page 0 of 16 PEW Reference Guide

21 Flow Mode 1. The flow can either adiabatic or isothermal.. For higher Mach numbers adiabatic theory is normally preferred as smaller errors are likely than for other conditions. 3. The isothermal theory is most suitable when pressure and velocity changes along the pipe are small relative to the pressure and velocity of the fluid. 4. For low Mach numbers, incompressible flow theory provides sufficiently accurate results Pipe Details The pipe dimensions must be provided in the appropriate boxes. The dimensions required are: The actual length of the pipe The internal pipe diameter - remembering to take into account any lining thickness The pipe roughness Fittings losses. The value of the pipe roughness depends on the material of construction of the pipe. Typical values for various materials are: Material of construction Roughness (mm) Roughness (in) Drawn tubing ( plastics ) Commercial steel tube Cast Iron Concrete, scaled pipes The fittings losses value is the total K value for the pipe and should take into account pipe entry and exit effects, fittings losses, bends, Tee's etc. If the Edit Fittings button is selected, the number and size of each fitting type can be entered and the losses are automatically calculated. A figure can also be supplied for miscellaneous losses which can include items such as partially open valves. Currently only simple fittings are included involving no change in pipe diameter or branches and the figures for valves assume they are fully open Fluid Properties The Density and Viscosity of the fluid are needed. Density The density at 0 C and 1 bara should be given as the calculation uses ideal gas theory to calculate the densities at operating conditions from this value. Viscosity The viscosity at mean operating conditions is needed. This implies that some idea of the answers is needed before running the program. As an example, the viscosity of steam is approximately 0.0 cp. The ratio of specific heats, gamma or Cp/Cv is needed for any compressible flow calculations. PEW Reference Guide Page 1 of 16

22 Process Conditions Inlet Pressure and Outlet Pressure Either the measured or the target value is required for each of these. The program will reject the input if the outlet pressure is greater than the inlet pressure. Inlet Temperature The inlet temperature is needed to calculate the actual density and, for adiabatic flow, the temperature loss. Mass Flowrate The mass flowrate down the pipe is needed as the flow key. A volume flowrate cannot be used as any of the conditions input can affect the actual mass flowrate...5. Pipe Fittings Losses - Bends Bends A circular bend is a quite smooth bend that turns through a right angle. A cut mitre has two elbows in it of 45 each. A 3 cut mitre has three elbows in it of 30 each. In each case for a 45 bend multiply the figure by 0.7 and for 180 bends by 1.4. Enter the figure under Miscellaneous losses. Radius/Diameter This is the ratio of the radius of curvature of the bend to the internal diameter of the pipe. The radius of curvature is taken to the centre line of the pipe. The values given for the bends and elbows below are for turbulent flow in rough round pipes (see R A Smith Estimation of pressure drop in pipe systems P/CP/4B ICI Engineering Dept. Design Code for more details). Elbows A 30 elbow is a sharp turn through 30. A 45 elbow is a sharp turn through 45. A 60 elbow is a sharp turn through 60. A 90 elbow is a sharp turn through 90. Dead leg of T A T-Junction with one leg blanked off it only has one entry and one exit of the same diameter. There is very little loss for flow past a blanked off branch. Flow into leg: Flow is towards the blanked off part. Flow out of leg: Flow is across the blanked off end. Page of 16 PEW Reference Guide

23 ..6. Pipe Fittings Losses - Valves Plug Valves - Rectangular Port Plug Valves The size of the port relative to the pipe area is shown in the prompt. Plug Valves - Circular Port Plug Valves For this data, the port size is the same as the pipe area. The values given for the following valves are all for turbulent flow through a fully open valve. See R A Smith - Estimation of pressure drop in pipe systems - P/CP/4B ICI Engineering Dept. Design Code for more details. The adjustment factors for partly closed valves (from the above ref.) are given for each valve type. To account for a partly open valve, multiply the heads lost by the factor and include the result in miscellaneous losses. Globe Valves There is no data for forged globe valves larger than two inches nominal diameter. % open Factor (approx.) Gate Valves Here the seat area is assumed to be the same as the pipe area. There is no data for valves smaller than four inches nominal diameter. % open Factor (approx.) Diaphragm Valves % open Factor (approx.) Butterfly Valves The thickness of the valve is shown in the prompt. % open Factor (approx.) Miscellaneous Losses This can be used to give any losses not specifically listed on the form. PEW Reference Guide Page 3 of 16

