Answer:
(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
<u>η = 0.835 = 83.5%</u>
(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)
<u>ΔP = 196000 Pa = 196 KPa</u>
