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.

Image Source ~ Crafted With ©Ishwaranand - 2020 ~ Image by ©Ishwaranand

Fig. This jet striking flat vertical moving plate

Let

v = Velocity of the jet (absolute)

a = Area from a cross-section about 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 of per jet with respect before the plate 

= (v- u) 

Mass about water striking each plate /sec 

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

= ρa x [v - u]

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 equal to W (watt).