[XLS]Fluid Flow - Pipe sizing · Web viewOrifice discharge pressure Permanent Loss Orifice...

Chapter 1: Fluid FlowRules of Thumb for Chemical Engineers, 5th Edition

by Stephen Hall

This Excel workbook includes Visual Basic for Application function subroutines.Macros must be enabled for them to work.

The following Text Boxes contain the syntax for the functions.Copy them to the worksheet where you want to use the functions for ready reference.

Function Subroutines in SI Units

Function NReSI(W, mu, d, Optional ro, Optional Tin, Optional Mw, Optional p)' W = Flowrate in kg/h' mu = Viscosity in mPa-s' d = PipeID in mm' ro = density in kg/m3 (required for liquid)' Tin = temperature, deg C (required for gas) - default 20 deg C' Mw = molecular weight (required for gas) - default 29' p = pressure, kPa (required for gas) - default 1000 kPa

Function FrictionSI(epsilon, NRe, d)' epsilon = Surface roughness is in units m' d = PipeID is in units mm

Function PDSI(W, Pin, Pout, d, L, f, Optional Density, Optional Tin, Optional Mw, Optional Gamma, Optional Isothermal)' Pressure Drop due to friction in a round pipe (adiabatic for compressible flow)' with the following arguments' Specify two of the following three; function will compute the third' W = mass flow rate, kg/h' Pin = inlet, or upstream, pressure, kPa' Pout = outlet, or downstream pressure, kPa' Pipe properties' d = pipe diameter, mm' L = pipe length, m' f = Darcy friction factor' Fluid properties' Density (optional) -- specify for liquids, kg/m3' Tin (optional) -- specify for gas, inlet temperature, deg C (default to 20)' Mw (optional) -- specify for gas, molecular weight (default to 29 for air)' Gamma (optional) -- specify for gas, ratio of Cp/Cv (default to 1.4)' Isothermal (optional) -- any value results in isothermal compressible calc, if missing then adiabatic calc

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Function Subroutines in US Units

Function NReUS(W, mu, d, Optional ro, Optional Tin, Optional Mw, Optional p)' W = Flowrate in lb/h' mu = Viscosity in cP' d = PipeID in inches' ro = density in lb/ft3 (required for liquid)' Tin = temperature, deg F (required for gas) - default 60' Mw = molecular weight (required for gas) - default 29' p = pressure, psia (required for gas) - default 115

Function FrictionUS(epsilon, NRe, d)' epsilon = Surface roughness is in units feet' d = PipeID is in units inches

Function PDUS(W, Pin, Pout, d, L, f, Optional Density, Optional Tin, Optional Mw, Optional Gamma, Optional Isothermal)' Pressure Drop due to friction in a round pipe (adiabatic or isothermal for compressible flow)' with the following arguments' Specify two of the following three; function will compute the third' W = mass flow rate, lb/hr' Pin = inlet, or upstream, pressure, psia' Pout = outlet, or downstream pressure, psia' Pipe properties' d = pipe diameter, inches' L = pipe length, feet' f = Darcy friction factor' Fluid properties' Density (optional) -- specify for liquids, lb/ft3' Tin (optional) -- specify for gas, inlet temperature, deg F (default to 60)' Mw (optional) -- specify for gas, molecular weight (default to 29 for air)' Gamma (optional) -- specify for gas, ratio of Cp/Cv (default to 1.4)' Isothermal (optional) -- any value results in isothermal compressible calc, if missing then adiabatic calc

Function PDUS(W, Pin, Pout, d, L, f, Optional Density, Optional Tin, Optional Mw, Optional Gamma, Optional Isothermal)' Pressure Drop due to friction in a round pipe (adiabatic or isothermal for compressible flow)' with the following arguments' Specify two of the following three; function will compute the third' W = mass flow rate, lb/hr' Pin = inlet, or upstream, pressure, psia' Pout = outlet, or downstream pressure, psia' Pipe properties' d = pipe diameter, inches' L = pipe length, feet' f = Darcy friction factor' Fluid properties' Density (optional) -- specify for liquids, lb/ft3' Tin (optional) -- specify for gas, inlet temperature, deg F (default to 60)' Mw (optional) -- specify for gas, molecular weight (default to 29 for air)' Gamma (optional) -- specify for gas, ratio of Cp/Cv (default to 1.4)' Isothermal (optional) -- any value results in isothermal compressible calc, if missing then adiabatic calc

SI Units US UnitsInputs

Flow Rate kg/h 10,000.0 lb/h 22,000.0 Viscosity mPa-s 1.2 cP 1.2 Pipe Diameter mm 38.1 in 1.5 Density kg/m3 961.5 lb/ft3 60.0

OutputDelta P Bar/100 m 1.83 psi/100 ft 8.09

Problem Statement:Calculate pressure drop per 100 m or 100 ft using the shortcut formula

Inputs Liquid GasParameter Units Example 1 Example 2Mass Flow Rate kg/h 10,000.0 1,200.0 Viscosity mPa-s 1.2 0.011 Pipe Diameter mm 38.1 26.6 Density kg/m3 961.0 Temperature C 40.0 Molecular Weight kg/kgmol 16.04 Pressure kPa, absolute 2,200.0

OutputReynolds Number dimensionless #VALUE! #VALUE!

Problem Statement:Calculate Reynolds Number using VBA function call.

