# Power Gained by Fluid from Pump or 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

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

## Related Topics

• Pumps - Piping systems and pumps - centrifugal pumps, displacement pumps - cavitation, viscosity, head and pressure, power consumption and more

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