24 In both isothermal and adiabatic modes the calculations deal with subsonic compressible fluid flow in a circular cross-section pipe. The calculations assume that the dynamic viscosity along the pipe is constant and the gas is ideal. Nomenclature Symbol Definition L Pipe length r Roughness of pipe wall K Velocity head losses in fittings; can be supplied as a list of fittings ρ Density of fluid at 0 C and 1 bara µ Viscosity of fluid at operating conditions γ Gamma (Ratio of specific heats Cp/Cv) T Inlet temperature D P in P out M F R e R Mach in H1 H Pipe diameter Inlet pressure Outlet pressure Mass flow Friction Factor Reynolds number Relative roughness Inlet Mach number. Total loss factor of pipe, velocity heads. Total head loss. ΣK V ρ in v in Velocity head loss due to bends, valves etc. Ratio of inlet to outlet velocity. Fluid density at pipe inlet. Fluid velocity at pipe inlet. Frictional Losses Frictional losses are characterised in the same way as for incompressible fluid flow, that is: Laminar Region R e < 000 F = 64 R e (1) where: R e = 4M πdµ Page 4 of 16 PEW Reference Guide

25 Turbulent Region R e > 4000 The Colebrook-White equation is applied: 1 F R.51 = log 10 + () 3.7 R e F where: R = r/d Transition Region 000 < R e < 4000 The variation of F with Re is considered to be a cubic function such that it, and its first derivative, are continuous at the laminar-transitional and transitional-turbulent limits. This method of calculating frictional losses is identical to that used in the PEL program FLONET and in the incompressible flow calculation in PEW. Calculation of Mach Number The Mach Number is calculated from: where: Mach = v (3) γp ρ 4M = πd ρ v Estimation of Critical Flow Conditions At critical flow (that is, the exit Mach number is unity for adiabatic flow and 1/g for isothermal flow) the ratio of outlet pressure to inlet pressure is: For adiabatic flow: P P out in = Mach in + ( γ ) 1 Mach 1+ γ in (4) For isothermal flow: P P out in = Mach in γ (5) PEW Reference Guide Page 5 of 16

26 Estimation Of Pressure Drop The total loss factor for frictional losses ( H1 ) in the pipe is given by: FL H 1 = + K (6) D Static head losses are assumed to be insignificant in a gas. The total loss factor (H) for any particular flow is calculated as follows: P P out in γ 1 1 = V 1+ 1 Mach V in (7) For adiabatic flow: H = 1 γ + + Mach γ in 1 γ 1 γ 1 ( 1 V ) + + log V e (8) For isothermal flow: P out P in 1 Pin Pout H = + log e (9) ρ v Pin in in Calculation Procedure Equations 1-9 are initialised with an estimate of the unknown variable (P in, P out, M or D) and evaluated iteratively until H1 and H are equated...7. Other Relevant Programs The following PEL programs give more detailed models than the PEW calculations. They should be used if the relevant assumptions are invalid for the problem or for critical applications. FLONET Calculates incompressible or isothermal compressible flow in a network of pipes. Does not handle sonic flow. ADRIAN Can perform relief calculations. Calculates adiabatic or isothermal compressible flow in limited pipe networks. Handles sonic flow and calculates all pressure discontinuities. PIPER Calculates the pressure changes with flow of a liquid and two-phase mixture of gas through an unbranched piping system. Makes allowance for heat transfer through the pipe wall and change of phase for any point in the system. Variations of phase composition and physical properties with temperature and pressure are accounted for during the calculation. Handles sonic flow. Page 6 of 16 PEW Reference Guide

