Problem 422 Consider an ordinary shower where hot water at 6

Problem 4-2-2

Consider an ordinary shower where hot water at 66 C is mixed with cold water at 6 C . A steady stream of warm water at 42 C is desired. The hot water enters at 6 kg/s . Assume heat losses from the mixing chamber to be negligible and the mixing takes place at a pressure of 140 kPa .

Part A

Determine the mass flow rate (m) of cold water using the SL model.

Solution

>> Tih = Inlet Temperature of Hot Water = 66 C

>> To = Mixture Temperature = 42 C

>> Tic = Inlet Temperature of Cold Water = 6 C

>> mh = Mass Flow Rate of hot water = 6 kg/s

>> mc = Mass Flow Rate of Cold Water = ?

>> As, HEAT LOSS BY HOT WATER = HEAT GAINED BY COLD WATER

=> mh*Ch*(Tih - To) = mc*Cc*(To - Tic)

Ch = Cc = Specific Heat of Water

=> 6*(66 - 42) = mc*(42 - 6)

Solving,

=> mc = 4 kg/s ....REQUIRED MASS FLOW RATE OF COLD WATER........ANSWER.....