Answer:
To calculate the outlet temperature of the cooling water, we can use the energy balance equation for a surface condenser:
Q_condensed + Q_cooled = Q_input
Where:
Q_condensed = m_dot * (h_fg)
Q_cooled = m_dot_water * C_water * (T_outlet - T_inlet)
Q_input = m_dot * h_in
Given:
Wet-steam flow rate (m_dot) = 3600 kg/hr = 1 kg/s
Mass of cooling water (m_dot_water) = 18 kg/s
Operating pressure = 10 kPa
Dryness factor = 0.82
Condensate temperature = 29 °C
Cooling water inlet temperature (T_inlet) = 18 °C
Specific heat capacity of water (C_water) = 4.187 kJ/kg.°C
First, calculate the enthalpy of the inlet condition of the steam (h_in):
Using steam tables at 10 kPa and dryness factor 0.82, find the enthalpy of saturated vapor (h_fg) and the enthalpy of saturated liquid (h_f). Then:
h_in = (1 - dryness factor) * h_f + dryness factor * h_fg
Next, rearrange the energy balance equation to solve for the outlet temperature of cooling water (T_outlet):
T_outlet = (Q_input - Q_condensed) / (m_dot_water * C_water) + T_inlet
Substitute the values into the equations, calculate h_in, h_condensed, and T_outlet to get the outlet temperature of cooling water.
Remember to convert units consistently throughout the calculations.
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