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Pipe Pressure Loss Calculation Methods

Principal Equaltions

Two principal equations used in computing pressure loss in pipes are:

Darcy-Weisbach Equation

[Darcy Equation]

Where l is pipe length, d is pipe diameter, v is average fluid velocity, λ is friction factor and h is amount of pressure loss.

Most pressure loss calculation methods are means to find λ which will then be used in Darcy equation to calculate pressure loss.

Reinolds Number

[Reinolds Number]

Where V is average fluid velocity, d is pipe diameter, ν is fluid viscosity.

Reinolds Number indicates amount of fluid turbulency, it is used in many pressure loss calculation methods as input parameter.

Pressure Loss Calculation Methods

Equation for Laminar Flow

[Laminar Flow Equation]

Only for laminar flow (Re<2300).

Konakov Equation

[Konakov Equation]

Only for smooth pipes and when reinolds number is between 2300 and 106.

Blasius Equation

[Blasius Equation]

Only for smooth pipes and when reinolds number is between 2300 and 105.

Hermann Equation

[Hermann Equation]

Only for smooth pipes and when reinolds number is between 2x104 and 2x106.

Prandtle Equation

[Prandtle Equation]

Only for smooth pipes and when reinolds number is between 2300 and 4x106.

Nikoradze Equation

[Nikoradze Equation]

Only for smooth pipes and when reinolds number is between 104 and 108.

Altshul Equation

[Altshul Equation]

Where k is absolute roughness (height of bumps on inside pipe surface) and d is pipe diameter.

Colebrook Equation

[Colebrook Equation]

Karman Equation

[Karman Equation]

Karman Equation 2

[Karman Equation 2]

Austrian Engineers Society Equation

[Austrian Engineers Society Equation]

Where V is average floid velocity, s is pressure loss per pipe length unit (Hydraulic Dip) and n is obtained from table below:

[n Equation]

Where k is in meters.

Chezy Equation

[Chezy Equation]

Where V is velocity in feet R is hydraulic radius in feet which is d/4 for pipes with circle profile and C equation's coefficient which can be obtained from table below:

Pipe TypeC coefficient
Very Smooth Pipe140
Smooth and New Cast-Iron Pipe130
Average Cast-Iron Pipe, New Steel Pipe, Sewerage Pipe110
Old Cast-Iron Pipe100
Very Old Cast-Iron Pipe80

Hazen-Williams Equation

[Hazen-Williams Equation]

Where V is velocity in feet per second R is hydraulic radius in feet and C equation's coefficient obtained from table below:

Nominal Diameter in Inches Actual Diameter in Inches Velocity in feet per second
12345 68101520
3/40.824 7781848687 8890929496
11.048 7984868889 9092949799
1 1/41.380 8185889091 93949699101
1 1/21.61 8287899093 949697101103
22.0 8488909394 959899103105
2 1/22.5 8589929496 97100101104106
33 8790949698 99101103106108
4495101104106107108111114116120
5597103106107110111114115118121
6699104107110111114115116121123
88101106110112114115118120123127
1010103108112114116118120121125129
1212105110114116118120121123127131
1515106112115118120121123125129134
1818108114116120121123125127131136
2020110115118121123125127129134136
2424111116120123125127129131136138
3030114118121125127129131134138141
3636115120123127129131134136141144
4242116121125129131134136138141144
4848118123127129131134136138144147
6060120125129131134136138141147150
7272121127131134136138141144147150
8484123129134136138141144147150153
9696125131136138141144147147153157

Colebrook's Main Equation

[Colebrook's Main Equation]

Plotted version of this equation is called Moody diagram which is a very popular method for computing pressure loss.

Swamee-Jain Equation

[Swamee-Jain Equation]

This equation actually estimates Colebrook's equation above with 2-5% error.

General Table 1

This table gives friction factor for certain pipe diameter and fluid velocity. Any value obtained from the table should be multiplied by 10-4.

Nominal Diameter in InchesActual Diameter in InchesVelocity in Feet per Second
123 456 81015 20
3/40.824430390365350340330320305290280
11.048415370350335325315305295275265
1 1/41.38395355335320310300290280265255
1 1/21.61385345325315300295280275255245
22370334315300290285270265245235
2 1/22.5355325305290280275260255240230
33345315295280270265255245230220
44285255240230225220210200190180
55275245230225215210200195185175
66265240225215210200195190175170
88255230215205200195185180170160
1010245220205200190185180175165155
1212235215200190185180175170160150
1414233210197188183178170165155148
1616228205194185180175167162152145
1818220200190180175170165160150140
2020215195185175170165160155145140
2424210190180170165160155150140135
3030200185175165160155150145135130
3636195180170160155150145140130125
4242190175165155150145140135130125
4848185170160155150145140135125120
6060180165155150145140135130120115
7272175160150145140135130125120115
8484170155145140135130125120115110
9696165150140135130125120120110105

General Table 2

This table gives friction factor for a certain pipe type, pipe diameter and fluid velocity. Any value obtained from the table should be multiplied by 10-4.

