Pump power calculation

A pump is a kind of equipment that consumes a considerable amount of energy in the industrial process. It is mainly driven by a motor, and in many cases, a kW meter or ampere meter is installed so that the power consumption can be calculated, but in many cases, this is not possible.

If know the pumping flow rate and pressure difference, user can calculate the amount of work required by the pump. Of course, the power usage of the motor requires assumptions.

The hydraulic power that drives the pump depends on mass flow rate, liquid density and height difference.

Formula of pump power consumption

Pump power equation is as follows.

W = ρ*Q*h*g/η

where
W = power (kg•m2/s3, ft-lbf/s)
ρ : density of fluid (kg/m3, lbm/ft3)
Q = volumetric flow (m3/s, gpm)
h = head (m or ft) the fluid has to be lifted
g : acceleration of gravity (9.8 m/s2, 32.174 ft/s2)
η = total efficiency (%, η of pump, η of motor)
1. In case of MKS (m/kg/sec/°C/bar/W) units
W = ρ*Q*h*g/η = (1000 kg/m3 * 1000 m3/s * 25 m * 9.8 m/s2) / (3600 * 1000 * 0.8) = 85.1 kW

where,
W : power (W)
ρ : density of fluid (kg/m3)
Q : flow (m3/h)
h : differential head (m)
g : acceleration of gravity (9.8 m/s2)
η : friver efficiency (%)
2. In case of FLS (ft/lb/sec/°F/psi/bt) units
W = ρ*Q*h/η = (62.4 lbm/ft3 * 1000 gpm * 106 ft) / (7.481 gal/ft3 * 33,000 ft-lb/min-hp * 70%) = 38.3 hp

Where,
W : power (hp)
ρ : density of fluid (kg/m3 or lbm/ft3)
Q : flow (gpm)
h : differential head (ft)
g : acceleration of gravity (32.174 ft/s2)
η : friver efficiency (%)

Python code of pump power consumption

The following is a Python example that calculates the pump power.

def pumpower(unit, d, q, h, n):
    if unit == "MKS" and n > 0:
        W = (d * q * h * 9.8) / (3600 * 1000 * n) # kW
    elif unit == "FLS" and n > 0:
        W = (d * q * h) / (7.481 * 33000 * n) # hp
    else:
        pass
    return W

pumppowerMKS = pumpower("MKS", 1000, 1000, 25, 0.8) # 1000 kg/m3, 1000 m3/hr, 25 m, 80%
pumppowerFLS = pumpower("FLS", 62.4, 1000, 106, 0.7) # 62.4 lbm/ft3, 1000 gpm, 106 ft, 70%

print("Pump power = ", pumppowerMKS, " kW")
print("Pump power = ", pumppowerFLS, " hp")

When run the code, you get the results below.

Pump power =  85.069 kW
Pump power =  38.275 hp