Question $2$

Determine the power of a pump $($using $K$ and $\frac{L}{D}eq$ methods$)$ that can transport fluid through a $0\mathrm{.}75$ in diameter $($pipe roughness of $0\mathrm{.}003m)$ fluid distribution network. The fluid distribution network has a $100ft$ horizontal pipe, joined by a $90$ elbow to a $80ft$ vertical pipe and finally linked with the aid of a second $90$ elbow to a $100ft$ horizontal pipe discharge at atmospheric pressure. The viscosity of fluid is $0\mathrm{.}003$ Pa$.$s and density of fluid is $1500k\frac{g}{m^3}.$ Pump efficiency of $({}_p)43\%$ and motor efficiency of $({}_m)90\%$ is expected to discharge a flowrate of the liquid equals $2\mathrm{.}3f\frac{t}{s}.$ The additional fittings $(K$ and $\frac{L}{D}eq)$ on the pipe network are: $2-90$ elbow &$30,6-$gate valves $(0\mathrm{.}17$&$8)$ and $5-$branched tees $(1\mathrm{.}0$&$60).$ Both ends of the pipe are at atmospheric condition. State the assumed conditions adopted for solving this problem. Use both the $K-$value and $\frac{L}{D}eq$ value methods for the determination of minor losses.

$(20$ marks$)$