A power washer used to clean the sidingof a hosue has water entering through a h

Question

A power washer used to clean the sidingof a hosue has water entering through a hose at 20C, 1atm and avelocity of 0.2m/s. A jet of water exits with a velocity of20m/s at an average elevation of 5m, with no significant change intemperature or pressure. At steady state, the magnitude ofthe heat transfer rate from the power washer to the surroundings is10% of the electrical power input. Evaluating electricity at8 cents per kW x h determine the cost of the power required, incents per liter of water delivered. Compare with the cost ofwater , assuming 0.05 centers per liter, andcomment.
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Explanation / Answer

at 20C, 1atm and velocity of jet = 0.2m/s; exit velocity = 20m/s; elevation of 5m; given change in pressure and temperature = negligible; power transferred by the water jet = .5 *d*A *v^3 power delivered by jet = .5 *1000*(20^3-.2^3); =1111.1 kWh; heat transfer rate = 10% of electrical power input ; electrical power input = heat transfer rate / 0.1; = 11111.1 kWh; cost of power = 8 *11111.1; = 88888cents ; cost of water = 1111.1*0.05; =555 cents

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