Lecture - 5 ( jet strikes on flat moving plate)


Let's continue after lecture4
Jet strikes with moving flat plate 
let us consider a plate which is free to move linearly with velocity 'U'. Point 1 represent the entry point of Jet on plate. Point 2 represent exit point of jet on Above and below ends of the plate. 'U1' represent velocity of entry point of plate and 'U2' represent velocity of exit point of plate. When Jet strikes the plate, it will move in linear direction so here U = U1 = U2. Now in these cases concepts of relative velocity will be used.
V1 represents velocity of jet at entry with respect to ground. Remember one thing that any relative term which is represented with respect to ground are absolute term. So here V1 is also called as absolute velocity of jet. Similarly U is also called as absolute velocity of plate because U is velocity of plate with respect to ground. V2 represents velocity of Jet at exit with respect to ground and it is also called as absolute velocity of Jet at exit.
Vr1 represent relative velocity of water jet at entry with respect to plate. Vr2 represent relative velocity of water Jet at exit with respect to plate.


We will study this condition in 2 different scenario.
Scenario1 is when our observer is at the ground
Point to be consider here is that the mass flow rate of water striking on the plate is not 'ρ*A*V1' like in previous cases, the mass flow rate of water striking on the plate is 'ρ*A*(V1-U1)' because here our plate is also moving with velocity U1.
If this linear velocity of plate (that is U1) is more than velocity of water Jet striking the plate (that is V1) then Water Jet will never able to strike the plate. Therefore velocity of plate should be less then velocity of water jet. And the term 'V1 - U1' itself represent relative velocity of water with respect to plate (that is Vr1)
Fx = Fn = force of jet acting on plate in normal direction or we can say in horizontal direction = m*V1 - [(m/2)*U2 + (m/2)*U2]
We know U = U1 = U2
Therefore,
Fx = Fn = m*V1 - m*U2 = m(V1 - U1) = ρ*A(V1-U1)*(V1-U1)
Fy = Fn = force of jet acting on plate in tangential direction or we can say in vertical direction = m*V2 - [(m/2)*Vr2 + (m/2)*(-Vr2)] = m*0 - 0 = 0

In previous cases our plate was fixed, so we were getting zero work done. Unlike previous cases in this case our plate is free to move, so here we are getting work. Work is simply defined as product of force and velocity
Work done = force (Fx ) * U
Now here in this force we do not have mass we have mass flow rate (that is kg/sec) therefore won't get work will get work done per second which is also called as power
Power = Fx * U = ρ*A*(V1-U1)*(V1-U1)*U watt

 In scenario 2 our observer is on the plate
If observer is on the blade then velocity of blade for the observer is zero. As in this case we are not observing from the ground so velocity of water jet will not be with respect to the ground, velocity of water jet will be with respect to blade (Vr1).
Fx = Fn = force of jet acting on plate in normal direction or we can say in horizontal direction = m*Vr1 - [(m/2)*U2 + (m/2)*U2] = m*Vr1 - [(m/2)*0 + (m/2)*0] = m*Vr1 = m*(V1 - U1)
As you see our final result is same because position of observer will never affect our final outcome

Let's continue to lecture 6

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