13 - Question 9 by Kambiz Ehsani - First Lat of the Thermodynamics - Pressure washer problem - 4/27/2018 - Solved

What is the increase of water temperature in the water being pumped by a pressure washer pump at a car wash? The inlet water temperature at the inlet of the pump is 70 degree F. We know that the pressure of the pump is 3000 psig. Please elaborate on your assumptions.

Solution:
In the absence of other information, it is common sense that the pump is adiabatic and isentropic. For isentropic compression and no change in Kinetic and Potential, the steady flow energy equation (SFEE) gives:

Wpump = m * (h2 -h1) = m * v * (v2 - v1)

Where :
v = specific volume of inlet water
v = 0.01672 ft^3 / lbm  (Sat. H20 at 1 atm)

and :
 p2 = 3000 lbf/ft^2
p1 = 14.7 lbf/inch^2

Then:
from the definition of c_p Delta _T
Delta _T = (9.2 Btu/lbm) / (1 Btu/lbm) = 9.2 Degree

Tout = 70 F + 9.2 F = 79.2 Degree F