Please ReadProcedure and Scope

This Pressure Drop Calculator is designed for Newtonian Liquids and is for general use.The methods used are Hooper's 2K and Darby's 3K method as they give the better curve fits for pressure lossvs k factor data for various fittings. The advantage with both the methods is that K values are compensatedfor change in Reynolds Number and pipe internal diameter as well, unlike other famous methods.This compensation brings more accuracy to the pressure drop calculation at any flowrate.

User can input the Pipe ID from the standard drop down list or use their own dataPlease check that proper option is chosen to input the pipe diameter

Though the spreadsheet takes input parameters in metric system, the corresponding calculated values in IP system give a clue to the user if they are not comfortable with metric system

The friction factor is calculated using Poiseuille's equation for laminar flow and Colebrook's equationfor transitional and turbulent flows. However, Katmar's (fellow member at eng-tips.com) version of Churchill be used as one single equation for all kinds of flow. I must appreciate Katmar (Harvey) for this.

I personally opine that, as both Hooper's and Darby's methods give better pressure loss values when compared with conventional methods, collective data can be used for final pressure drop calculation, in the absence of suitable correlations. For ex. as there are no correlations of K, incase of Darby, for miters other than 2 weldsand also for reducers, expanders and orifices, Hooper's values can be included to the final valueof Darby's. I didn't include this in my calculation, at this juncture, and it is users discretionto use any other suitable method or logic.

This calculator is comfortable with single pipe size and I suggest, if there is a variation of pipe size, to calculate the sections independantly. In a nut shell, my suggestion is not to calculate reducer and expanderpressure drops in a single step.

The friction factor worksheet calculates Darcy's friction factor by Colebrook's equation. However,When dealing with Colebrook's equation, 5 steps of iteration are generally sufficient.I also included other explicit equations for the calculation of friction factor, based on the articleEstimate friction factor accurately by TK Serghides appeared in March' 84 volume of Chemical EngineeringMagazine.Good Luck,Ravi Sankar

Pressure DropPressure Drop Calculator

Select the Option StandardUse Cells C4 and D4101815.54Nominal Size and Schedule4"4013.830.2714.1Pipe ID (For pipes not in above list)4.0000inches15.560.3115.87Flow Rate (Input)16m3/hr70.45gpm15.490.3115.8Density(r) (Input)1000kg/m362.43lb/ft3Dynamic Viscosity () (Input)1cPAbsolute Roughness (e) (Input)0.005mm0.0002inches

Velocity (V)0.54m/s1.77feet/secInner Diameter (ID)0.1023m4.026inchesReynolds Number (NRe)55330Friction Factor (f)0.022013Procedure2-K3-KTotal Pressure Drop (m)13.7213.60Total Pressure Drop (Pa)134505.58133319.94Total Pressure Drop (psi)19.4819.33Shear Force222N/m2

