Horizontal disk of mass M is constrained horizontally, but is free to move verti

Question

Horizontal disk of mass M is constrained horizontally, but is free to move vertically. A jet of fluid strikes the disk from below. The jet leaves the nozzle at initial speed Vo. The fluid jet decelerates to velocity V1 before it hits the plate due to gravity on the jet. The plate sits at an equilibrium height of ho above the jet exit plane. At the equilibrium position the net force on the plate is 0. -> Apply the integral mass conservation equation between control surfaces 0 and 1 to find an equation for the area of the fluid jet striking the plate A1.

Explanation / Answer

Mass of disk is M initial speed of jet is Vo final speed of jet is V1 the plate is at height ho let the acceleration of fluid be a we know that Vo^2 - V1^2 = 2aho or a = (Vo^2 - V1^2/2ho) the force acting on fluid is F = M * a the pressure on fluid is P = pgho where p is density of fluid and g = 9.8 m/s^2 we know that P = F/A where A is area of plate A1 or A = F/P = M * a/pgho

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