Question 4.20: Problem: A water pump raises 5 kg / s of water from a reserv...
Problem: A water pump raises 5 kg / s of water from a reservoir sunk 10 m underground to a tank located 30 m above ground. The pressure at the reservoir level is 20 kPa and in the tank is 100 kPa. What is the power required to drive the pump?
Find: Power to drive the pump \dot{W} .
Known: Mass flow rate of water \dot{m} = 5 kg s/ , exit height z_2 = 30 m, inlet height z_1 = –10 m, exit pressure P_2 = 100 kPa, inlet pressure P_1 = 20 kPa.
Assumptions: Negligible heat losses from the pump, negligible changes in kinetic energy between inlet and outlet, water is incompressible with specific volume v = 10^{–3} m³ / kg, acceleration due to gravity is at earth’s surface g = 9.81 m / s² .
Governing Equation:
Rate of shaft work (pump) \dot{W} _{shaft}=\dot{m} \left[v\left(P_2-P_1\right) + g\left(z_2-z_1\right) \right]
\dot{W} _{shaft} = 5 \ kg/s\left[10^{-3} \ m^3/kg \times \left(100 \times 10^3 \ N/m^2 – 20 \times 10^3 \ N/m^2\right) + 9.81 \ m/s^2\left(30 \ m -\left(-10 \ m\right) \right) \right]
\dot{W} _{shaft} = 2362.0 \ W=2.36 \ kW
Answer: The pump requires a power input of 2.36 kW.