Pump and Fan Efficiency

The overall pump and fan efficiency is the ratio of power actually gained by the fluid - to the shaft power supplied

For a fluid flow process involving a pump or fan the overall efficiency is related to the

• hydraulic
• mechanical
• volumetric

loss in the pump or fan.

Hydraulic Loss and Hydraulic Efficiency

Hydraulic loss relates to the construction of the pump or fan, and is caused by the friction between the fluid and the walls, acceleration and retardation of the fluid and the change of the fluid flow direction.

The hydraulic efficiency can be expressed as:

η_h = w / (w + w_l) (1)

where

η_h = hydraulic efficiency

w = specific work from the pump or fan

w_l = specific work lost due to hydraulic effects

Mechanical Loss and Mechanical Efficiency

Mechanical components - as transmission gear and bearings - generates a mechanical loss that reduces the power transferred from the motor shaft to the pump or fan impeller.

The mechanical efficiency can be expressed as:

η_m = (P - P_l) / P (2)

where

η_m = mechanical efficiency

P = power transferred from the motor to the shaft

P_l = power lost in the transmission

Volumetric Loss and Volumetric Efficiency

Due to leakage of fluid between the back surface of the impeller hub plate and the casing, or through other pump components - there is a volumetric loss reducing the pump efficiency.

The volumetric efficiency can be expressed as:

η_v = q / (q + q_l) (3)

where

η_v = volumetric efficiency

q = volume flow out of the pump or fan

q_l = leakage volume flow

Total Loss and Overall Efficiency

The overall efficiency is the ratio of power actually gained by the fluid to the shaft power supplied. The overall efficiency can be expressed as:

η = η_h η_m η_v (4)

where

η = overall efficiency

The losses in the pump or fan converts to heat transferred to the fluid and the surroundings. As a rule of thumb the temperature increase in a fan transporting air is approximately 1 ^oC.

Example - Hydraulic Efficiency for a Pump

An inline water pump works between pressure 1 bar (1 10⁵ N/m²) and 10 bar (10 10⁵ N/m²). Density of water is 1000 kg/m³. The hydraulic efficiency η_h = 0,91.

The actual water head (water column) can be calculated as:

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 pump must be constructed for the specific work:

w_c = g h / η_h

    = (9.81 m/s²) (91.7 m) / 0.91

    = 988.6 m²/s²

The construction or design head is:

h = w_c / g

    = (988.6 m²/s²) / (9.81 m/s²)

    = 100.8 m - water column

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