What is the temperature differential if a heat exchanger with a flow rate of 10 gallons per minute transfers 50,000 Btu/h?

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To calculate the temperature differential in a heat exchanger, you can use the formula:

[ \Delta T = \frac{Q}{(C_p \times \dot{m})}

]

where:

(\Delta T) = temperature differential in degrees Fahrenheit
(Q) = heat transfer in Btu/h
(C_p) = specific heat capacity of the fluid (for water, C_p is approximately 1 Btu/lb°F)
(\dot{m}) = mass flow rate in lb/h

First, you need to determine the mass flow rate of the water. Water has a density of approximately 8.34 lb/gallon.

The flow rate of 10 gallons per minute can be converted to hours:

[ 10 \text{ gallons/min} \times 60 \text{ min/h} = 600 \text{ gallons/h} ]

Now, calculating the mass flow rate:

[ \dot{m} = 600 \text{ gallons/h} \times 8.34 \text{ lb/gallon} \approx 5004 \text{ lb/h} ]

Now, substituting the values into the formula:

[ \