(Solved):   (b) In a chemical processing plant a liquid is pumped from an open tank, through a \( 0.1 ...

 

(b) 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 the figure below. A valve is located in the pipe, and the minor loss coefficient for the valve as a function of the valve setting is shown below also. The pump head capacity relationship is given by the equation \( \mathrm{h}_{\mathrm{a}}=52.0-1.01 \times 10^{3} \mathrm{Q}^{2} \) with \( \mathrm{h}_{\mathrm{a}} \) in meters when \( \mathrm{Q} \) is in \( \mathrm{m}^{3} / \mathrm{s} \). Assume the Darcy friction factor \( \mathrm{f}=0.02 \) for the pipe and all minor losses except for the valve are negligible. The fluid levels in the two tanks can be assumed to remain approximately constant. (i) Determine the flowrate with the valve wide open. (15 marks) (ii) Determine the required valve setting (percent open) to reduce the flowrate by \( 50 \% \).