We have already seen the derivation and fundamentals of stagnation properties i.e. stagnation pressure, stagnation temperature and stagnation density for compressible fluid flow in our previous posts.

Now we will see here the derivation of expression of force exerted by a jet on a curved plate when the plate is moving in the direction of jet with the help of this post.

Let us first brief here the basic concept of impact of jets and after that we will derive the expression of force exerted by a jet on a curved plate when the plate is moving in the direction of jet.

### Impact of jets

Let us consider that we have one pipe through which liquid is flowing under pressure. Let us assume that a nozzle is fitted at outlet of pipe. Liquid which will come through the outlet of nozzle will be in the form of jet.

If a plate, which may be moving or fixed, is placed in the path of jet, there will be one force which will be exerted by the jet over the surface of plate. The force which will be exerted by the jet over the surface of plate, which might be moving or fixed, will be termed as impact of jet.

### Force exerted by a jet on a curved plate when the plate is moving in the direction of jet

Let us consider a jet of water striking a curved plate at the center of the plate which is moving with a uniform velocity in the direction of jet as displayed here in following figure.
Let us consider the following terms from above figure
V = Absolute velocity of jet
a = Area of jet
u = Velocity of the plate in the direction of jet

Relative velocity of water jet or velocity with which the water jet strikes the curved plate = (V-u)

Let us consider that plate is smooth and loss of energy due to the impact of jet is zero. We will have the similar velocity with which the jet will be leaving the curved plate i.e. (V-u)

Velocity will be resolved into two components. One component will be in the direction of jet and second component will be in the direction perpendicular to the jet.

Component of the velocity in the direction of jet = - (V- u) Cos θ

We have taken negative sign as at the outlet, the component will be in the opposite direction of jet.

Component of the velocity in the direction perpendicular to the jet = (V- u) Sin θ

Mass of the water striking the plate = ρ a (V-u)

Force exerted by the jet of water on the curved plate in the direction of jet

Work done by the jet per second on the plate will be given by following equation

Above equation, derived above, force exerted by the jet of water on the curved plate in the direction of jet and works done by the jet per second on the plate when water jet strikes the curved plate when the plate is moving in the direction of jet.

Do you have any suggestions? Please write in comment box.

Reference:
Fluid mechanics, By R. K. Bansal