Question

A motor driven water pump operates with an inlet pressure of 96 kPa (absolute) and mass flow rate of 120 kg/min. The motor consumes 0.8 kW of electrical power, determine the maximum water pressure at the discharge of the pump.

Answer 1

The maximum water pressure at the discharge of the pump (exit) = 496 kPa

Step-by-step explanation:

The equation expressing the relationship of the power input of a pump can be computed as:

`E _(pump,u) = (m(P_2-P_1))/(\rho)`

where;

m = mass flow rate = 120 kg/min

the pressure at the inlet
`P_1` = 96 kPa

the pressure at the exit
`P_2` = ???

the pressure
`\rho` = 1000 kg/m³

∴

`0.8 * 10^(3) \ W = ((120 \ kg/min * 1min/60 s)(P_2-96000))/(1000)`

`0.8 * 10^(3)* 1000 = {(120 \ kg/min * 1min/60 s)(P_2-96000)}`

`800000 = {(120 \ kg/min * 1min/60 s)(P_2-96000)}`

`(800000)/(2) = P_2-96000`

400000 = P₂ - 96000

400000 + 96000 = P₂

P₂ = 496000 Pa

P₂ = 496 kPa

Thus, the maximum water pressure at the discharge of the pump (exit) = 496 kPa