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Impact of jet means the force exerted by the jet on the plate which maybe stationary or moving in nature.
The jet after striking the plate will move along the plate. But since the plate is vertical hence it is at right angle of the jet. Hence the angle of deflection will be 90°.The jet after striking the plate will move along the plate. But since the plate is vertical hence it is at right angle of the jet. Hence the angle of deflection will be 90°.
Since the angle of deflection is 90 degree therefore the velocity of a jet on striking the plate becomes 0.
Since the force in case of impact of jets is calculated by the rate of change of momentum. Hence the formula used is in terms of mass and velocity. Where mass remains the same but the velocity changes therefore two velocities are considered here one is initial and other is final velocity.
So in case of force exerted on a jet it is calculated by taking change in velocity as final velocity – initial velocity.
In this case the situation is inverse as the given condition is defining about the force is being exerted on a plate by the jet. So therefore the force value can be known by calculating the rate of change of momentum. And the change in velocity will be here
Initial – final velocity
Because, the velocity of the jet will be maximum at the initial point from where it is starting to flow but on striking the plate irrespective of the angle it is placed either it will be zero or negative.
The given condition addresses that the curved plate is moving in the direction of jet. Hence the velocity of the jet taking as ‘V' and for the moving plate the velocity taking as ‘u’ the difference in velocity will give us the relative velocity
Now for calculating the force value the equation comes as
Fx = ρa(V-u)²[1+cosθ]
And work done will be given as
Work done = ρa(V-u)²×u[1+cosθ]
Work done per second per unit weight of fluid striking per second
= 1/g [Vw1± Vw2]×u Nm/N
Work done per second per unit mass of fluid striking per second
= (Vw1± Vw2)×u Nm/kg
Efficiency of jet: The work done by the jet on the vane given by the equation, is the output of the jet whereas initial kinetic energy of the jet is the input. Hence, the efficiency (η) of the jet is expressed as
η = output/input
η = ρaVr1 [Vw1±Vw2]×u / ½(ρaV1)×V1²
Propulsion or the movement of the bodies such as ships, aircrafts, rockets, etc. with the help of jet is called Jet propulsion.
Efficiency of jet propulsion of a tank with an orifice will be given as
η = 2Vu/(V+u)²
Here, V=u
Since in the case-1 the inlet orifices are placed at right angle to the direction of motion of the ship. Hence the kinetic energy to be developed by the pump for the jet propulsion of the ship is more. Whereas, in the second case the inlet orifice is in the direction of motion of the ship, hence the required kinetic energy will be less in this case as compared to the case 1.
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