Input the values in appropriate cells of Column C below

ComponentQtyUnitHooper 2-KDarby 3-KElevation12.5m12.50012.500Pipe Length300m0.9640.964900 ElbowThreaded, r/D = 10No0.0000.000Threaded, Long Radius, r/D = 1.50No0.0000.000Flanged, Welded, Bend, r/D = 110No0.0490.052Flanged, Welded, Bend, r/D = 20No0.000Flanged, Welded, Bend, r/D = 40No0.000Flanged, Welded, Bend, r/D = 60No0.000Mitered, 1 Weld, 90 Degree0No0.0000.000Mitered, 2 Welds, 45 Degree0No0.0000.000Mitered, 3 Welds, 30 Degree0No0.0000.000Mitered, 4 Welds, 22.5 Degree0No0.000Mitered, 5 Welds, 18 Degree0No0.000450 ElbowStandard, r/D = 10No0.0000.000Long Radius, r/D = 1.50No0.0000.000Mitered, 1 Weld, 45 Degree0No0.0000.000Mitered, 2 Welds, 22.5 Degree0No0.0000.0001800 ElbowThreaded, r/D = 10No0.0000.000Flanged/ Welded, r/D = 10No0.0000.000Long Radius, r/D = 1.50No0.0000.000TeesAs ElbowStandard, Threaded, r/D = 10No0.0000.000Long Radius, threaded, r/D = 1.50No0.0000.000Standard, Flanged/Welded, r/D = 1 4No0.0600.062Stub-in Branch0No0.0000.000Run Through Threaded, r/D = 10No0.0000.000Run Through Flanged/Welded, r/D = 10No0.0000.000Run Through Stub in Branch0No0.0000.000ValvesAngle Valve - 45 Degree, b = 10No0.0000.000Angle Valve - 90 Degree, b = 10No0.000Globe Valve, b = 10No0.0000.000Plug Valve, Branch Flow0No0.000Plug Valve, Straight Through0No0.0000.000Plug Valve, 3-way, Flow Through0No0.000Gate Valve, b = 10No0.0000.000Ball Valve, b = 12No0.0060.002Butterfly Valve0No0.000Diaphragm Valve, Dam Type0No0.0000.000Swing Check Valve, Vmin = 35r-1/21No0.0280.025Lift Check Valve, Vmin = 40r-1/20No0.0000.000Tilting Disk Check Valve0No0.000ReducersSecond ID1.3779InchesAngle45DegreesSquare Reducer0No0.000Tapered Reducer0No0.000Round Reducer1No0.108ExpanderSecond ID1InchesAngle45DegreesSquare Expander0No0.000Tapered Expander0No0.000Round Expander0No0.000OrificeDiameter (ID of Orifice)1InchesLength (Thickness of the Thick Orifice)1InchesThin0No0.000Thick0No0.000

Friction FactorExplicit Equations of Friction Factor and Colebrook's Equation

1Churchill's Equation (for any Re and /D)

f =8((8/Re)12 + 1/(A+B)1.5)1/12

A =(-2.457ln((7/Re)0.9+0.27/D))16

B =(37530/Re)16e
Author: Standard 0.000045720.00004572

R55330.3994228581/D0.0004470939

A2.98E+20B2.01E-03f0.02206851

2Serghides' Equation (Re>2100 and for any /D)

f = [A - ((B-A)2/(C-2B+A))]-2

A =-2.0 log((/D/3.7) + (12/Re))

B = -2.0 log ((/D/3.7)+(2.51A/Re))

C = -2.0 log ((/D/3.7) + (2.51B/Re))

A6.9428988979B6.7214398624C6.7416976571f0.02201305

3Moody's Equation (4000 Re 107 and /D 0.01)

f =5.5 x 10-3 (1+ (2 x 104/D + 106/Re)1/3)

f0.02200308

4Wood's Equation (Re 4000 and for any /D)

f = 0.094(/D)0.225 + 0.53(/D) + 88(/D)0.44Reaa = -1.62(/D)0.134

a-0.5763263085f0.02227213

5Jain's Equation (5000 < Re < 107 and 0.00004 < /D < 0.05)

1/f1/2 =1.14 - 2.0log(e/D + (21.25/Re0.9))or f =1/(1.14 - 2.0log(e/D + (21.25/Re0.9)))2

f0.02203772

6Chen's Equation (for any Re and /D)

1/f1/2 =-2.0 log((/D/3.7065) - (5.0452A/Re))or f =1/(-2.0 log((/D/3.7065) - (5.0452A/Re)))2A =log((/D)1.1098/2.8257 + (5.8506/Re0.8981))

A-3.40937057f0.02207828

7Zigrang and Sylvester's Equation (4000 < Re < 108 and 0.00004 < /D < 0.05) - (1)

1/f1/2 =-2.0Aor f =1/4A2A =log((/D/3.7) - (5.02/Re)* log ((/D/3.7) + (13/Re)))

A-3.3627718959f0.02210778

8Zigrang and Sylvester's Equation (4000 < Re < 108 and 0.00004 < /D < 0.05) - (2)

1/f1/2 =-2.0log ((e/d/3.7) - (5.02A/Re))or f =1/(-2.0log ((e/d/3.7) - (5.02A/Re)))2

f0.02200444

9Colebrook's Equation

1/f1/2 =-2.0 log((e/D/3.7) + (2.51/Ref1/2))or f =1/(-2.0 log((e/D/3.7) + (2.51/Ref1/2)))2f =0.02

f0.022210800.021995010.022014840.022013000.02201317

Note:Friction factor from Colebrook's equation generally converges after 4 steps of iteration.If it doesn't converge, copy paste the previous cell to next cell and input the correct cell values forReynolds Number(C11) and Effective Roughness(F11)

