Force Exerted by the Jet on a stationary Vertical Plate

Assumption :

1. Fluid density remains constant
2. Vertical plate is made of a rigid body and does not move 
3. Velocity remains constant
4. Distance between the nozzle and vertical plate remains constant
5. The momentum of fluid remains constant
6. The Velocity of the water jet in the direction of the jet is zero after striking
7. The angle between the plate and the jet is 90∘ 
   
   
   
   
   

V = velocity of the fluid from the jet (m/s)

d = diameter of the jet (m)

a  = area of cross-section of the jet (m^2)= 

$$\frac{\pi d^{2} }{4}

m = mass  (ρaV) (kg/s)

$$F_{x} \frac{\pi d^{2} }{4}

we know that force exerted by the jet on water in the direction of jet is rate of change of momentum of fluid

 Fx =  mV

       =  rate of change of momentum

        = (mass X velocity of jet before striking - mass X velocity of jet after striking)/time

        =(mass/time)(velocity of jet before striking -  velocity of jet after striking)

        = ρaV[V−0] (remember assumption no.6 this is where 0 comes from )

$\rho a V^{2}$

Applications: The force calculated by this method is use for water cutting jet machine . In real life they don't have any much applications