=NReSI(D8,D9,D10,D11) =NReSI(E8,E9,E10,,E12,E13,E14)

US Customary Units Liquid GasUnits Example 1a Example 2alb/h 22,000.0 2,645.0 cP 1.2 0.011 in 1.5 1.047 lb/ft3 60.0 F 104.0 lb/lbmol 16.04 psia 319.0

#VALUE! #VALUE!

=NReSI(E8,E9,E10,,E12,E13,E14)=NReUS(I8,I9,I10,I11) =NReUS(J8,J9,J10,,J12,J13,J14)

Inputs LiquidParameter Units Example 3Mass Flow Rate kg/h 290.0 Viscosity mPa-s 1.2 Pipe Diameter mm 38.1 Density kg/m3 961.0 Temperature CMolecular Weight kg/kgmolPressure kPa, absolute

Pipe Roughness m 0.0000457

OutputReynolds Number dimensionless #VALUE!

Darcy Friction Factor dimensionless #VALUE!

Problem Statement:Calculate Darcy Friction Factor using VBA function call.

=FrictionSI(D16,D19,D10)

US Customary Units LiquidUnits Example 3alb/h 22,000.0 cP 1.2 in 1.5 lb/ft3 60.0 Flb/lbmolpsia

ft 0.00015

#VALUE!

#VALUE!

=FrictionUS(I16,I19,I10)

Inputs Liquid GasParameter Units Example 4 Example 5Mass Flow Rate kg/h 10,000.0 1,200.0 Pressure in (upsteam) kPa, absolute 700.0 2,200.0

Viscosity mPa-s 1.2 0.011 Pipe Diameter mm 38.1 26.6 Equivalent Length of Pipe m 40.0 60.0 Density kg/m3 961.0 Temperature C 40.0 Molecular Weight kg/kgmol 16.04 Cp/Cv 1.35

Pipe Roughness m 0.0000457 0.0000457


Darcy Friction Factor dimensionless #VALUE! #VALUE!

Pressure Out, given Mass Flow and Pressure in #VALUE! #VALUE!

Problem Statement:Calculate Pressure Drop due to Friction

=PDSI(D8,D9,,D12,D13,D24,D14)

=PDSI(E8,E9,,E12,E13,E24,,E15,E16,E17)

US Customary Units Liquid GasUnits Example 4a Example 5alb/h 22,000.0 3,080.0 psia 101.5 319.0

cP 1.2 0.011 in 1.5 1.047 ft 131.0 197.0 lb/ft3 60.0 F 104.0 lb/lbmol 16.04

1.35

ft 0.00015 0.00015

#VALUE! #VALUE!

#VALUE! #VALUE!

#VALUE! #VALUE!

=PDUS(I8,I9,,I12,I13,I24,I14)

=PDUS(J8,J9,,J12,J13,J24,,J15,J16,J17)

Inputs GasParameter Units Example 5GUESS Mass Flow Rate kg/h 1200Pressure in (upsteam) kPa, absolute 2200Pressure out (downstream) 1340Viscosity mPa-s 0.011Pipe Diameter mm 26.6Equivalent Length of Pipe m 60

Temperature C 40Molecular Weight kg/kgmol 16.04Cp/Cv 1.35

Pipe Roughness m 0.0000457



Mass Flow, given Pressure in and out #VALUE!

Difference between GUESS and calculated rate, E8-E26 #VALUE!

Problem Statement:Calculate Flow Rate given upstream and downstream pressures

=PDSI( ,E9,E10,E12,E13,E24,E14,E15,E16,E17)

Use Goal Seek to find a value for the Guessed flow rate (Cell E8) that equals the calculated flow rate (Cell E26). Notice that Reynolds Number is calculated using the Guess.

US Customary Units GasUnits Example 5alb/h 3,080.4 psia 319.0 psia 116cP 0.011 in 1.047 ft 197.0

F 104.0 lb/lbmol 16.04

1.35

ft 0.00015

#VALUE!

#VALUE!

#VALUE!

#VALUE!

Use Goal Seek to find a value for the Guessed flow rate (Cell E8) that equals the calculated flow rate (Cell E26). Notice that Reynolds Number is calculated using the Guess.

=PDUS( ,L9,L10,L12,L13,L24,,L15,L16,L17)

Inputs Liquid GasParameter Units Example 4 Example 5Mass Flow Rate kg/h 10,000.0 1,200.0 Pressure in (upsteam) kPa, absolute 700.0 2,200.0

Viscosity mPa-s 12.0 0.011 Pipe Diameter mm 50.0 26.6 Length of Pipe m 38.1 60.0 Density kg/m3 961.0 13.6 Temperature C 40.0 Molecular Weight kg/kgmol 16.04 Cp/Cv 1.35

Pipe Roughness m 0.0000457 0.0000457

Fittings Quantity90 deg, welded r/D = 1 6TEE, through branch (as elbow) 2Plug valve, straight 2Swing check, Vmin = 35 ro^0.5 1



Pressure Drop, given Mass Flow and Pressure in #VALUE! #VALUE!

Equivalent length of fittings m 14.80 7.87

Pressure Drop, equiv length method #VALUE! #VALUE!

Mass flux kg/m2-s 1,414.71 599.83 Velocity m/s 1.47 44.25

Fitting pressure loss kg/m2 #VALUE! #VALUE!kPa #VALUE! #VALUE!

