A lawn sprinkler consists of two sections of curved pipe rotating about a vertical axis as shown. The sprinkler rotates with an angular velocity ω, and the effective discharge area is A, the water is discharged at a rate Q = 2vP_rA, where v_ris the velocity of the water relative to the rotating pipe. A constant friction torque M_fresists the motion of the sprinkler. Find an expression for the speed of the sprinkler in terms of the significant variables.

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Ur R R.