Efficiency in Pumps or Fans

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

• hydraulic
• mechanical
• volumetric

losses in the pump or fan.

Hydraulic Loss and Hydraulic Efficiency

Hydraulic losses relates to the construction of the pump or fan and is caused by the friction between the fluid and the walls, the 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 (J/kg)

w_l = specific work lost due to hydraulic effects (J/kg)

Mechanical Loss and Mechanical Efficiency

Mechanical components - like transmission gear and bearings - creates mechanical losses 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 (W)

P_l = power lost in the transmission (W)

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 (m³/s)

q_l = leakage volume flow (m³/s)

Total Loss and Overall Efficiency

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

η = η_hη_mη_v                               (4)

where

η = overall efficiency

The losses in a pump or fan converts to heat that is 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). The density of water is 1000 kg/m³. The hydraulic efficiency is 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 (J/kg, 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