A counterflow single pass heat exchanger $($HX$)$ uses water to cool light oil as shown in Figure $8.$ The water exists in the tank at $70$ F and atmospheric pressure. Assume the properties of water are constant at $70$ F$.$ The oil enters the heat exchanger at $210$ F and exits the heat exchanger at $130$ F$.$ Assume the properties of oil are constant at $200$ F$.$ The mass flowrate of the oil is $6\mathrm{.}288$ lbm$/$s$.$ The cooling water exits the heat exchanger at $90$ F $($Point B$).$ The HX overall heat transfer coefficient $($U$)$ is $130\mathrm{.}4$ Btu$/$hr$-$ft$2-$F$.$ Assume the heat transfer area on the oil side is equal to the heat transfer area on the water side.

What is the heat exchanger area in units of ft$2?$

Select the answer that is closest to the true value.

A$)81\mathrm{.}8$ B$)177\mathrm{.}1$ C$)254$ D$)500$

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A

B

C

D