A centrifugal pump having a pump head$-$discharge relationship $($pump characteristic curve$)$

given by the following equation $h_a=180-5*Q^2,$ with $h_a$ in ft and Q in $f\frac{t^3}{s},$ is to be used

with a system of two open$-$tanks and a single pipe $(4-$in diameter$)$ that has three elbows $(K_e$

$=0\mathrm{.}51$ and a globe valve $)=(5\mathrm{.}80.$ The total length of the pipe is $600$ ft $.$ Both tanks have

water in them, with water flowing from $(1)$ to $(2).$ The elevations of points $(1)$ and $(2)$ are $100$

ft and $150$ ft $,$ respectively. Calculate the design volumetric flow rate $($ cfs $)$ in the pipe. Neglect

entrance and exit losses. The friction factor for the pipe flow is $0\mathrm{.}020.$