(Solved): Problem: \( \quad \) Determine the size of the pump (in \( \mathrm{kW} \) ) needed to pump a feed ...

Problem: \( \quad \) Determine the size of the pump (in \( \mathrm{kW} \) ) needed to pump a feed stream to a unit operating at a pressure of \( 4 \mathrm{~atm} \) (gauge). The feed solution is to be pumped from an open tank that has a liquid level \( 2 \mathrm{~m} \) above the floor through \( 120 \mathrm{~m} \) of pipe that has an inside diameter of \( 0.040 \mathrm{~m} \). There are three \( 90^{\circ} \) square elbows and four \( 180^{\circ} \) medium radius return bends in the piping, and the feed section to which the fluid is pumped is \( 10 \mathrm{~m} \) above the floor. A flow of 7 \( \mathrm{kg} / \mathrm{s} \) of feed solution is required. The viscosity of the feed solution is \( 2 \mathrm{cP} \), while the density is \( 845 \mathrm{~kg} / \mathrm{m}^{3} \). The efficiency of the pumping system with the motor is \( 35 \% \). You may assume the piping is commercial steel. Determine the cost of this designed pump, the PED, FCI, and TCI. For friction factors: