Water is being pumped from a large lake to a reservoir 25 m above at a rate of 25 L/s by a 10-kW (shaft) pump. If the irreversible head loss of the piping system is 5 m, determine the mechanical efficiency of the pump.

Step 1 of 5</p>

The pump is moving the water from the large lake to a higher reservoir at 25m as shown in the figure below. The head loss of the pipe is given to be 5m, here we need to calculate the mechanical efficiency of the pump using the energy equation.

Step 2 of 5</p>

The density of water is taken to be and it is considered to be incompressible. The flow is assumed to be steady.

Let us consider two points 1 and 2 as shown in the figure above, at the free surface of the lake and the reservoir respectively. As both are open to atmosphere, pressure at both the points is equal to atmospheric pressure, that is . By considering the surface of lake as reference (). Also the velocities at both the points are negligible, that is .

Step 3 of 5</p>

For Steady, incompressible and control volume flow through these two points through pump and pipes, energy equation is given by,

Substituting ,

…………..1