The piping system shown in Figure $($which does not show details of all the fittings$)$ is used to connect a large reservoir to a pump where it is then pumped to a small wilderness hostel. The pipe is $0\mathrm{.}05$ m diameter cast iron and must deliver $0\mathrm{.}3\frac{m^3}{m}in$ of $15\mathrm{.}0C$ water. The $90$ m long pipeline contains four swing check valves and five $90$ standard elbows. All connections are threaded. Find the head loss between points $1$ and $2.$