QUESTION $3(20$ marks$)$

A network of pipes is to be used to deliver fire flow to various fire hydrants $($F$-1$ to F$-8)$ in an industrial facility. All pipes have Hazen$-$Williams coefficients of $110$ and internal diameters of $150$ mm $.$ All distances between fire hydrants $($i$.$e$.,$ located at nodes indicated by black circles$)$ are equal with a pipe length of $100$ m$.$ If the fire hydrant at $F-7$ is opened to the atmosphere $($and all other fire hydrants remain closed$),$ determine the flow rate $($in $\frac{L}{m}in)$ that will be delivered when the height of water in the reservoir is $50$ m above the level of the fire hydrant exit. Assume that all minor head losses $($e$.$g$.,$ entrance, elbows, valves$)$ and the head loss in the pipe leading from the elevated reservoir to the first node are insignificant.