A pump with a power of 5 kW (pump power, and not useful pump power) and an efficiency of 72 percent is used to pump water from a lake to a pool through a constant diameter. The free surface of the pool is 25 m above the free surface of the lake. If the irreversible head loss in the piping system is 4 m, determine (a) the mass flowrate of water and (b) the pressure difference across the pump.

a) The mass flow rate of water is 14.683 kilograms per second.

b) The pressure difference across the pump is 245.175 kilopascals.

Explanation:

a) Let suppose that pump works at steady state. The mass flow rate of the water (), in kilograms per second, is determined by following formula:

(1)

Where:

- Pump power, in watts.

- Efficiency, no unit.

- Gravitational acceleration, in meters per square second.

- Hydrostatic column, in meters.

If we know that , , and , then the mass flow rate of water is:

The mass flow rate of water is 14.683 kilograms per second.

b) The pressure difference across the pump (), in pascals, is determined by this equation:

(2)

Where is the density of water, in kilograms per cubic meter.

If we know that , and , then the pressure difference is:

The pressure difference across the pump is 245.175 kilopascals.

answer:

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