10Katmar - Using Churchill, but with Colebrook substituted for "A"

A3.043E+20B2.007E-03f0.02201317

ComparisonComparision of Friction Factors from various Explicit Equations w.r.to Colebrook's EquationRee/DColebrookChurchillSerghideMoodyWoodJainChenZigrangKatmar55330.39942285810.00044709390.022013170.022068510.022013050.022003080.022272130.022037720.022078280.022004440.02201317Error (%)0.251-0.001-0.0461.1760.1120.296-0.040-0.000Note:Zigrang's equation considered in this comparison is the second equation

Hooper 2KHooper's 2-K Friction Factor Method

FittingTypeGeometryK1KK4.0260IDElbow - 90 DegreeStandard, Screwedr/D = 18000.400.51455330.40NReStandard, Flanged/Weldedr/D = 18000.250.3271.3779Second ID Long Radius, all typesr/D = 1.58000.200.2640.39275AngleMitered, 1 Weld, 90 Degreer/D = 1.510001.151.4541Second ID (E)Mitered, 2 Welds, 45 Degreer/D = 1.58000.350.4510.39275Angle (E)Mitered, 3 Welds, 30 Degreer/D = 1.58000.300.3890.0220131735fMitered, 4 Welds, 22.5 Degreer/D = 1.58000.270.3521ID (O)Mitered, 5 Welds, 18 Degreer/D = 1.58000.250.3270.0254Length (O)Elbow - 45 DegreeStandard, all typesr/D = 15000.200.259Long Radius, all typesr/D = 1.55000.150.196Mitered, 1 Weld, 45 Degree5000.250.321Mitered, 2 Welds, 22.5 Degree5000.150.196Elbows - 180 DegreeStandard, Screwedr/D = 110000.600.767Standard, Flanged/Weldedr/D = 110000.350.455Long Radius, all typesr/D = 1.510000.300.393TeesThrough Branch (as elbow)Standard, Screwed5000.700.883Long Radius, Screwed8000.400.514Standard, Flanged/Welded8000.801.013Stub-in Branch10001.001.266Run Through Threadedr/D = 12000.100.128Run Through Flanged/Weldedr/D = 11500.500.627Run Through Stub-in Branch1000.000.002ValveGate ValveFull Line Size, b = 13000.100.130Ball ValveReduced Trim, b = 0.95000.150.196Plug ValveReduced Trim, b = 0.910000.250.330GlobeStandard15004.005.021GlobeAngle or Y type10002.002.515Diaphragm ValveDam-Type10002.002.515Butterfly Valve8000.250.327Check ValveLift200010.0012.520Check ValveSwing15001.501.900Check ValveTilting Disk10000.500.642ReducerSquare Reducer39.287Tapered Reducer24.305Round Reducer7.253ExpanderSquare Expander235.377Tapered Expander234.224Round Expander235.377OrificeThin682.02Thick677.003

Formula

K = K1/NRe + K(1+1/ID)Reference:The two-K method predicts by William B. Hooper published in August, 1981 issue ofChemical Engineering MagazineCalculate head loss caused by change in pipe size by William B. Hooper in November, 1988 issue of Chemical Engineering Magazine

