A 10-m-long, 5.042-cm I.D. copper pipe has two fully open gate valves, a swing check valve, and a sudden enlargement to a 9.919-cm I.D. copper pipe. The \(9.919 \mathrm{~cm}\) copper pipe is \(5.0 \mathrm{~m}\) long and then has a sudden contraction to another \(5.042-\mathrm{cm}\) copper pipe. Find the head loss for a \(20^{\circ} \mathrm{C}\) water flow rate of \(0.05 \mathrm{~m}^{3} / \mathrm{s}\).