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# Power Gained by Fluid from Pump or Fan

## Calculate 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.

## Related Documents

• ### Centrifugal Pumps - Viscosity Influence

Hydrodynamic losses through pumps depends on fluid viscosities.
• ### Efficiency in Pumps or Fans

The overall pump and fan efficiency is the ratio power gained by the fluid to the shaft power supplied.
• ### Power

Power is the rate at which work is done or energy converted.
• ### Pump Power Calculator

Calculate pumps hydraulic and shaft power.
• ### Pumping Water - Required Horsepower

Horsepower required to pump water.
• ### Pumps - Suction Specific Speed

Suction Specific Speed can be used to determine stable and reliable operations for pumps with max efficiency without cavitation.
• ### Pumps, Fans and Turbines - Horsepower

British Horse Power as used for pumps, fans and turbines - and how to convert to other units.

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## Citation

• The Engineering ToolBox (2004). Power Gained by Fluid from Pump or Fan. [online] Available at: https://www.engineeringtoolbox.com/pump-fan-power-d_632.html [Accessed Day Month Year].

Modify the access date according your visit.

9.19.12