Darby 3KDarby's 3-K Friction Factor Method

FittingTypeGeometryKmKiKdKf4.026IDElbow - 90 DegreeThreaded, Standardr/D = 18000.144.00.52355330.40NReThreaded, Long Radiusr/D = 1.58000.0714.20.282Flanged, Welded, Bendr/D = 18000.0914.00.345Flanged, Welded, Bendr/D = 28000.0563.90.214Flanged, Welded, Bendr/D = 48000.0663.90.250Flanged, Welded, Bendr/D = 68000.0754.20.297Mitered, 1 Weld, 90 Degree10000.274.00.999Mitered, 2 Welds, 45 Degree8000.0684.10.266Mitered, 3 Welds, 30 Degree8000.0354.20.146Elbow - 45 DegreeThreaded, Standardr/D = 15000.0714.20.276Long Radiusr/D = 1.55000.0524.00.198Mitered, 1 Weld, 45 Degree5000.0864.00.322Mitered, 2 Welds, 22.5 Degree5000.0524.00.198Elbows - 180 DegreeThreaded, Colsed Return Bendr/D = 110000.234.00.854Flangedr/D = 110000.124.00.454Allr/D = 1.510000.104.00.381TeesThrough Branch (as elbow)Threadedr/D = 15000.2744.01.005Threadedr/D = 1.58000.144.00.523Flangedr/D = 18000.284.01.032Stub-in Branch10000.344.01.254Run Through Threadedr/D = 12000.0914.00.334Flangedr/D = 11500.0174.00.064Stub-in Branch100000.002ValvesAngle Valve - 45 DegreeFull Line Size, b = 19500.254.00.926Angle Valve - 90 DegreeFull Line Size, b = 110000.694.02.525Globe ValveStandard, b = 115001.703.65.757Plug ValveBranch Flow5000.414.01.499Plug ValveStraight Through3000.0843.90.305Plug ValveThree-Way (flow through)3000.144.00.514Gate ValveStandard, b = 13000.0373.90.137Ball ValveStandard, b = 13000.0174.00.067Diaphragm ValveDam-Type10000.694.92.934Swing Check ValveVmin = 35r-1/215000.464.01.699Lift Check ValveVmin = 40r-1/220002.853.810.017

Formula

Kf = (Km/Nre)+Ki[1+(Kd/Din0.3)]Reference:Correlate Pressure Drops Through Fittings By Ron Darby published in April 2001 Issue of Chemical Engineering Journal

