Water at \(20^{\circ} \mathrm{C}\) flows by gravity from a large reservoir at a high elevation to a smaller one through a 35-m-long, 5-cm-diameter cast iron piping system that includes four standard flanged elbows, a well-rounded entrance, a sharp-edged exit, and a fully open gate valve. Taking the free surface of the lower reservoir as the reference level, determine the elevation \(z_{1}\) of the higher reservoir for a flow rate of \(0.3 \mathrm{~m}^{3} / \mathrm{min}\). Answer: \(8.08 \mathrm{~m}\)