wl = specific work lost due to hydraulic effects (J/kg)
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:
ηm = (P - Pl) / P (2)
ηm = mechanical efficiency
P = power transferred from the motor to the shaft (W)
Pl = power lost in the transmission (W)
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:
ηv = q / (q + ql) (3)
ηv = volumetric efficiency
q = volume flow out of the pump or fan (m3/s)
ql = leakage volume flow (m3/s)
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 = ηhηmηv (4)
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 1oC.
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 ηh = 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:
wc = g h /ηh
= (9.81 m/s2) (91.7 m) / 0.91
= 988.6 (J/kg, m2/s2)
The construction or design head is:
h =wc / g
= (988.6 m2/s2) / (9.81 m/s2)
= 100.8 m - water column
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