Liquid Pumps
Technical Equations and Information Tables

Efficiency Formulas for Rotary Positive Displacement Pumps    Rules of Thumb for Motors    
Approximate rpm at Full Load for Medium Sized Motors    
Atmospheric Pressure Conversion    
Loss of Air Pressure Due to Friction    
Loss of Air Pressure Due to Pipe Bends    
Flow of Air through Orifice

Efficiency Formulas for Rotary Positive Displacement Pumps

Liquid HP =
GPM x psi
1747

Volumetric
efficiency
=
Actual GPM
Theoretical GPM

Overall pump
efficiency
=
HP of fluid discharge
HP of driving motor

Mechanical
efficiency
=
Overall pump efficiency
Volumetric efficiency

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Pipe Velocity

Velocity
(ft/sec)
=
     GPM x 0.321     
(pipe ID in inches)2

  • It is best to allow 10 pipe diameter upstream and 5 pipe diameter downstream leading to the pump suction.
  • Try to keep pipe velocities around 10 ft/sec for good practical results.
  • Doubling the pipe diameter increases the capacity of the pipe four times.

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Rules of Thumb for Motors

At 3600 rpm: motor develops 1.5 ft/lb per hp

At 1800 rpm: motor develops 3.0 ft/lb per hp

At 1200 rpm: motor develops 4.5 ft/lb per hp

 

At 575 volts, a 3-phase motor draws 1.00 amps per hp

At 460 volts, a 3-phase motor draws 1.25 amps per hp

At 230 volts, a 3-phase motor draws 2.50 amps per hp

 

hp =
Torque ft/lb x rpm
5252

Torque (ft/lb) =
hp x 5252
rpm

Torque (in/lb) =
hp x 63,025
rpm

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Approximate rpm at Full Load for Medium Sized Motors

Poles rpm
60 Hz
Synch
speed
rpm
50 Hz
Synch
speed
2 3500 3600 2850 3000
4 1750 1800 1450 1500
6 1150 1200 950 1000
8 850 900 700 750

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Atmospheric Pressure Conversion

Altitude
in feet
Pressure
in psia
Altitude
in feet
Pressure
in psia
0 14.7 5000 12.23
100 14.64 7000 11.34
300 14.54 10,000 10.11
500 14.43 15,000 8.29
700 14.33 20,000 6.76
1000 14.17 25,000 5.45
1500 13.92 30,000 4.36
2000 13.66 40,000 2.72
3000 13.17 50,000 1.68
4000 12.69 60,000 1.04

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Loss of Air Pressure Due to Friction
(Per 100 Feet of Pipe, 100 psi Initial Pressure)

Free-air
capacity in cfm
(at 14.7 psi)
Equivalent
capacity in cfm
(at 100 + 14.7 psi)
Loss of pressure in psi per pipe ID
1/2" 3/4" 1" 1-1/4" 1-1/2" 2"
10 1.28 1.38 0.09 0.03 0.007  
20 2.56 1.42 0.34 0.10 0.026 0.012 
30 3.84 3.13 0.74 0.23 0.056 0.026 
40 5.13 5.55 1.28 0.38 0.096 0.044 0.013
50 6.41 8.65 2.00 0.60 0.146 0.067 0.020
60 7.69   2.84 0.84 0.210 0.095 0.027
70 8.97   3.85 1.12 0.280 0.130 0.036
80 10.25   5.01 1.44 0.360 0.160 0.046
90 11.53   6.40 1.85 0.450 0.200 0.058
100 12.82   7.80 2.21 0.550 0.250 0.069
125 16.02   12.40 3.41 0.850 0.380 0.107
150 19.22   18.10 4.91 1.200 0.540 0.150
175 22.43     6.80 1.640 0.730 0.200
200 25.63     8.79 2.120 0.950 0.260
250 32.04       3.300 1.480 0.400
300 38.45       4.710 2.100 0.570
350 44.86       6.450 2.860 0.770
400 51.26       8.300 3.700 0.990
450 57.67         4.650 1.270
500 64.08         5.790 1.560
600 76.90         8.45 2.230
700 89.71           3.000
800 102.50           4.000
900 115.30           5.050
1000 128.20           6.200

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Loss of Air Pressure Due to Pipe Bends
(Per 100 Feet of Straight Pipe)

Angle of
pipe bend
Loss of pressure in psi per pipe ID
1/2" 3/4" 1" 1-1/4" 1-1/2" 2"
45° 0.73 0.92 1.18 1.55 1.85 2.35
90° 1.60 2.00 2.50 3.40 4.00 5.10

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Flow of Air through Orifice
(with Discharge of Orifice at 14.7 psia and 70°F)

Supply
pressure
(psig)
Flow of air in cfm per orifice size
1/32" 1/16" 3/32" 1/8" 5/32" 3/16" 7/32" 1/4" 9/32" 5/16"
65 1.15 4.49 10.10 17.90 27.90 40.30 55.20 71.80 89.90 111.70
70 1.21 4.77 10.80 19.10 29.70 42.80 58.80 76.40 95.70 118.80
75 1.30 5.06 11.40 20.20 31.50 45.40 62.30 81.00 105.50 126.00
80 1.37 5.35 12.10 21.10 33.30 48.00 65.80 85.60 107.40 133.10
85 1.44 5.64 12.70 22.50 35.10 50.60 69.40 90.30 113.20 140.30
90 1.52 5.92 13.40 23.70 36.90 53.20 72.90 94.80 119.00 147.50
95 1.59 6.21 14.00 24.80 38.70 55.70 76.50 99.40 124.90 154.60
100 1.66 6.50 14.70 26.00 40.50 58.30 80.00 104.60 130.70 161.80
125 2.03 7.94 17.90 31.70 49.50 71.40 97.78 127.10 159.80 197.50
150 2.40 9.28 21.20 37.50 58.40 84.40 115.40 150.40 189.00 233.30

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