2. (40 pts). In a chemical processing plant, a liquid is pumped from an open tank through a 0.1 m diameter vertical pipe and into another open tank as shown

in Figure 2a. A valve is located in the pipe, and the minor loss coefficient is a function of the valve setting as shown in Figure 2b. Assume a friction factor f = 0.02 for the pipe. All minor losses except for the valve are negligible. The fluid levels in the two tanks remains constant. The pump head capacity curve is given as h_{a}=52.0-1.01 \times 10^{3} Q^{2} \text { where } h_{a} \text { is in meters and } Q \text { is in } \mathrm{m}^{3} / \mathrm{s} \text {. } (a) (10 pts) Write the energy (system) equation for the problem and include all of the known values (b) (10 pts) Determine the expected flowrate. Show this solution graphically by plotting the pumpcapacity curve and system equation as a function of Q. (c) (10 pts) Determine the power required by the motor assuming an 80% pump efficiency and theliquid is ethyl alcohol at 20 deg C. (d) (10 pts) Determine the required valve setting (percent open) to reduce the flowrate in (b) by 50%.Show, graphically, the solution by plotting the pump capacity curve and system equation (with the reduced flow) as a function of Q.