MASS OF COOLING WATER REQUIRED IN A CONDENSER

Let   ṁ_w = mass flow rate of circulating water, kg/h

ṁ_s = mass flow rate of steam condensed, kg/h

t = temperature of wet exhaust steam, °C

t_c = temperature of condensate, °C

h_f = enthalpy of water at t°C, kJ/kg

h_fg = enthalpy of evaporation of steam at t°C, kJ/kg

x = dryness fraction of exhaust steam

t_iw = inlet temperature of cooling water, °C

t_ow = outlet temperature of cooling water, °C

h_c = enthalpy of condensate, kJ/kg = c_pw t_c

c_pw = specific heat of cooling water, 4.1868 kJ/kg.K

Now Heat given by steam = Heat absorbed by water

For jet condenser,

t_ow = t_c

For surface condenser,

m_s (h_f + xh_fg − h_c) = m_w c_pw (t_ow − t_iw)

Example 8.2

A 200 kW steam engine has a steam consumption of 10 kg/kWh. The back pressure of the engine is equal to the condenser pressure of 0.15 bar. The condensate temperature is 32°C. The cooling water temperature at inlet and outlet are 20°C and 30°C, respectively. Calculate the mass of cooling water required per hour if the exhaust steam is dry saturated.

Solution

At 0.15 bar, h_f = 225.91 kJ/kg, h_fg = 2373.1 kJ/kg, t_c = 32°C, t_ow = 30°C, t_iw = 20°C

Total steam used per hour = 200 × 10 = 2000 kg

Total circulating water used = 58.88 × 2000 = 117760 kg/h