Power Gained by Fluid from Pumps or Fans

The power gained by fluid from operating pumps or fans

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

m = mass flow rate

w = specific work

Specific Work

Specific work - w - can be expressed:

w = g h         (2)

where

h = head

g = acceleration of gravity

Mass Flow Rate

Mass flow rate - m - can be expressed:

m = ρ Q         (3)

where

ρ = density

Q = volume flow rate

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

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 1,000 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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