Power Gained by Fluid from 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