A power washer is being used to clean the siding of a house. Water at the rate of 0.1 kg/s enters at 20°c and 1 atm, with the velocity 0.2m/s. The jet of water exits at 23°c, 1 atm with a velocity 20m/s at an elevation of 5m. At steady state, the magnitude of the heat transfer rate from power unit to the surroundings is 10% of the power input. Determine the power input to the motor in kW.
Answer:
Net power of 1.2 KW is being extracted
Explanation:
We are given;
Mass flow rate; m' = 0.1kg/s
Inlet temperature; T1 = 20°C = 293K
Inlet pressure; P1 = 1 atm = 10^(5) pa
Inlet velocity; v1 = 0.2 m/s
Exit Pressure; P2 = 1 atm = 10^(5) pa
Exit Temperature; T2 = 1 atm = 296K
Exit velocity; V2 = 20m/s
Change in elevation; h = Z2 - Z1 = 5m
We are told that the magnitude of the heat transfer rate from the power unit to the surroundings is 10% of the power input.
Thus;
Q = -0.1W
From Bernoulli equation;
Q - W = ∆Potential energy + ∆Kinetic energy + ∆Pressure energy
Where;
∆Potential energy = mg(z2 - z1)
∆Kinetic energy = ½m(v2² - v1²)
∆Pressure energy = mc_p(T2 - T1)
Thus;
-0.1W - W = [m'g(z2 - z1)] + [½m'(v2² - v1²)] + [m'c_p(T2 - T1)]
Where C_p is specific heat capacity of water = 4200 J/Kg.k
Plugging in the relevant values, we have;
-1.1W = (0.1 × 9.81 × 5) + (½ × 0.1(20² - 0.2²)) + (0.1 × 4200 × (296 - 293))
-1.1W = 4.905 + 19.998 + 1260
-1.1W = 1284.903
W = -1284.903/1.1
W ≈ -1168 J/s ≈ -1.2 KW
The negative sign means that work is extracted from the system.