27 .3. Gravity Flow.3.1. Scope of Gravity Flow Calculation Calculates one of the fluid flowrate, fluid level or pipe diameter in a sloping container. It can be used for both partially or full pipes and for ducts. It is limited to accurate results for Froude numbers under 0.5 although it will provide results for all Froude numbers..3.. Source of Theory The following publication provided the source: 1. Chemical Engineering Calculations A31880 and A31883 C G Dickinson, 9 th October 1986, amended 1 May Assumptions The main assumption of the calculation is that the potential energy lost by the flow along the downward inclined pipe is dissipated exactly by the frictional forces incurred. The temperature, density and viscosity assumed constant along the length of the duct. If the program is to calculate the pipe diameter then it assumes it is to be a standard British size. The routine only handles one duct and cannot handle bends. It also ignores the gas flow above the liquid Input Data Dimensions and Fluid Properties Title This is only used to identify each calculation. It is not essential. Container Type This can be a pipe (a closed vessel) or a duct (an open vessel). Calculated Variable Define the unknown variable. This can be the mass flowrate in the container, the depth of the fluid in the container or, in the case of a pipe, the diameter of the pipe. Dimensions Lining thickness If the pipe or duct is unlined or the lining thickness has been included in the diameter, enter a value of 0.0. A typical epoxy or ebonite lining has a thickness of 6 mm. Roughness of wall The value depends on the material of construction with typical values as follows: Material of Construction Roughness (mm) Roughness (in) Drawn tubing (plastics) Commercial steel tube Cast Iron Concrete, scaled pipes PEW Reference Guide Page 7 of 16

28 Slope A positive fraction is required. A slope of 0.05 (1:40) is recommended as any larger will lead to wave formation. Smaller slopes are more difficult to install though slopes of (1:00) are commonly found in chlorine cellroom headers Fluid Properties Density The density of the fluid at the operating conditions is required. Viscosity The viscosity of the fluid at the operating conditions is required Pipe Conditions Pipe Diameter The internal diameter of the pipe is required if this is not the calculated variable. This is the actual inner diameter as the lining thickness is subtracted if lining is present. If the pipe diameter is to be calculated then the program assumes it to be an ANSI 150 standard carbon steel pipe as follows: 1-1+ in Schedule 80-6 in Schedule in Schedule in Standard Wall 0,4 in Schedule 80 Above 4 in Metric sizes Relative Depth of Liquor If the flowrate is the calculated variable, the observed relative depth is required, that is, the observed depth of liquid / pipe diameter. Values above 0.8 can mean that the maximum stable flow limitation is being approached. Maximum Relative Depth of Liquor If the pipe diameter is the calculated variable, then the maximum relative depth allowable before a larger pipe size is required, should be entered. Values above 0.8 can mean that the maximum stable flow limitation is being approached. Liquor Flowrate The actual mass flowrate is required. If this is not available use the calculated variable Duct Conditions Duct Width Liquor Level Liquor Flowrate The duct width is required; the program subtracts the lining thickness if one is specified. The actual fluid level in the duct is required, if not the calculated variable. The actual mass flowrate is required, if not the calculated variable. Page 8 of 16 PEW Reference Guide

