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# Flat vertical plate moving of jet

## Force on the flat vertical plate moving in the direction of the jet

Fig. shows a jet of water punching a flat vertical plate moving with a similar velocity away from the jet.

Let

v = Velocity of the jet (absolute)

a = Area from a cross-section of the jet

u = Velocity of the flat plate.

• During this case, the jet does not strike the plate by a velocity v, though it strikes with a relative velocity, which is equal to the absolute velocity of a jet from water minus some velocity of the plate.

Hence, the relative velocity per jet with respect to the plate

= (v- u)

Mass of water striking each plate /sec

= ρ x Area of jet x Velocity with which jet strikes the plate

= ρa x [v – u]

The force exerted by the jet on the moving plate in the direction of the jet,

Fx  = Mass of water striking per sec x [Initial velocity with which water strikes – Final velocity]

= ρa (v – u) [(v – u) – 0]

( Final velocity in the direction of jet is zero)

= ρa (v – u)^2

• In this case, the work will be done by the jet on the plate, as the plate is moving.
• For the stationary plates, the work done is zero.
• Work was done per second by the jet on the plate

= Forces x (Distance in each direction of force / Times)

= Fx X u

= ρa(v – u)^2 x u

• In the above equation, if the value of ρ for water is taken in S.I. units (i.e., 1000 kg/m3), the work is done will be in N m/s.
• The term N m/s is equal to W (watt).

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