Pressure Drop, 3-K method #VALUE! #VALUE!

Pressure Drop, Crane method #VALUE! #VALUE!

Problem Statement:Compare pressure drop calculations using equivalent length and K-value methods for fittings.

Eq L 3-K Methodtotal KfEx 4 Ex 5

(L/D)eq Km Ki Kd Total L/D20 800 0.091 4 120 #VALUE! #VALUE!20 800 0.28 4 40 #VALUE! #VALUE!18 300 0.084 3.9 36 #VALUE! #VALUE!

100 1500 0.46 4 100 #VALUE! #VALUE!296 #VALUE! #VALUE!

Pressure Drop, PaFlow Regime Equiv L Crane K 3-K

50 Laminar 0.060 0.043 0.051 100 Laminar 0.120 0.087 0.102 500 Laminar 0.598 0.446 0.525

1000 Laminar 1.196 0.921 1.089 2000 Laminar 2.392 1.960 2.331

10000 Turbulent 41.079 35.508 38.774 30000 Turbulent 284.129 257.934 278.315 50000 Turbulent 716.261 663.917 715.526 70000 Turbulent 1,328.928 1,247.301 1,344.249

Problem Statement:Compare pressure drop calculations using equivalent length and K-value methods for fittings.

US Customary UnitLiquidUnits Example 4alb/h 63,000.0 psia 101.5

cP 10.0 in 3.1 3 nominal sizeft 31.5 lb/ft3 112.5 F 127.0 lb/lbmol

Crane

ft Crane K ft 0.00015

0.019213 2.31 0.019213 0.77 #VALUE!0.019213 0.69 0.019213 1.92 #VALUE!

5.69 Delta P, pipe #VALUE!Velocity 3.03 f, full turbulence 0.017314983

Leq Crane K 3-K90 Ell 2 10.23 0.692599 #VALUE!Branch tee 1 5.11 0.3463 #VALUE!Swing check 1 25.57 1.731498 #VALUE!Plug valve 1 4.60 0.31167 #VALUE!3 x 1 reducer 1 822.68 57.92 57.92

868.19 61.00 #VALUE!

Delta P, comparison #VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! 1

Inputs LiquidParameter Units Example 6Mass Flow Rate kg/h 10,000.0

P0 Pressure in (upsteam) kPa, absolute 700.0 Viscosity mPa-s 1.2 Pipe Diameter mm 38.1 Equivalent Length of Pipe m 60.0 Density kg/m3 961.0 Temperature CMolecular Weight kg/kgmolCp/Cv

Pipe Roughness m 0.0000457 Orifice Diameter mm 19.1



P1 Pressure out (downstream) kPa, absolute #VALUE!V1 Velocity through orifice m/s 10.1

Sonic velocity m/sβ Orifice diameter ratio dimensionless 0.5 C Orifice Coefficient of Discharge dimensionless #VALUE!

rY Expansion factor dimensionless 1.0 P2 Orifice discharge pressure kPa, absolute #VALUE!P3 Permanent Loss kPa, absolute #VALUE!

DeltaP P1-P3 kPa #VALUE!

K flow coefficient dimensionless #VALUE!Equivalent Length m #VALUE!

Compare equivalent length ratio to pressure drop ratioPipe L / Orifice L #VALUE!Pipe Pressure Drop / Orifice Pressure Drop #VALUE!

Problem Statement:Calculate Permanent Pressure Drop Through Orifice

Pipe Header at 700 kPa absolute

60 m, 38.1 mm ID

P0

Result

Close enough, although not perfect

Stolz equation, Radius Taps

D31

Stolz equation, Radius Taps

60 m, 38.1 mm IDRO

P1

P2

P3

Close enough, although not perfect

Inputs Steam-Water at Saturated Conditions WaterTotal Mass Flux kg/m2-s 1,356.0 Quality Mass Fraction Vapor 0.5 Inlet Pressure Bar 1.01 Pipe Diameter mm 5.0 Equivalent Length of Pipe m 1.0 Pipe Roughness m 0.0000015 (Smooth Tube = 0.0000015 m)

Calculations / Property LookupParameter Units Total as Liq Vapor Props MixtureCross-sectional area m2 1.963495E-05Total Mass Flow Rate kg/h 95.8 Inlet Pressure kPa 101.0 Temperature C 97.4 Viscosity mPa-s 0.28 0.012 0.023 Molecular Weight kg/kgmol 18.0 Density kg/m3 998.7 0.6 1.2 Cp/Cv 1.31




Liquid PD Multiplier phi #VALUE!phi^2 #VALUE!

Pressure Drop, 2-Phase Flow kPA #VALUE!

Problem Statement:Calculate Pressure Drop due to Friction for Water-Steam Mixture

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11

10

100

1000

10000

1.01 Bar

6.89 Bar

34.4 Bar

68.9 Bar

103 Bar

138 Bar

172 Bar

207 Bar

221.2 Bar

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11

10

100

1000

10000

1.01 Bar

6.89 Bar

34.4 Bar

68.9 Bar

103 Bar

138 Bar

172 Bar

207 Bar

221.2 Bar

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

50

100

150

200

250

G=339

G=1356

G=5424

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

50

100

150

200

250

G=339

G=1356

G=5424

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

Awad

Janssen

Property Correlations for all correlations, t = deg CVapor Pressure: log(mm Hg) = A - B / (t+C)A B C

R12 6.99 918.17 253.38 R22 7.04 850.10 245.18 Water 8.31 1,986.50 268.74

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

Awad

Janssen

Reference: IPC2004-721

Comparison Case R12

2,000.0 0.9 6.00 50.0 1.0

(Smooth Tube = 0.0000015 m) 0.0000015 (Smooth Tube = 0.0000015 m)

Total as Liq Vapor Props Mixture0.001963495408494

14,137.2 600.0 22.0 0.20 0.013 0.015 120.9 1,325.3 29.6 32.8

1.17

#VALUE! #VALUE!

