Force exerted on curved plate

Force exerted by a jet on a fixed curved plate

Jet strikes the curved plate at the centre

• Sign a jet of water strikes a fixed curved plate at the middle as shown in Fig. 
• Some jet after striking the plate comes out with the identical velocity if the plate is smooth and there is never a loss of energy due to impact of the jet, into the tangential direction of the curved plate. 
• This velocity at the outlet of the plate can be resolved within two components, one in the direction of jet also other perpendiculars over the direction of the jet.
• Component of velocity in the direction of jet = -v cosθ. 

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

Fig. Jet striking a fixed curved plate at the centre 

(-ve sign is taken as the velocity at an outlet is in the opposite direction of the jet of water coming out from nozzle). 

Component of velocity perpendicular to the jet = v sinθ

Force exerted on the jet into the direction of jet, 

@ Fx = Mass per secx (Vx1 - Vx2) 

where,

Vx1 = Initial velocity in the direction of jet = v

Vx2 = Final velocity in the direction of jet = - v cosθ 

Fx = ρav {v - (-v cosθ)}

= ρav (v + v cosθ)

= ρav^2 (1 + cosθ)

@ Fy = Mass per secx (Vy1 - Vy2)

where,

Vy1 = Initial velocity into the direction of y = 0

Vy2 = Final velocity into the direction of y = v sinθ 

Fy = ρav [0 – vsinθ] 

= ρav^2 sinθ 

-ve sign means that force is acting in the downward direction.