Consider an ordinary shower where hot water at 70 C is mixed

Consider an ordinary shower where hot water at 70 C is mixed with cold water at 14 C . A steady stream of warm water at 40 C is desired. The hot water enters at 3 kg/s . Assume heat losses from the mixing chamber to be negligible and the mixing takes place at a pressure of 140 kPa .

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

Solution

For water at 140 kPa and 70 deg C, we get enthalpy h_hot = 293 kJ/kg

For water at 140 kPa and 14 deg C, we get enthalpy h_cold = 58.9 kJ/kg

For water at 140 kPa and 40 deg C, we get enthalpy h_mix = 168 kJ/kg

Using SL model and neglecting kinetic and potential energies we get,

m_hot*h_hot + m_cold*h_cold = m_mix*h_mix

3*293 + m_cold*58.9 = (3 + m_cold)*168

Solving this, we get m_cold = 3.437 kg/s