An adiabatic pump receives liquid water at 25°C and 100 kPa. The water exits at 30.0 MPa and 40.0°C. Using your pump model, plot the power required for this pumping operation for entering volumetric flow rates ranging from 0.001 m3/s to 1.0 m3/s.
Given: P1 = 100 kPa; T1 = 25°C; P2 = 30,000 kPa; T2 = 40°C
Water (Take State 1 as the inlet, State 2 as the outlet.)
Assume: Q?=0 (adiabatic). For a compressor, assume steady-state, steady-flow, single-inlet, single-outlet flow, with ?KE = ?PE = 0
What will be an ideal response?
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 = 104.93 kJ/kg
v1 = 0.001003 m3/kg
h2 = 193.91 kJ/kg
The mass flow rate will be found from the volumetric flow rate: m?=V1?/v1
The power as a function of volumetric flow rate is then
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