#VALUE! #VALUE!

#VALUE!

#VALUE!#VALUE!

#VALUE!

Phi^2Quality 1.01

0 10.03 46.4164529170.05 73.3322877010.08 111.18442840.11 147.185195030.15 193.407243

0.2 249.365252850.3 357.76001856

User inputs are in RED

Temperature, viscosity, and density are determined from correlation parameters in lookup table (down at the bottom of the worksheet). These are affected by the inlet pressure variable. It is assumed that the temperature is the saturation temperature at the pressure.

Calculations for Re, f, and pressure drop are performed in VBA subroutines -- other worksheets in this workbook verify that those subroutines are correct.

Clicking on the "Re-Run All Inputs" button at cell L35 runs a macro that runs the calculation on various combinations of inputs, based on the charts in IPC2004-721.

It seems like the only way to get a straight line (per the reference) for Figure 7 (Row 123) is to do the friction factor calculations once, then recalculate phi for a range of qualities (0 to 1) without recomputing the mixture viscosity and density for each quality.

0.6 670.814720450.8 875.24415635

1 1078.089605

Phi^2Quality 339

0 10.1 21.6534250950.2 38.3850694880.3 53.6973728250.4 68.2383666620.5 82.2854480210.6 95.9861279070.7 109.42928050.8 122.673018090.9 135.75760735

1 148.71218525

Phi^2Quality 2278

0 10.1 3.22501956550.2 5.33662512760.3 7.38660328340.4 9.39836089590.5 11.3843663610.6 13.351996190.7 15.3059474050.8 17.2493789520.9 19.184507397

1 21.112941761

Liquid Viscosity: ln(cP) = A + B / (C+t) Vapor Viscosity: ln(cP) = A + B / (C+t)A B C

(8.77) 5,134.3 693.01 (9.00) (4,611.86) (1,008.87) 20.79 46,143.5 (2,064.89) (3.47) (278.74) 286.66 4.34 6,927.32 (1,332.33) (4.92) (200.49) (502.57)

6.89 34.4 68.9 103 138 172 207 221.21 1 1 1 1 1 1 1

8.2246286814 2.481189524 1.724209 1.471297363 1.341214662 1.26543664 1.21338118 1.19694412.648349219 3.423306769 2.1931 1.779418297 1.565753054 1.44090455 1.354939381 1.32775518.938059212 4.787807808 2.879825 2.233848908 1.898624121 1.70203456 1.566278589 1.5232724.952165389 6.108328833 3.550296 2.68027314 2.22725028 1.96085338 1.776471526 1.71797132.688893582 7.818775751 4.424186 3.265040944 2.659601824 2.302653 2.05503895 1.97635542.057764239 9.897995236 5.491334 3.982109516 3.191936121 2.72512011 2.400697587 2.29747260.186021611 13.92653169 7.565445 5.380827356 4.23461845 3.55633082 3.084285707 2.933941

User inputs are in RED

Temperature, viscosity, and density are determined from correlation parameters in lookup table (down at the bottom of the worksheet). These are affected by the inlet pressure variable. It is assumed that the temperature is the saturation temperature at the pressure.

Calculations for Re, f, and pressure drop are performed in VBA subroutines -- other worksheets in this workbook verify that those subroutines are correct.

Clicking on the "Re-Run All Inputs" button at cell L35 runs a macro that runs the calculation on various combinations of inputs, based on the charts in IPC2004-721.

It seems like the only way to get a straight line (per the reference) for Figure 7 (Row 123) is to do the friction factor calculations once, then recalculate phi for a range of qualities (0 to 1) without recomputing the mixture viscosity and density for each quality.

112.37701881 25.49339436 13.52198 9.405154978 7.245188894 5.96923649 5.084696574 4.804169146.37112572 32.99858782 17.37767 12.00665506 9.191022614 7.53131397 6.385775821 6.024389180.06197041 40.42083912 21.18376 14.57066284 11.10631356 9.06799534 7.667059217 7.227597

Sonic Velocity

489.4987227 m/s

Pipe flow area 1.9635E-05 m2Velocity, m/s

1356 5424 Mass Flux Density 339 1356 5424 kg/m2-s1 1 998.66 0.34 1.36 5.43

22.971645115 24.52214386 5.87 57.75 231.02 924.06 YELLOW = > Mach 0.342.057764239 46.41929046 2.94 115.17 460.67 1,842.69 RED > Mach 160.186021611 67.86402318 1.96 172.58 690.33 2,761.33 77.835381378 89.1071994 1.47 230.00 919.99 3,679.96 95.199862654 110.2399061 1.18 287.41 1,149.65 4,598.59 112.37701881 131.3042622 0.98 344.83 1,379.30 5,517.22 129.42255839 152.322783 0.84 402.24 1,608.96 6,435.85 146.37112572 173.308745 0.74 459.66 1,838.62 7,354.48 163.24563525 194.2705549 0.66 517.07 2,068.28 8,273.11 180.06197041 215.213833 0.59 574.48 2,297.94 9,191.74

