Problem $6.$ Water is pumped from large tanks B to A through the system shown in the figure below. The $4-$inch diameter pipe is $180$ feet long and the $8-$inch diameter pipe is $100$ feet long. Both are made of cast iron. The entrance to the pipe system is sharp$-$edged and the elbows are regular $90$ flanged. The pump provides a pumping power of $5$ horsepower and a flow rate of $1$ cubic foot per second. Determine the elevation difference between the two tanks, shown as $z$ in the figure below. $=1\mathrm{.}94$ slugs $\frac{?}{f{t}^3},v=1\mathrm{.}21{10}^{-5}f\frac{t^2}{s},g=32\mathrm{.}17f\frac{t}{s^2}$