In a steam power plant in Philadelphia engineers are trying

In a steam power plant in Philadelphia, engineers are trying to size and select a replacement pump to pump condensed water in the condenser unit of the power plant. The nameplate on the original pump is worn out and they cannot recognize its model to order a replacement. A recently graduated mechanical engineer claims that he can size (=find the mass flow rate pump handles) the pump by measuring the cooling water temperatures in and out and also knowing cooling water mass flow rate. He set up thermometers and could measure the cold water temperature entering the condenser at 11 degree and warm water temperature leaving the condenser at 29 degree C. Also he could measure the mass flow rate of cooling water at 82kg/s. Having said that steam is entering at 70 degree C and condensed water (steam changed to liquid water) is also at 70 degree C do you think he can size the condensed water pump based on these information? If your answer is no, list the other piece of information that he would need to get. If your answer is yes, calculate the mass flow rate of condensed steam to select the replacement pump. You may assume that steam pressure does not change through the whole phase change process.

Solution

a)

By energy balance, heat lost by steam = heat gained by cooling water

m_steam*(h_steam - h_liq) = m_water*Cp*(Tout - Tin)

Since everything in this equation is known except m_steam, the engineer can size the pump based on this info.

b)

From steam properties at 70 deg C, we have h_vap = 2630 kJ/kg and h_liq = 293 kJ/kg

Hence, heat energy lost by converting 1 kg steam at 70 C to 1 kg water at 70 C = 2630 - 293 = 2337 kJ

Heat gained by water = m_water*Cp*(Tout - Tin)

= 82*4.185*(29 - 11)

= 6177.1 kW

m_steam*2337 = 6177.1

m_steam = 2.643 kg/s