Umax = √Z γ R TM

Mass Flux13

5.578

9.511.5

Density: kg/m3 = m t + b Density: lb/ft3 = m t + b Molecular Cp/Cv m b m b Weight

(3.09) 1,393.40 (0.19) 86.99 120.91 1.170 (3.20) 1,279.33 (0.20) 79.87 86.48 1.250 (1.56) 1,150.42 (0.06) 64.24 18.00 1.310

YELLOW = > Mach 0.3RED > Mach 1

Inputs Steam-Water at Saturated Conditions R12Total Mass Flux kg/m2-s 100.0 Quality Mass Fraction Vapor 0.5 Inlet Pressure Bar 9.40 Pipe Diameter mm 10.0 Equivalent Length of Pipe m 1.0 Pipe Roughness m 0.0000015 (Smooth Tube = 0.0000015 m)

Calculations / Property LookupParameter Units Liquid VaporCross-sectional area m2 7.853982E-05Total Mass Flow Rate kg/h 14.1 14.1 Inlet Pressure kPa 940.0 940.0 Temperature C 39.2 39.16 Viscosity mPa-s 0.17 0.014 Molecular Weight kg/kgmol 120.9 120.9 Density kg/m3 1,272.5 43.8 Cp/Cv 1.17 Velocity (assuming avg density) m/s 1.18 Critical Velocity m/s 158.70




Lower Bound 0.13 Upper Bound 0.34

Average kPa 0.23 = Pa 231.83

Problem Statement:Calculate Pressure Drop due to Friction for R12 at Saturation

10 100 1000 1

10

100

1,000

10,000

100,000

mass flux (kg/m2-s)

fric

tiona

l pre

ssur

e gr

adie

nt (P

a/m

)

10 100 1000 1

10

100

1,000

10,000

100,000

mass flux (kg/m2-s)

fric

tiona

l pre

ssur

e gr

adie

nt (P

a/m

)

Reference: IMECE2005-81493

Comparison Case R12

2,000.0 0.9 6.00 50.0 1.0

(Smooth Tube = 0.0000015 m) 0.0000015 (Smooth Tube = 0.0000015 m)

Liquid Vapor0.00196349541 1,413.7 12,723.5 600.0 600.0 22.0 22.05 0.20 0.013 120.9 120.9 1,325.3 29.6

1.31 61.05 163.26

#VALUE! #VALUE!

#VALUE! #VALUE!

#VALUE! #VALUE!

7.67 12.94

10.30

Quality

Mass Flux2080

200400600

1000

Sonic 158.7016

0.5

Lower Average Upper Density Velocity, m/s 8 14 20 84.6277 0.236329 86 157 228 0.945317 425 780 1,134 2.363292 1,431 2,623 3,815 4.726585 2,909 5,333 7,756 7.089877 7,112 13,037 18,962 11.81646

Inputs Steam-Water at Saturated Conditions R12Total Mass Flux kg/m2-s 100.0 Quality Mass Fraction Vapor 0.5 Inlet Pressure Bar 9.40 Pipe Diameter mm 10.0 Equivalent Length of Pipe m 1.0 Pipe Roughness m 0.0000015 (Smooth Tube = 0.0000015 m)

Calculations / Property LookupParameter Units Liquid VaporCross-sectional area m2 7.853982E-05Total Mass Flow Rate kg/h 14.1 14.1 Inlet Pressure kPa 940.0 940.0 Temperature C 39.2 39.16 Viscosity mPa-s 0.17 0.014 Molecular Weight kg/kgmol 120.9 120.9 Density kg/m3 1,272.5 43.8 Cp/Cv 1.17




dp/dz Pa/m #VALUE! #VALUE!

Fitting parameter p 0.8

Total pressure drop kPa/m #VALUE!

Problem Statement:Calculate Pressure Drop due to Friction for R12 at Saturation

Reference: IMECE2004-61410

waterComparison Case Reference article, Figure 1

R12 Water-Air 2,000.0 591.0 0.9 0.035 6.00 1.30 50.0 27.0 1.0 1.0

(Smooth Tube = 0.0000015 m) 0.0000015 (Smooth Tube = 0.0000015 m) 0.0000015

Liquid Vapor Liquid0.00196349541 0.00057256 1,413.7 12,723.5 1,197.6 600.0 600.0 130.0 22.0 22.05 20.0 0.20 0.013 0.39 120.9 120.9 18.0 1,325.3 29.6 1,119.3

1.31

#VALUE! #VALUE! #VALUE!



kPa/m #VALUE! #VALUE! #VALUE!

0.3 This method depends on fitting parameter, p 0.25

#VALUE! #VALUE!#VALUE!

Reference article, Figure 1

(Smooth Tube = 0.0000015 m)

Vapor

20.6 130.0 20.00 0.020 29.0 1.55 1.40

#VALUE!

#VALUE!

#VALUE!

#VALUE!

