Power Gained by Fluid from a Pump or a Fan
The power gained by fluid from an operating pump or fan
Power Gained by Fluid
The power gained by the fluid from a pump or fan can be expressed as:
P = m w (1)
where
P = power (W)
m = mass flow rate (kg/s)
w = specific work (Nm/kg, J/kg)
Specific Work
Specific work - w - can be expressed:
w = g h (2)
where
h = head (m)
g = acceleration of gravity (9.81 m/s2)
Mass Flow Rate
Mass flow rate - m - can be expressed:
m = ρ Q (3)
where
ρ = density (kg/m3)
Q = volume flow rate (m3/s)
Combining (1), (2) and (3) the power gained by the fluid from a pump or fan can be expressed as:
P = ρ Q g h (4)
With specific weight expressed as:
γ = ρ g (5)
where
γ = specific weight (N/m3)
equation (4) can be modified so the power gained by the fluid from a pump or fan can be expressed as:
P = γ Q h (6)
Since head can be expressed as
h = (p2 - p1) / γ (7)
equation (4) can be modified so the power gained by the fluid from a pump or fan can be expressed as:
P = Q (p2 - p1) (8)
Example - Head Rise of a Inline Pump
An inline water pump works between measured pressure 1 bar (1 105 N/m2) and 10 bar (10 105 N/m2). Density of water is 1000 kg/m3. The volume flow is measured to 1 10-3 m3/s.
The actual water head (water column) can be calculated using (7):
h = (p2 - p1) / γ
= (p2 - p1) / ρ g
= ((10 105 N/m2) - (1 105 N/m2)) / (1,000 kg/m3) (9.81 m/s2)
= 91.7 m - water column
The power gained by the fluid can be calculated using equation (4):
P = ρ Q g h
= (1,000 kg/m3) (1 10-3 m3/s) (9.81 m/s2) (91.7 m)
= 899.6 kg.m2/s3 (W)
= 0.9 kW
