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# A horizontal jet of water (diameter, D = 0.01 m) with velocity V = 30 m/s impinges on a vane moving horizontally at U = 5 m/s as in Figure 1.

A horizontal jet of water (diameter, D = 0.01 m) with velocity V = 30 m/s impinges ona vane moving horizontally at U = 5 m/s as in Figure 1. Part of the jet flow rate strikes the top surface ( = 60°) with mass flow rate m2 and part the bottom surface ( = 40°) with flow rate m3. The mass-less vane sits on top of a cart moving at the same speed via a spring with spring constant K = 20,000 N/m. Recall that the force of the spring is given by F = -K*x, where x is the displacement of the spring from its relaxed length (L). Find the mass flow rate ratio m2/m3 that will cause the spring length (d) to be 0.05m. Assume incompressible, steady, fully developed flow and uniform velocity everywhere. Neglect body and surface forces.