3.6 The hot water needs of a residence are met by a 20-gal hot water heater rated at 6000 Btu/h. The tank is initially filled with hot water at 175°F. As the hot water supply is drawn from the tank, it is replaced by cold water at 50°F at a flow rate sufficient to keep the tank full at all times. During this replenishing process in the tank, the water is heated at the water heater’s full rated capacity.

Water this hot is great for washing clothes or dishes, but it is far too hot for other purposes, like taking a shower. To use the hot water for a shower, it must be mixed with cold water. Consider a case where the hot water from the tank is mixed with cold water at 50°F as shown in Figure P3.6. The cold water enters the mixing process at a flow rate of 0.95 gpm. After an 8-minute shower, the temperature in the water tank has dropped to 140°F.

Determine the following:

a. Volumetric flow rate of the hot water from the tank during the shower (gpm)

b. Average temperature of the water delivered to the shower (°F)

c. Number of gallons of water used during the shower Note: When solving this problem, the instantaneous water temperature in the tank can be approximated as a constant value at the average temperature in the tank during the shower.