This method depends on fitting parameter, p

Inputs Steam-Water at Saturated Conditions waterTotal Mass Flux kg/m2-s 110.6 Quality Mass Fraction Vapor 0.1 Inlet Pressure Bar 14.83 Pipe Diameter mm 38.1 Equivalent Length of Pipe m 30.5 Pipe Roughness m 0.0000457

Calculations / Property LookupParameter Units Liquid VaporCross-sectional area m2 0.0011400918Total Mass Flow Rate kg/h 392.7 61.3 Inlet Pressure kPa 1,482.8 1,482.8 Temperature C 197.7 197.70 Viscosity mPa-s 0.17 0.014 Molecular Weight kg/kgmol 18.0 18.0 Density kg/m3 842.4 6.8 Cp/Cv 1.40




Lockhart and Martinelli MethodX dimensionless #VALUE!Phi-liquid dimensionless #VALUE!

Total Pressure Drop, 2-phase kPa #VALUE!psi/100 ft #VALUE! Branan: 0.49 psi/100 ft

Rukan: 0.28 psi/100 ft

Problem Statement:Calculate Pressure Drop due to Friction for Water-Steam Mixture

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

Comparison of Two-Phase ModelsR12, 6 Bar pressure, 100 kg/m2-s in 50 mm smooth pipe

HomogeneousSplitAsymptoticLockhart

Quality

Pres

sure

Dro

p, k

Pa p

er m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10



Quality

Pres

sure

Dro

p, k

Pa p

er m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -

20

40

60

80

100

120

140

160



Quality

Pres

sure

Dro

p, k

Pa p

er m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -

20

40

60

80

100

120

140

160



Quality

Pres

sure

Dro

p, k

Pa p

er m

Reference: Branan, Rules of Thumb, 4th Edition

Comparison Case WallisR12

2,000.0 0.9 6.00 50.0 1.0 0.0000015

Liquid Vapor0.0019634954

1,413.7 12,723.5 600.0 600.0 22.0 22.05 0.20 0.013 120.9 120.9 1,325.3 29.6

1.31

#VALUE! #VALUE!

#VALUE! #VALUE!

#VALUE! #VALUE!

#VALUE! Phi^2, lo 20.893051#VALUE! Phi, lo 4.5708917

#VALUE! #VALUE!

Mass Flux Quality Velocity Homog Split100 0 0.075 0.00 0.00 100 0.1 0.406 0.01 0.01 100 0.2 0.737 0.01 0.02 100 0.3 1.068 0.02 0.03 100 0.4 1.399 0.02 0.03 100 0.5 1.729 0.03 0.04 100 0.6 2.060 0.03 0.05

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10



Quality

Pres

sure

Dro

p, k

Pa p

er m

100 0.7 2.391 0.04 0.05 100 0.8 2.722 0.04 0.05 100 0.9 3.052 0.04 0.05 100 1 3.383 0.05

10 0.5 0.159 0.003 0.005 50 0.5 0.795 0.051 0.084

100 0.5 1.590 0.176 0.284 200 0.5 3.179 0.613 0.954 300 0.5 4.769 1.285 1.940 400 0.5 6.359 2.184 3.209 500 0.5 7.948 3.304 4.742 600 0.5 9.538 4.641 6.524 700 0.5 11.128 6.194 8.545 800 0.5 12.717 7.961 10.794

1000 0.5 15.897 12.133 15.951 1000 0 0.755 0 0 1000 0.1 4.062 1 1 1000 0.2 7.370 1 1 1000 0.3 10.678 1 2 1000 0.4 13.986 2 2 1000 0.5 17.294 2 2 1000 0.6 20.601 2 3 1000 0.7 23.909 3 3 1000 0.8 27.217 3 3 1000 0.9 30.525 3 3 1000 1 33.833 4 2000 0 1.509 0 0 2000 0.1 8.125 2 2 2000 0.2 14.740 3 4 2000 0.3 21.356 5 5 2000 0.4 27.972 6 6 2000 0.5 34.587 7 8 2000 0.6 41.203 9 9 2000 0.7 47.818 10 10 2000 0.8 54.434 11 10 2000 0.9 61.050 13 10 2000 1 67.665 14 5000 0 3.773 2 2 5000 0.1 20.312 11 11 5000 0.2 36.851 19 18 5000 0.3 53.390 28 25 5000 0.4 69.929 36 32 5000 0.5 86.468 44 38 5000 0.6 103.007 52 43 5000 0.7 119.546 60 48 5000 0.8 136.085 68 51 5000 0.9 152.624 76 51 5000 1 169.163

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10



Quality

Pres

sure

Dro

p, k

Pa p

er m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -

20

40

60

80

100

120

140

160



Quality

Pres

sure

Dro

p, k

Pa p

er m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -

20

40

60

80

100

120

140

160



Quality

Pres

sure

Dro

p, k

Pa p

er m

Asymp Lockhart Fluid Inlet Pres Pipe Diam EquivalentPipe RoughnessR12 6.00 50.0 1.0 0.0000015

0.01 0.02 R12 6.00 50.0 1.0 0.0000015 0.02 0.03 R12 6.00 50.0 1.0 0.0000015 0.03 0.04 R12 6.00 50.0 1.0 0.0000015 0.03 0.05 R12 6.00 50.0 1.0 0.0000015 0.04 0.06 R12 6.00 50.0 1.0 0.0000015 0.05 0.07 R12 6.00 50.0 1.0 0.0000015

