Force Exerted By Jet On Moving Vertical Plate

Force Exerted By Jet On Moving Vertical Plate Assignment Help | Force Exerted By Jet On Moving Vertical Plate Homework Help

Force Exerted by Jet on Moving Vertical Plate

Consider a jet impinging normally on a plate. As a result of impact of jet, the plate moves in the direction of jet as shown in.




Let v = velocity of the jet

v1 = velocity of the plate

a = c/s area of jet

Then relative velocity = (v - v1) as the plate moving in the same direction as that jet.

Force exerted by jet = mass x change in velocity = ρ a (v – v1) x (v – v1) – 0)

F = ρ a (v – v1)2

Work done = Force x displacement / sec = ρ a (v – v1)2 v1

Kinetic energy of the jet,

K.E. = ½ ( ρ a v) v2 = ½  ρ a v3

Efficiency = Work done / Energy supplied = ρ a (v – v1)2 v1 / ½ ρ a v3

η  =  2 ( v - v1)2 v1 / v3

The efficient becomes maximum when (v – v1)2 v1 becomes maximum. For maximum efficiency, differentiate (v – v1)2 w.r.t v1 and equate to zero

(v2 – 2 v. v1 + v12)

dη  / dv1 = v2 – 4 v. v1 + 3v12 = 0 = (v – 3v1) (v - v1) = 0

either v - v1 = 0, which is not practicable

or v- 3v1 = 0, v = 3v is the condition for maximum efficiency

ηmax  = 2 (3v1 – v1)2 v1 / (3v1) x v1

ηmax  = 8 / 27

For more help in Force Exerted by Jet on Moving Vertical Plate click the button below to submit your homework assignment