A heat exchanger is to be designed to heat raw water by the use of condensed water at \(67{ }^{\circ} \mathrm{C}\) and \(0.2 \mathrm{bar}\), which will flow in the shell side with a mass flow rate of \(50,000 \mathrm{~kg} / \mathrm{h}\). The heat will be transferred to \(30,000 \mathrm{~kg} / \mathrm{h}\) of city water coming from a supply at \(17{ }^{\circ} \mathrm{C}\left(C_{p}: 4184 \mathrm{~J} / \mathrm{kg}-\mathrm{K}ight)\). The fouling resistance equal to \(0.000176 \mathrm{~m}^{2} \mathrm{~K} / \mathrm{W}\) is assumed. The maximum pressure drop on the shell side is \(5.0 \mathrm{psi}\). The water outlet temperature should not be less than \(40^{\circ} \mathrm{C}\). Calculate the heat exchanger length and pressure drops in both streams. The TEMA standard shell and tube heat exchanger with the following geometrical parameters is selected.

Shell internal diameter: \(0.39 \mathrm{~m}\)

Number of tubes: 124 Outer tube diameter: \(19 \mathrm{~mm}\)

Inner tube diameter: \(16 \mathrm{~mm}\)

Thermal conductivity of tube material: \(60 \mathrm{~W} / \mathrm{m}^{2}-\mathrm{K}\)

Pitch size: \(0.024 \mathrm{~m}\)

Number of tube passes: 2