Water is pumped from a lake to a storage tank 18 m above at a rate of 70 L/s while consuming20.4 kW of electric power. Disregarding any frictional losses in the pipes and any changes in kinetic energy, determine (a) the overall efficiency of the pump-motor unit and(b) the pressure difference between the inlet and the exit of the pump.

Solution 20P

Step 1</p>

In this problem, there is a motor which is taking power and pumping a specific amount of water into a tank which is at a particular height. So, in part (a), we have to calculate the overall efficiency of the pump motor unit and in part (b), we have to calculate the pressure difference between the inlet and exit of the pump.

Provided data,

Height of the storage tank,

Pumping rate of the motor,

Power consumed by the motor,

We know the density of water,

Step 2</p>

a) Rate of mass of water displaced

Rate of mass of water displaced from lake to storage tank,

That is,

We know that,

Therefore,

Here,

Therefore,

Rate of mass of water displaced,

Step 3</p>

a) Calculating the energy per mass of water

We know that, the potential energy,

Where, - mass of water

- Acceleration due to gravity =

The energy per mass is,

Here, we can write,

The energy per mass is,