$120$

$3.$ The $5-$pipe water distribution network shown in Figure $3$ has a fixed$-$head reservoir $(R_1)$ with water level of $70m.$ The pipe $(P_1)$ that connects the fixedhead reservoir to the rest of the network is $100m$ in length, and has an inner diameter of $610mm$ and a $\text{'}C\text{'}$ factor of $140.$ Pipes $2$ to $5$ have the following parameters: length $=500m,$ Hazen$-$Williams $\text{'}C\text{'}$ factor $=130,$ and inner diameter $=203mm.$ Node $1$ is at elevation $5m,$ Node $2$ at elevation $10m,$ Node $3$ at elevation $25m$ and Node $4$ at elevation $15m.$ Demand at Node' $1$ is $Q_1=50\frac{L}{s},$ demand at Node $2$ is $Q_2=23\frac{L}{s},$ demand at Node $3$ is $Q_3=18\frac{L}{s},$ and demand at Node $4$ is $Q_4=17\frac{L}{s}.$

a$)$ Calculate the flows in the $5$ pipes.

b$)$ Calculate the pressure head at all nodes.

Figure $3.$ Water network with fixed$-$head reservoir.