Water at $70F$ flows by gravity from a large reservoir at a high elevation to a smaller one through a $56-$ ft $-$long, $2-$in$-$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 $10f\frac{t^3}{m}in.$ The density and dynamic viscosity of water at $70$ F are $=62\mathrm{.}30lb\frac{m}{f}{t}^3$ and $=2\mathrm{.}360lb\frac{m}{f}t*h=6\mathrm{.}556{10}^{-4}lb\frac{m}{f}t*s.$ The roughness of the cast iron pipe is $=0\mathrm{.}00085ft.$

The elevation $z_1$ of the higher reservoir is $$ ft$.$