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

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

• A. 5 degrees
• B. 10 degrees
• C. 15 degrees
• D. 20 degrees

Answer: (B)

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: \[ \

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:

[

\