An insulated pump receives liquid water at 20°C and 100 kPa, and exhausts the water at 20.0 MPa and 40°C. The mass flow rate of the water is 15 kg/s. Determine the power required by the pump.

Question

Given: P1 = 100 kPa; T1 = 20°C; m?= 15 kg/s; P2 = 20,000 kPa; T2 = 40°C
Water (Take State 1 as the inlet, State 2 as the outlet.)
Assume: Q?=0 (insulated). For a compressor, assume steady-state, steady-flow, single-inlet, single-outlet flow, with ?KE = ?PE = 0

What will be an ideal response?

Answer 1

With these assumptions, the First Law for open systems reduces to W?=m?(h1?h2)
As the pressure of the exit is very large, we will use compressed liquid data for the water:
h1 = 84.01 kJ/kg
h2 = 185.17 kJ/kg
Solving: W?= -1,520 kW = -1.52 MW