$(9)(25$ pts$)$ A large lawn sprinkler with two identical arms is used to generate power by attaching a generator to its rotating head. Water enters the sprinkler from the base along the axis of rotation at a total volumetric flow rate of $\backslash (1\mathrm{.}40\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$min$\}\backslash ),$ splits equally and leaves the $2$ nozzles all in the tangential direction $($no radial velocity component$).$ The sprinkler rotates at a rate of $280$ rpm in a horizontal plane. The diameter of each jet is $2\mathrm{.}2$ cm $,$ and the normal distance between the axis of rotation and the center of each nozzle is $75$ cm $.$ Determine the torque applied by the rotating sprinkler system to the generator in $\backslash (\backslash$mathrm$\{$N$\}\backslash$cdot $\backslash$mathrm$\{$m$\}=\backslash$mathrm$\{$J$\}\backslash )($which in turn could be multiplied by the rotation frequency to get power $($W$)).$

If you wanted this system to generate more power with the same sprinkler geometry $($arm length and nozzle diameter and shape$)$ and water flow rate, what would you want to see happen to the rotations per minute in this system? Briefly explain whether, all else being equal, the power output would be greater if the system operated at more or fewer rpm$\text{'}$s and explain on a physical basis referring to the momentum balance why this is the case.