A lawn sprinkler consists of two sections of curved pipe rotating about a vertical axis as...

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