Wednesday, 30 January 2019

We have already seen the derivation of continuity equationBernoulli’s equationmomentum equationvelocity of sound in an isothermal process, velocity of sound in an adiabatic process, fundamentals of stagnation properties i.e. stagnation pressure, stagnation temperature and stagnation density for compressible fluid flow in our previous posts.

Now we will start here the basics and derivation of expression of force exerted by a jet on stationary inclined flat plate 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 stationary inclined flat plate.

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.

In order to determine the expression of force exerted by the jet over the surface of plate i.e. impact of jet, we will use the basic concept of Newton’s second law of motion and impulse-momentum equation.

Force exerted by jet on stationary inclined flat plate

We have already seen the expression for force exerted by jet on vertical flat plate. Let us derive here the expression of force exerted by jet on stationary inclined flat plate.

Let us consider a jet of water, which is coming from the outlet of nozzle fitted at the pipe, strikes a flat inclined flat plate as displayed here in following figure.
V = Velocity of the jet in x direction
d = Diameter of the jet
a = Area of cross-section of the jet = (π/4) x d
θ = Angle between the jet and the plate

Let us determine the mass of water per second striking the plate
Mass of water per second striking the plate = ρ a V

Let us assume that inclined plate is smooth and there is no loss of energy due to the impact of jet. Considering this assumption, we can say that jet will move over the surface of inclined plate after striking the plate with a velocity equivalent to the initial velocity i.e. V.

Now we will determine the force Fn exerted by the jet on the plate in a direction normal to the plate.

Fn = Mass of jet striking per second x [Initial velocity of jet before striking in the direction of n - final velocity of jet after striking in the direction of n]

Fn = ρ a V x [V Sin θ - 0]

Fn = ρ a V2 Sin θ

Above force will be resolved in two components i.e. one component in the direction of jet and second component in the direction perpendicular to the jet.

Above equation, derived here, provides the components of force exerted by the liquid jet on the inclined plate in the direction of jet and in the direction perpendicular to the jet.

Now we will discuss the force exerted by a jet on stationary curved plate in our next post.

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

Reference:

Fluid mechanics, By R. K. Bansal