Water is pumped from a lake to a storage tank 20 m above at a rate of 95 L/s while consuming 22.3 kW of electric power. Disregarding any frictional losses in the pipes and any changes in kinetic energy, determine (a) the overall efficiency of the pump-motor unit and (b) the pressure difference between the inlet and the exit of the pump.

(a) η = 0.835 = 83.5%

(b) ΔP = 196000 Pa = 196 KPa

Explanation:

(a)

The useful output of the pump-motor system will the power required to pump the water to the storage tank. That power is given as:

P = ρghQ

where,

P = Power to pump = ?

ρ = density of water = 1000 kg/m³

g = 9.8 m/s²

h = height = 20 m

Q = Volume Flow Rate = (95 L/s) (0.001 m³/1 L) = 0.095 m³/s

Therefore,

P = (1000 kg/m³) (9.8 m/s²) (20 m) (0.095 m³/s)

P = 18620 W = 18.62 KW

So, now the efficiency is given as:

η = Desired Output/Required Input

where,

η = overall efficiency = ?

Desired Output = Power to Pump = 18.62 KW

Required Input = Electric Power = 22.3 KW

Therefore,

η = 18.62 KW/22.3 KW

η = 0.835 = 83.5%

(b) The pressure difference between inlet and the outlet is given by the formula:

ΔP = ρgh

where,

ΔP = Pressure Difference = ?

ρ = density of water = 1000 kg/m³

g = 9.8 m/s²

h = height = 20 m

Therefore,

ΔP = (1000 kg/m³) (9.8 m/s²) (20 m)

ΔP = 196000 Pa = 196 KPa