0.05 0.08 R12 6.00 50.0 1.0 0.0000015 0.06 0.09 R12 6.00 50.0 1.0 0.0000015 0.06 0.08 R12 6.00 50.0 1.0 0.0000015

R12 6.00 50.0 1.0 0.0000015 0.007 0.011 R22 9.10 10.0 1.0 0.0000015 0.076 0.124 R22 9.10 10.0 1.0 0.0000015 0.272 0.443 R22 9.10 10.0 1.0 0.0000015 0.940 1.527 R22 9.10 10.0 1.0 0.0000015 1.945 3.157 R22 9.10 10.0 1.0 0.0000015 3.273 5.311 R22 9.10 10.0 1.0 0.0000015 4.913 7.969 R22 9.10 10.0 1.0 0.0000015 6.859 11.123 R22 9.10 10.0 1.0 0.0000015 9.105 14.762 R22 9.10 10.0 1.0 0.0000015 11.648 18.882 R22 9.10 10.0 1.0 0.0000015 17.613 28.542 R22 9.10 10.0 1.0 0.0000015

R12 6.00 50.0 1.0 0.0000015 1 1 R12 6.00 50.0 1.0 0.0000015 1 2 R12 6.00 50.0 1.0 0.0000015 2 3 R12 6.00 50.0 1.0 0.0000015 2 4 R12 6.00 50.0 1.0 0.0000015 3 4 R12 6.00 50.0 1.0 0.0000015 3 5 R12 6.00 50.0 1.0 0.0000015 4 6 R12 6.00 50.0 1.0 0.0000015 4 6 R12 6.00 50.0 1.0 0.0000015 4 6 R12 6.00 50.0 1.0 0.0000015

R12 6.00 50.0 1.0 0.0000015 R12 6.00 50.0 1.0 0.0000015

2 4 R12 6.00 50.0 1.0 0.0000015 4 7 R12 6.00 50.0 1.0 0.0000015 6 10 R12 6.00 50.0 1.0 0.0000015 8 13 R12 6.00 50.0 1.0 0.0000015 10 16 R12 6.00 50.0 1.0 0.0000015 12 19 R12 6.00 50.0 1.0 0.0000015 14 22 R12 6.00 50.0 1.0 0.0000015 15 24 R12 6.00 50.0 1.0 0.0000015 16 24 R12 6.00 50.0 1.0 0.0000015

R12 6.00 50.0 1.0 0.0000015 R12 6.00 50.0 1.0 0.0000015

14 25 R12 6.00 50.0 1.0 0.0000015 24 41 R12 6.00 50.0 1.0 0.0000015 35 58 R12 6.00 50.0 1.0 0.0000015 46 76 R12 6.00 50.0 1.0 0.0000015 58 93 R12 6.00 50.0 1.0 0.0000015 69 111 R12 6.00 50.0 1.0 0.0000015 79 126 R12 6.00 50.0 1.0 0.0000015 88 138 R12 6.00 50.0 1.0 0.0000015 94 141 R12 6.00 50.0 1.0 0.0000015

R12 6.00 50.0 1.0 0.0000015

Pipe Roughness

Hashizume's Data90 0.1

120 0.23185 0.4250 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -

1

2

3

4

5

6

7


LockhartAsymptoticSplitHomogeneous

Quality

Fric

tiona

l Pre

ssur

e D

rop,

kPa

per

m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -

1

2

3

4

5

6

7



Quality

Fric

tiona

l Pre

ssur

e D

rop,

kPa

per

m

10 100 1000 0.001

0.010

0.100

1.000

10.000

100.000

Comparison of Two-Phase ModelsR22, 9.1 Bar pressure, 0.5 Quality in 10 mm smooth tube

LockhartAsymptoticSplitHomogenousHashizume's Data

Mass Flux, kg/m2-s

Pres

sure

Dro

p, k

Pa p

er m

10 100 1000 0.001

0.010

0.100

1.000

10.000

100.000



Mass Flux, kg/m2-s

Pres

sure

Dro

p, k

Pa p

er m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -

1

2

3

4

5

6

7



Quality

Fric

tiona

l Pre

ssur

e D

rop,

kPa

per

m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -

1

2

3

4

5

6

7



Quality

Fric

tiona

l Pre

ssur

e D

rop,

kPa

per

m

10 100 1000 0.001

0.010

0.100

1.000

10.000

100.000



Mass Flux, kg/m2-s

Pres

sure

Dro

p, k

Pa p

er m

10 100 1000 0.001

0.010

0.100

1.000

10.000

100.000



Mass Flux, kg/m2-s

Pres

sure

Dro

p, k

Pa p

er m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -

1

2

3

4

5

6

7



Quality

Fric

tiona

l Pre

ssur

e D

rop,

kPa

per

m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -

1

2

3

4

5

6

7



Quality

Fric

tiona

l Pre

ssur

e D

rop,

kPa

per

m

10 100 1000 0.001

0.010

0.100

1.000

10.000

100.000



Mass Flux, kg/m2-s

Pres

sure

Dro

p, k

Pa p

er m

10 100 1000 0.001

0.010

0.100

1.000

10.000

100.000



Mass Flux, kg/m2-s

Pres

sure

Dro

p, k

Pa p

er m

Inputs Steam-Water at Saturated Conditions WaterTotal Mass Flux kg/m2-s 1,356.0 Quality Mass Fraction Vapor 0.1 Inlet Pressure Bar 6.00 Pipe Diameter mm 50.0 Equivalent Length of Pipe m 1.0 Pipe Roughness m 0.0000015 (Smooth Tube = 0.0000015 m)

Calculations / Property LookupParameter Units Total as Liq Vapor Props MixtureCross-sectional area m2 0.0019634954Total Mass Flow Rate kg/h 9,585.0 Inlet Pressure kPa 600.0 Temperature C 158.3 Viscosity mPa-s 0.21 0.013 0.084 Molecular Weight kg/kgmol 18.0 Density kg/m3 903.7 3.0 29.2 Cp/Cv



Pressure Drop, given Mass Flow and Pressure in #VALUE!