Pipe Diameter in InchesPipe TypeVelocity in Feet per Second
123456810152030
4old435415410405400395395390385375370
average355320310300290285280270260250250
new300265250240230225220210200190185
very smooth240205190180170165155150140130120
6old425410405400395395390385380375365
average335310300285280275265260250240235
new275250240225220210205200190180175
very smooth220190175165160150145140130120115
8old420405400395390385380375370365360
average320300285280270265260250240235225
new265240225220210205200190185175170
very smooth205180165155150140135130120115110
10old415405400395390385380375370365360
average315295280270265260255245240230225
new260230220210205200190185180170165
very smooth200170160150145135130125115110105
12old415400395395390385380375365360355
average310285275265260255250240235225220
new250225210205200195190180175165160
very smooth190165150140140135125120115110105
16old405395390385380375370365360350350
average300280265260255250240235225215210
new240220205200195190180175170160155
very smooth180155140135130125120115110105100
20old400395390385380375370365360350350
average290275265255250245235230220215205
new230210200195190180175170165160150
very smooth17015013513012512011511010510095
24old400395385380375370365360355350345
average285265255250245240230225220210200
new225200195190185180175170165155150
very smooth16514013512512012011511010510095
30old400385380375370365360355350350345
average280255250245240230225220210205200
new220195190185180175170165160155150
very smooth16013513012011511511011010510095
36old395385375370365360355355350345340
average275255245240235230225220210200195
new215195185180175170165160155150145
very smooth1501351251201151101101051009590
48old395385370365360355350350345340335
average265250240230225220215210200195190
new205190180175170165160155150145140
very smooth140125120115110110105100959090

German Engineers Society Tables

This table directly gives pressure loss in meters of H20 for a certain pipe type, pipe diameter and flow.

Flow in litres per secondDiameter in millimeters
40507080100125150200250300
133.510.81.780.930.32     
1.57522.43.81.960.660.220.09   
213038.56.53.31.120.370.15   
328283.5147.052.350.770.310.074  
4 14524.112.13.981.310.520.1230.042 
5 2213718.56.051.960.780.1850.062 
6 31252.5268.582.741.090.2550.0870.033
7  70.134.911.53.61.450.3390.1140.044
8  91.545.214.74.651.840.430.1450.056
9  11456.518.35.752.290.530.1780.07
10  14069.522.372.790.650.2180.085
15   1514915.35.951.360.450.178
20    8426.310.32.320.760.302
30     572251.60.64
40     9837.58.652.751.09
50      5713.34.211.65
60      8018.85.952.34
70       25.38.053.12
Flow in litres per secondDiameter in millimeters
400500600700800900100011001200
100.021        
150.044        
200.0750.025       
300.1570.0520.02      
400.2650.0880.0350.017     
500.4050.1320.0520.0260.014    
600.5650.1840.0740.0360.0180.011   
700.7550.2450.0980.0470.0250.014   
Flow in litres per secondDiameter in millimeters
40507080100125150200250300
80       32.910.34.05
90       41.2135.05
100       50.515.96.2
150        34.113.65
200         23.5
300          
Flow in litres per secondDiameter in millimeters
400500600700800900100011001200
800.970.3140.1250.060.0310.0180.011  
901.320.390.1560.0740.0390.0220.013  
1001.490.480.190.090.0470.0270.0160.01 
1503.221.020.4050.1920.0990.0560.0340.0210.014
2005.551.750.6950.3250.170.0940.0560.0350.023
30012.13.81.50.70.3630.1990.120.0730.048
40020.96.62.61.20.620.3390.2020.1240.082
500 10.23.951.850.940.5150.310.190.123
600 14.45.62.61.320.7250.4370.2650.174
700 197.553.51.770.9750.5820.3550.231
800  9.74.492.291.250.750.4520.295
900  12.25.62.851.580.940.570.37
1000  14.88.853.521.941.150.6950.455
1500   14.87.74.232.51.510.99
2000     7.44.32.61.71
3000      9.45.73.7
4000        6.35
Flow in litres per secondDiameter in millimeters
40507080100125150200250300
133101.80.90.30.94    
1.574223.81.90.630.2050.78   
2125396.53.251.080.360.138   
32758314.57.32.320.750.2950.076  
44751502512.841.30.510.1280.039 
5 2303919.86.220.790.1920.06 
6 3205628.392.81.120.2710.0860.034
7  7638.5123.81.50.3650.1150.046
8  10049.515.54.951.950.460.1470.059
9  1256219.66.22.450.580.1830.074
10   7724.57.72.950.70.2240.091
15   1755416.86.451.520.480.196
20    9529.611.22.60.8450.34
30     65255.81.850.73
40      4410.23.21.28
50      68164.951.95
60       22.772.78
70       30.39.43.7
Flow in litres per secondDiameter in millimeters
400500600700800900100011001200
100.021        
150.045        
200.0780.025       
300.1680.0550.022      
400.2850.0980.0370.018     
500.4350.1450.0570.0270.0140.0270.014  
600.610.2050.0810.0380.01950.011   
700.830.2750.1080.0510.0260.0145   
Flow in litres per secondDiameter in millimeters
40507080100125150200250300
80       3912.24.8
90        15.36
100        197.4
150        42.516.5
200         29
300         65
Flow in litres per secondDiameter in millimeters
400500600700800900100011001200
801.070.360.140.0640.0330.01850.0108  
901.350.450.170.080.0410.0230.0135  
1001.650.550.210.0970.050.0280.01650.012 
1503.71.20.460.2150.1080.060.0360.0220.0145
2006.52.60.80.370.1850.1030.0610.0380.025
30014.54.551.760.810.410.230.1320.0830.054
4002583.11.420.720.40.230.1450.094
500 12.54.82.21.10.610.3550.220.145
600 186.83.21.550.870.510.310.205
700 24.59.24.252.11.170.690.420.275
800  125.52.681.50.90.550.355
900  15.483.41.91.120.70.45
1000  198.64.22.311.370.850.55
1500   18.59.55.131.851.2
2000     95.43.22.08
3000       74.55
4000        7.9