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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 pumpā€“motor unit and (b) the pressure difference between the inlet and the exit of the pump.

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hamzaahmeds

Answer:

(a) Ī· = 0.835 = 83.5%

(b) Ī”P = 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 = ĻghQ

where,

P = Power to pump = ?

Ļ = density of water = 1000 kg/mĀ³

g = 9.8 m/sĀ²

h = height = 20 m

Q = Volume Flow Rate = (95 L/s)(0.001 mĀ³/1 L) = 0.095 mĀ³/s

Therefore,

P = (1000 kg/mĀ³)(9.8 m/sĀ²)(20 m)(0.095 mĀ³/s)

P = 18620 W = 18.62 KW

So, now the efficiency is given as:

Ī· = Desired Output/Required Input

where,

Ī· = overall efficiency = ?

Desired Output = Power to Pump = 18.62 KW

Required Input = Electric Power = 22.3 KW

Therefore,

Ī· = 18.62 KW/22.3 KW

Ī· = 0.835 = 83.5%

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

Ī”P = Ļgh

where,

Ī”P = Pressure Difference = ?

Ļ = density of water = 1000 kg/mĀ³

g = 9.8 m/sĀ²

h = height = 20 m

Therefore,

Ī”P = (1000 kg/mĀ³)(9.8 m/sĀ²)(20 m)

Ī”P = 196000 Pa = 196 KPa

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