Liquid PD Multiplier phi #VALUE!phi^2 #VALUE!

Pressure Drop, 2-Phase Flow kPA #VALUE!

Sonic Velocity

475.6

Pipe flow area 0.001963495Velocity, m/s

Quality Density 5424 kg/m2-s0 903.75 6.00

0.01 226.40 23.96 YELLOW = > Mach 0.3

Problem Statement:Calculate Pressure Drop Through an Elbow for Different Steam Qualities

Umax = √Z γ R TM

0.02 129.41 41.91 RED > Mach 10.03 90.60 59.87 0.04 69.69 77.83 0.05 56.63 95.78 0.06 47.69 113.74 0.07 41.19 131.69 0.08 36.24 149.65 0.09 32.36 167.61 0.1 29.23 185.56

0.11 26.65 203.52 0.12 24.49 221.47 0.13 22.65 239.43 0.14 21.07 257.39 0.15 19.70 275.34 0.16 18.49 293.30 0.17 17.43 311.25 0.18 16.48 329.21 0.19 15.62 347.17 0.2 14.86 365.12

0.21 14.16 383.08 0.22 13.53 401.03 0.23 12.95 418.99 0.24 12.41 436.95 0.25 11.92 454.90 0.26 11.47 472.86 0.27 11.05 490.81 0.28 10.66 508.77 0.29 10.30 526.73 0.3 9.96 544.68

0.31 9.64 562.64 0.32 9.34 580.59 0.33 9.06 598.55

Property Correlations for all correlations, t = deg CVapor Pressure: log(mm Hg) = A - B / (t+C)A B C

R12 6.99 918.17 253.38 R22 7.04 850.10 245.18 Water 8.31 1,986.50 268.74

(Smooth Tube = 0.0000015 m)

Km Ki Kdm/s 800 0.091 4

m2 K #VALUE! elbow

#VALUE! kPa#VALUE!

-0.1 -2.77555756156289E-17 0.1 0.2 0.3 -

2.00

4.00

6.00

8.00

10.00

12.00

Pressure Drop Through a DN Elbow

Velocity

#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!

-0.1 -2.77555756156289E-17 0.1 0.2 0.3 -

2.00

4.00

6.00

8.00

10.00

12.00


Velocity

Liquid Viscosity: ln(cP) = A + B / (C+t) Vapor Viscosity: ln(cP) = A + B / (C+t)A B C

(8.77) 5,134.3 693.01 (9.00) (4,611.86) (1,008.87) 20.79 46,143.5 (2,064.89) (3.47) (278.74) 286.66 4.34 6,927.32 (1,332.33) (4.92) (200.49) (502.57)

-0.1 -2.77555756156289E-17 0.1 0.2 0.3 -

2.00

4.00

6.00

8.00

10.00

12.00


Velocity

Density: kg/m3 = m t + b Density: lb/ft3 = m t + b Molecular Cp/Cv m b m b Weight

(3.09) 1,393.40 (0.19) 86.99 120.91 1.170 (3.20) 1,279.33 (0.20) 79.87 86.48 1.250 (1.56) 1,150.42 (0.06) 64.24 18.00

Inputs SI Units Value US Units ValueGas molecular weight 17.4 17.4 Temperature C 37.8 F 100 Pipe diameter mm 102 in 4.026 Pipe length km 32.2 miles 20 Inlet pressure kPa abs 13,700 psia 2,000 Outlet pressure kPa abs 10,300 psia 1,500 Elevation difference m 30.5 ft 100 Efficiency 1 1 Average compressibility factor 1 1

ConstantsBase temperature C - F 60 Base pressure kPa abs 100 psia 14.7 Pipe roughness m 0.0000457 ft 0.00015

CalculationsIsothermal Gas CalculationReynolds Number 200,000 200,000 Friction factor #VALUE! #VALUE!Flow Rate kg/h #VALUE! lb/h #VALUE!Standard volumetric rate MM m3/day #VALUE! MM ft3/day #VALUE!

Intermediate CalcsGas specific gravity 0.60 0.60 Average temperature K 311 R 560 Average pressure kPa abs 12,080 psia 1,762 Head correction kPa 49 psi 7

WeymouthStandard volumetric rate MM m3/day MM ft3/day 10,151

Panhandle AStandard volumetric rate MM m3/day 402 MM ft3/day 15,110

Panhandle BStandard volumetric rate MM m3/day 428 MM ft3/day 16,034

Problem Statement:Compare the Panhandle and Weymouth formulas with the Isothermal gas calculation

Problem Statement:Compare the Panhandle and Weymouth formulas with the Isothermal gas calculation

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