Pipe SizesPipe Size DataPipe Size Data Rearranged

Nominal Outside Dia.CS Pipe SS PipeThicknessInside Dia.Inside Dia.SizeinchTypeSch No.inchinchmmSize102030406080100120140160STDXSXSS1/80.405--10S0.0490.3077.801/8"0.2690.215Invalid1/8STD4040S0.0680.2696.831/4"0.3640.302Invalid1/8XS8080S0.0950.2155.463/8"0.4930.423Invalid1/40.540--10S0.0650.41010.411/2"0.6220.5460.4660.2521/4STD4040S0.0880.3649.253/4"0.8240.7420.6120.4341/4XS8080S0.1190.3027.671"1.0490.9570.8150.5993/80.675--10S0.0650.54513.841.25"1.3801.2781.1600.8963/8STD4040S0.0910.49312.521.5"1.6101.5001.3381.1003/8XS8080S0.1260.42310.742"2.0671.9391.6871.5031/20.840--5S0.0650.71018.032.5"2.4692.3232.1251.7711/2--10S0.0830.67417.123"3.0682.9002.6242.3001/2STD4040S0.1090.62215.803.5"3.5483.3641/2XS8080S0.1470.54613.874"4.0263.8263.6243.4383.1521/2-160-0.1870.46611.845"5.0474.8134.5634.3134.0631/2XXSXXS-0.2940.2526.406"6.0655.7615.5015.1874.8973/41.050--5S0.0650.92023.378"8.1258.0717.9817.8137.6257.4377.1877.0016.8136.8753/4--10S0.0830.88422.4510"10.25010.13610.0209.7509.5629.3129.0628.7508.5003/4STD4040S0.1130.82420.9312"12.25012.09011.93811.62611.37411.06210.75010.50010.12612.00011.75010.7503/4XS8080S0.1540.74218.8514"13.50013.37613.25013.12412.81212.50012.12411.81211.50011.18813.25013.0003/4-160-0.2190.61215.5416"15.50015.37615.25015.00014.68814.31213.93813.56213.12412.81215.25015.0003/4XXSXXS-0.3080.43411.0218"17.50017.37617.12416.87616.50016.12415.68815.25014.87614.43817.25017.00011.315--5S0.0651.18530.1020"19.50019.25019.00018.81218.37617.93817.43817.00016.50016.06219.25019.0001--10S0.1091.09727.8622"21.50021.25021.000Invalid20.25019.75019.25018.75018.25017.75021.25021.0001STD4040S0.1331.04926.6424"23.50023.25022.87622.62422.06221.56220.93820.37619.87619.31223.25023.0001XS8080S0.1790.95724.3126"25.37625.000Invalid25.25025.0001-160-0.2500.81520.7028"27.37627.00026.75027.25027.0001XXSXXS-0.3580.59915.2130"29.37629.00028.75029.250Invalid1 1/41.660--5S0.0651.53038.8632"31.37631.00030.75030.62431.250Invalid1 1/4--10S0.1091.44236.6334"33.31233.00032.75032.62433.25033.0001 1/4STD4040S0.1401.38035.0536"35.37635.00034.75034.50035.25035.0001 1/4XS8080S0.1911.27832.461 1/4-160-0.2501.16029.46Standard1 1/4XXSXXS-0.3820.89622.76User1 1/21.900--5S0.0651.77044.961 1/2--10S0.1091.68242.721 1/2STD4040S0.1451.61040.891 1/2XS8080S0.2001.50038.101 1/2-160-0.2811.33833.991 1/2XXSXXS-0.4001.10027.9422.375--5S0.0652.24557.022--10S0.1092.15754.792STD4040S0.1542.06752.502XS8080S0.2181.93949.252-160-0.3441.68742.852XXSXXS-0.4361.50338.182 1/22.875--5S0.0832.70968.812 1/2--10S0.1202.63566.932 1/2STD4040S0.2032.46962.712 1/2XS8080S0.2762.32359.002 1/2-160-0.3752.12553.982 1/2XXSXXS-0.5521.77144.9833.500--5S0.0833.33484.683--10S0.1203.26082.803STD4040S0.2163.06877.933XS8080S0.3002.90073.663-160-0.4382.62466.653XXSXXS-0.6002.30058.423 1/24.000--5S0.0833.83497.383 1/2--10S0.1203.76095.503 1/2STD4040S0.2263.54890.123 1/2XS8080S0.3183.36485.4544.500--5S0.0834.334110.084--10S0.1204.260108.204STD4040S0.2374.026102.264XS8080S0.3373.82697.184-120-0.4383.62492.054-160-0.5313.43887.334XXSXXS-0.6743.15280.0655.563--5S0.1095.345135.765--10S0.1345.295134.495STD4040S0.2585.047128.195XS8080S0.3754.813122.255-120-0.5004.563115.905-160-0.6254.313109.555XXSXXS-0.7504.063103.2066.625--5S0.1096.407162.746--10S0.1346.357161.476STD4040S0.2806.065154.056XS8080S0.4325.761146.336-120-0.5625.501139.736-160-0.7195.187131.756XXSXXS-0.8644.897124.3888.625--5S0.1098.407213.548--10S0.1488.329211.568-20-0.2508.125206.388-30-0.2778.071205.008STD4040S0.3227.981202.728-60-0.4067.813198.458XS8080S0.5007.625193.688-100-0.5947.437188.908-120-0.7197.187182.558-140-0.8127.001177.838XXSXXS-0.8756.875174.638-160-0.9066.813173.051010.750--5S0.13410.482266.2410--