29 .3.5. Calculation Method Nomenclature Symbol Definition Unit ρ Fluid density kg/m 3 µ Fluid viscosity N.s/m l Lining thickness mm R Roughness of wall mm i Slope of pipe For pipes: Symbol Definition Unit d Pipe diameter mm q Liquor flowrate kg/s h/d Relative pipe depth For ducts: Symbol Definition Unit w Duct width mm q Mass flowrate kg/s dep Depth in duct mm Q Volumetric flowrate = q/ρ m 3 /s V Liquid velocity m/s a Cross-sectional area of flow m g Acceleration due to gravity m/s m Mean hydraulic depth m Kn Kinematic viscosity = µ /ρ m /s Basic Theory The uniform flow is characterised by two equations, the first is the overall mass balance: V = Q / a and the second is the frictional losses: V = 3gmi log R 14.8m 0.Kn + m gmi For a rectangular duct the two geometric factors, a and m, are defined as: a = w * dep and m = w * dep / ( w+*dep ) In pipes the geometric factors are given by: a= (β-cosβsinβ)d /4 PEW Reference Guide Page 9 of 16

30 where the angle ß is defined as: h β = arccos 1 d d h w This can be seen from the simple geometry of a circle, where 'h' is the depth of the liquid and 'd' is the diameter. The hydraulic mean depth is defined as the ratio of the cross-sectional area of flow and the wetted perimeter. The wetted perimeter P is given by: where: P = ß d β = radians. This then gives: m = (b-cosβsinβ) 4β d The program checks the Froude number to see if a loss of surface head will occur due to surface waves. These losses are usually small but if the Froude number approaches 1 they become significant. For flow in open rectangular ducts the Froude number (Fr) is given by: where: Fr = v / c c = velocity of a small wave on the surface v = bulk liquor velocity. c is given by: c = gh giving Fr = v gh Page 30 of 16 PEW Reference Guide

31 For pipes this equation can also be used if 'h' is replaced by h b, where: d(β-cosβsinβ) h b = 4sinβ The system also runs a number of checks for stability of the flow and Froude number. Unstable flow can occur if the pipe is partially full, 90-97%, as here the frictional losses can be less than those in a full pipe. The system checks for this case by calculating the carrying capacity of the full pipe by inserting p for b and evaluating the two geometric factors. It then uses these to calculate the maximum stable flowrate using the equation: πd 4R 0.Kn Qmax = 8gdi log d d gdi 8 If the volumetric flowrate was an input value this is automatically checked and the value is not accepted if the flowrate exceeds the maximum value as there are then two real solutions possible. If the flowrate is the calculated variable then a warning is flagged if the calculated result exceeds 80% of the maximum stable amount. Once the calculation has converged, the Froude number is checked and a message is flagged if the number exceeds 0.5. In this type of pipe the Froude number is found to be a function of the dimensionless superficial volumetric flux of the liquid, J, as given by: d J = Q gd 4 The ratio of Froude number to J is then given by: 1 Fr J d = h Possible Errors in the Calculation d h d h All areas that give rise to errors are flagged by the routine and warning messages are issued as to the likely consequences. 3 PEW Reference Guide Page 31 of 16

32 .4. Manifold and Symmetrical T junctions.4.1. Scope of Manifold and Symmetrical T junctions Calculations These calculations give the pressure drop through various types of T-junction in round pipes. Both manifold flow and symmetrical flow are considered..4.. Source of Theory The following publications provided the sources: 1. Manifold T-Junctions: HTFS report DR35 - Header and Manifold Design Part 1a R A Smith. Ref. AERE - R 9713 Feb Symmetrical T-Junctions: Estimation of Pressure Drop in Pipe Systems R A Smith 1977, revised ICI Engineering department NE group Design Guide Ref. P/CP/4B Assumptions The following assumptions are made: 1. Sonic flow is not reached through the fitting. The calculation displays the velocities so that this can be checked.. The fluid is single phase, with no phase change occurring. For a two phase flow call the Hotline for advice (see page for contact details). 3. Flow is well established turbulent flow. 4. The correlations used have been derived for turbulent flow and are likely to give significantly low results as the laminar flow region is approached. Therefore, PEW does not save any results produced with Re<100 when laminar flow is normally well established although it does display the results immediately after calculation to give what information it can. 5. For Re between 100 and PEW warns that the results may be low but save them as usual Input Data Symmetrical T Junction Flows The calculation is valid for T-junctions consisting of a straight manifold of constant bore with a branch pipe of the same bore at right angles to it. The junction should have a sharp edged join with all the flow entering or leaving via the branch. They are two types combining or dividing. Flow is symmetrical about the branch, either entering or leaving through both arms of the T. See the Calculation Method (section.4.6) for an example of the configuration. Page 3 of 16 PEW Reference Guide

