Question

A small water pump is used for an irrigation project. The pump takes water in from a river at 10^oC, 100 kPa at a mass flow rate of 16.83 kg/s. The exit line enters a pipe that goes up to an elevation 26.15 mm above the pump and river, where the water runs into an open channel. Assume the process is adiabatic and that the water stays at 10 ^oC. Find the required pump work.

Answer 1

Given: Temperature of water, T=10⁰C

Pressure of water, P=100 kPa

Mass flow rate of water at inlet, _in=16.83 kg/s

Elevation at the exit line, z_exit=26.15 mm=0.02615 m

Assumption:

1. Constant volume system with steady state flow.
2. No heat transfer takes place. i.e., Q=0
3. Velocity remains same at inlet and outlet. i.e., V_in=V_exit=V

For a steady state process, the continuity equation is

where _in  and _exit is the Mass flow rate at inlet and exit respectively.

The energy equation is

where is the Rate of heat transfer

is the Mass flow rate

h_in and h_exit is the Specific enthalpy of water at inlet and exit respectively

In this case, h_in=h_exit as temperature is same at inlet and outlet

V_in and V_exit is the Velocity at inlet and exit respectively

z_in and z_exit is the Elevation at inlet and exit respectively

g is Acceleration due to gravity, g=9.81 m/s²

is the Pump Work or Power

Thus the energy equation reduces to

Substitute the values