(Solved): A water pump is used to pump water from one large reservoir to another large ...

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A water pump is used to pump water from one large reservoir to another large reservoir that is at a higher elevation. The free surfaces of both reservoirs are exposed to atmospheric pressure. Comparing the results of two cases, the volume flow rate increases as expected when one doubles the inner diameter of the pipe. One might expect that the Reynolds number increases as well. Therefore, compare the results of the Reynolds number when velocity and diameter are given respectively for each case: Case 1: \( D=2.03 \mathrm{~cm} \) and \( V=0.59603 \mathrm{~m} / \mathrm{s} \) Case 2: \( D=4.06 \mathrm{~cm} \) and \( V=0.19869 \mathrm{~m} / \mathrm{s} \) \( \begin{aligned} z_{2}-z_{1} & =7.85 \mathrm{~m} \text { (elevation difference) } \\ D & =2.03 \mathrm{~cm} \text { (pipe diameter) } \\ K_{L, \text { entrancx }} & =0.50 \text { (pipe entrance) } \\ K_{L, \text { valve }} & =17.5 \text { (valve) } \\ K_{L} \text { elbow } & =0.92 \text { (each elbow-there are } 5 \text { ) } \\ K_{L, \text { exit }} & =1.05 \text { (pipe exit) } \\ L & =176.5 \mathrm{~m} \text { (total pipe length) } \\ \varepsilon & =0.25 \mathrm{~mm} \text { (pipe roughness) }\end{aligned} \) The density and viscosity of water at \( T=20^{\circ} \mathrm{C} \) are \( 998.0 \mathrm{~kg} / \mathrm{m}^{3} \) and \( 1.002 \times 10^{-3} \mathrm{~kg} / \mathrm{m} \cdot \mathrm{s} \), respectively. The Reynolds number of the larger-diameter pipe is than that of the smaller-diameter pipe.