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 jetstriking the plate A1. Picture below should be vertical

Explanation / Answer

Mass=M
initial speed =Vo
Let the area of the disk be A.

then as it is in equilibrium: net force on it =0
P0 *A + Mgh0 = P1*A ,
where P1 is the pressure due to the jet on the plate.
=> A = Mgh0/(P1 - P0)
From equation of continuity,
A1v1 = A2v2 [ 1= nozzle , 2 = point of striking]
=> A1 * v0 = A * v1
=> A1 = A*v1/v0
=> A1 = [Mgh0/(P1 - P0)](v1/v0) = area of the fluid jet striking the plate
SO the required area,A1= [Mgh0/(P1 - P0)](v1/v0)
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