10S0.16510.420264.6710-20-0.25010.250260.3510-30-0.30710.136257.4510STD4040S0.36510.020254.5110XS6080S0.5009.750247.6510-80-0.5949.562242.8710-100-0.7199.312236.5210-120-0.8449.062230.1710XXS140-1.0008.750222.2510-160-1.1258.500215.901212.750--5S0.15612.438315.9312--10S0.18012.390314.7112-20-0.25012.250311.1512-30-0.33012.090307.0912STDSTD40S0.37512.000304.8012-40-0.40611.938303.2312XSXS80S0.50011.750298.4512-60-0.56211.626295.3012-80-0.68811.374288.9012-100-0.84411.062280.9712XXS120-1.00010.750273.0512-140-1.12510.500266.7012-160-1.31210.126257.201414.000--5S0.15613.688347.6814--10S0.18813.624346.0514-10-0.25013.500342.9014-20-0.31213.376339.7514STD30-0.37513.250336.5514-40-0.43813.124333.3514XSXS-0.50013.000330.2014-60-0.59412.812325.4214-80-0.75012.500317.5014-100-0.93812.124307.9514-120-1.09411.812300.0214-140-1.25011.500292.1014-160-1.40611.188284.181616.000--5S0.16515.670398.0216--10S0.18815.624396.8516-10-0.25015.500393.7016-20-0.31215.376390.5516STD30-0.37515.250387.3516XS40-0.50015.000381.0016-60-0.65614.688373.0816-80-0.84414.312363.5216-100-1.03113.938354.0316-120-1.21913.562344.4716-140-1.43813.124333.3516-160-1.59412.812325.421818.000--5S0.16517.670448.8218--10S0.18817.624447.6518-10-0.25017.500444.5018-20-0.31217.376441.3518STDSTD-0.37517.250438.1518-30-0.43817.124434.9518XSXS-0.50017.000431.8018-40-0.56216.876428.6518-60-0.75016.500419.1018-80-0.93816.124409.5518-100-1.15615.688398.4818-120-1.37515.250387.3518-140-1.56214.876377.8518-160-1.78114.438366.732020.000--5S0.18819.624498.4520--10S0.21819.564496.9320-10-0.25019.500495.3020STD20-0.37519.250488.9520XS30-0.50019.000482.6020-40-0.59418.812477.8220-60-0.81218.376466.7520-80-1.03117.938455.6320-100-1.28117.438442.9320-120-1.50017.000431.8020-140-1.75016.500419.1020-160-1.96916.062407.972222.000--5S0.18821.624549.2522--10S0.21821.564547.7322-10-0.25021.500546.1022STD20-0.37521.250539.7522XS30-0.50021.000533.4022-60-0.87520.250514.3522-80-1.12519.750501.6522-100-1.37519.250488.9522-120-1.62518.750476.2522-140-1.87518.250463.5522-160-2.12517.750450.852424.000--5S0.21823.564598.5324-1010S0.25023.500596.9024STD20-0.37523.250590.5524XSXS-0.50023.000584.2024-30-0.56222.876581.0524-40-0.68822.624574.6524-60-0.96922.062560.3724-80-1.21921.562547.6724-100-1.53120.938531.8324-120-1.81220.376517.5524-140-2.06219.876504.8524-160-2.34419.312490.522626.000-10-0.31225.376644.5526STDSTD-0.37525.250641.3526XS20-0.50025.000635.002828.000-10-0.31227.376695.3528STDSTD-0.37527.250692.1528XS20-0.50027.000685.8028-30-0.62526.750679.453030.000--5S0.25029.500749.3030-1010S0.31229.376746.1530STDSTD-0.37529.250742.9530XS20-0.50029.000736.6030-30-0.62528.750730.253232.000-10-0.31231.376796.9532STDSTD-0.37531.250793.7532XS20-0.50031.000787.4032-30-0.62530.750781.0532-40-0.68830.624777.853434.000-10-0.34433.312846.1234STDSTD-0.37533.250844.5534XS20-0.50033.000838.2034-30-0.62532.750831.8534-40-0.68832.624828.653636.000100.31235.376898.5536STDSTD0.37535.250895.3536XS200.50035.000889.0036300.62534.750882.6536400.75034.500876.30

PumpingPump Power Calculation

Select UnitsSIUnit ConversionHead137m449.36ftIPDischarge70cu.mtr/hr308.21UsgpmSISpecific Gravity1Pump Efficiency50%Motor Efficiency90%

Water Power26.13kW35.51HPBreak Power52.27kW71.03HPMotor Power58.07kW78.92HP

Formula in IP Units

WHP = H x Q x 8.33 x SG/33000

H =Head in FeetQ = Flowrate in Usgpm8.33 is conversion factor for gallons to lbs33000 is conversion factor foot-pounds/minute to HP

Formula in SI Units

WKW = H x Q x 1000 x SG x g/[3600 x 1000]

H = Head in metersQ = Flowrate in m3/hr1000 is coversion factor from m3 to kgg = Acceleration due to gravity - 9.81m/s23600 is conversion factor for hr to seconds1000 is conversion factor from W to kW