(Solved): Water at \( 70^{\circ} \mathrm{F} \) flows by gravity from a large reservoir at a high elevation t ...

Water at \( 70^{\circ} \mathrm{F} \) flows by gravity from a large reservoir at a high elevation to a smaller one through a 62 -ft-long, 2-Indiameter cast Iron piping system that includes four standard flanged elbows, a well-rounded entrance, a sharpedged 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 \( 10 \mathrm{ft}^{3} / \mathrm{min} \). The density and dynamic viscosity of water at \( 70^{\circ} \mathrm{F} \) are \( \rho=62.30 \mathrm{lbm} / \mathrm{ft}^{3} \) and \( \mu=2.360 \mathrm{lbm} / \mathrm{ft} \cdot \mathrm{h}=6.556 \times 10^{-4} \mathrm{lbm} / \mathrm{ft} \cdot \mathrm{s} \). The roughness of the cast Iron pipe is \( \varepsilon=0.00085 \mathrm{ft} \). The elevation \( z_{1} \) of the higher reservoir is \( \mathrm{ft} \).