Question 10.10: The coils in Fig. 10-27 are identical and require 20 gpm of ......
The coils in Fig. 10-27 are identical and require 20 gpm of water at full load. The water enters at 45 F and the flow controllers are set for 55 F discharge temperature. A partial load condition exists where the flow rate through the coils is reduced to 12 gpm. Find the temperature of the water being returned to the chiller for each type of control valve.
he two-way valve system will return the water at 55 F assuming the controller can maintain the water temperature leaving the coil at exactly 55 F. In the case of the threeway valve system, water at 45 F is mixed with 55 F water leaving the coil. An energy balance on the valve assuming constant specific heat and density yields
\dot{Q}_{1} T_{1} + \dot{Q}_{2} T_{2} = \dot{Q}_{3} T_{3}
T_{3} = \frac{\dot{Q}_{1} T_{1} + \dot{Q}_{2} T_{2}}{\dot{Q}_{3}} = \frac{8(45) + 12(55)}{20} = 51 F
It is clear that the two-way valve leads to variable flow and a fixed temperature differential, whereas the three-way valve gives a constant flow rate with a variable temperature differential.