33 These correlations are only valid for turbulent flow, so PEW checks this is the case and gives a warning if it is not. If the Reynolds number in any part of the T falls below 4000, the resulting pressure drops, although displayed immediately on completion of the calculation, are not shown in the summary to avoid misunderstandings. Other Points The title is optional to identify a particular calculation. Combining or dividing flow must be specified. Mass flow into the junction, either through the branch (for dividing flow) or through one leg of the T (one side of the manifold) for combining flow must be supplied. For combining flow, this must be less than the flow out through the branch. Mass flow out of the T-junction, either through the branch (for combining flow) or through one leg (for dividing flow) must also be provided. For dividing flow this must be less than the flow in through the branch. The branch and the main part of the T-junction are assumed to have the same diameter Fluid Properties Inlet and Outlet Densities The density of the inlet and outlet fluid should be given at the operating conditions. Note these correlations are for single phase flow only. Viscosity This is only required to check the Reynolds Number if in doubt make it too large rather than too small Calculation Method for Symmetrical T-junctions The equations here just give static (measured) pressure drop and are: Combining Flow V in V branch Figure 1 Combining Flow Pressure drop: P = ρinv in 1.5vinvbranchρbranch + 1.5ρ branch v branch PEW Reference Guide Page 33 of 16

34 Dividing Flow V out Figure Dividing Flow Pressure drop: P = 0.65ρ out v out where out refers to the relevant leg of the T. These come from page 9 of the R A Smith Design code Input Data Manifold T Junction Flows The calculation is valid for T-junctions consisting of a straight manifold of constant bore with a (smaller) branch pipe at right angles to it. They are of two types, combining or dividing (see section.4.6 for diagrams of these configurations). The correlations are likely to over rather than under-estimate the pressure drop, but are only valid for turbulent flow. If the Reynolds number in any part of the T falls below 4000, the resulting pressure drops, although displayed immediately on completion of the calculation, are not shown in the summary to avoid misunderstandings. The title is an optional name to identify a particular calculation. Combining or dividing flow must be specified. The mass flow into the T along the manifold and the mass flow away from the T along the manifold are required. PEW calculates the branch flow from the mass flow into the manifold and the mass flow out of the manifold. If the two known flowrates include the branch flow, the calculator can be used to calculate the missing manifold flow. Manifold Diameter This is the diameter of the main pipe this is assumed to be straight with the branch at right angles. Branch Diameter This is the diameter of the branch. This must not be greater than the manifold diameter. The branch-manifold join is assumed to be sharp-edged with no rounding. Page 34 of 16 PEW Reference Guide

35 Fluid Properties Densities The density of the fluid in the inlet and outlet manifolds should be supplied at the operating conditions. The density of the fluid in the branch at the operating conditions is also needed these correlations are for single phase flow only. Viscosity This is only required to check the Reynolds Number if in doubt, make it too large rather than too small Calculation Method for Manifold T-junctions These can be either combining or dividing and the pressure drop to the branch or to the outlet manifold can be calculated. Both the static (measured) pressure drop and the frictional pressure drop are calculated. The equations used (v-velocity, r-density) are: Dividing Junctions V in V out V branch Figure 3 Dividing Junctions Manifold static pressure drop: P = k d ( ρ v ρ v ) out out Manifold frictional pressure drop: P = where: ( )( ) in in 1 k x x d b b in in ρ v k d = 1 0.7x b 1 4 and: massflowin branch x b = combinedmassflow Branch static pressure drop: P = 0.75ρ branch v branch PEW Reference Guide Page 35 of 16