II$.$ There is a pump with power $12hp(1hp=550lbff\frac{t}{s})$ and efficiency of $70\%,$ and it

pumps water from a lake to a pool at a flow rate of $1\mathrm{.}2f\frac{t^3}{s},$ as shown in the figure. The

water surface of the pool is $35ft$ above that of the lake. Ignores the velocity in the lake

and the pool. $g=32\mathrm{.}2f\frac{t}{s^2},=62\mathrm{.}4lb\frac{m}{f}{t}^3.$

a$)$ Compute the head loss, $h_L,$ of the pumping system $($in $ft)(10pts)$

b$)$ Suppose $90\%$ of the head loss, h $h_L,$ comes from the major head loss in the pipelines

before and after the pump, the diameter of the pipelines is $0\mathrm{.}5,$ and the wall

roughness of the pipelines is $0\mathrm{.}001$ f$.$ Estimate the length of the total length of the

pipelines. Note: you can use either the Swamee and Jain formula or the Moody

diagram, at the end of this exam paper, to evaluate the friction coefficient $(15pts).$

c$)$ Plot EGL and HGL from the entrance to the exit of the pipelines $($there is head loss at

the entrance and the exit$)(10$ pts$)$