Hot water at \(100,000 \mathrm{lb} / \mathrm{hr}\) and \(160^{\circ} \mathrm{F}\) is cooled with \(200,000 \mathrm{lb} / \mathrm{hr}\) of cold water at \(90^{\circ} \mathrm{F}\), which is heated to \(120^{\circ} \mathrm{F}\) in a countercurrent shell-and-tube heat exchanger. The exchanger has \(20-\mathrm{ft}\) steel tubes with 0.75 -in. O.D. and 0.62 -in. I.D. The tubes are on a 1 -in. square pitch. The thermal conductivity of copper is \(25.9 \mathrm{Btu} /\left(\mathrm{ft}-\mathrm{hr}{ }^{-} \mathrm{F}\right)\). The mean heat-transfer coefficients are estimated as \(h_{i}=200 \mathrm{Btu} / \mathrm{hr}-\mathrm{ft}^{2}-^{\circ} \mathrm{F}\) and \(h_{o}=200 \mathrm{Btu} / \mathrm{hr}^{-}-\mathrm{ft}^{2}-{ }^{\circ} \mathrm{F}\). Estimate:

(a) The area for heat transfer

(b) The diameter of the shell