We have already seen the derivation of

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*continuity equation**,**Bernoulli’s equation**,**momentum equation**,**velocity 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.

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**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

^{2 }
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 V

^{2}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.

You should also find out here some quite important posts as mentioned below

- Metal cutting tools: definition and classification
- Explain the geometry and nomenclature of a single point cutting tool
- Positive and negative effects of friction
- Classifications of friction
- Coulomb's law of dry friction
- Some guidelines for solving frictional problems
- Concept of rolling resistance or rolling friction
- Wedge friction and concept of self- locking
- Hook’s law
- Concept of eccentric loading
- Assumptions made in the Euler’s column theory
- Difference between long column and short column
- Euler’s formula and its limitations

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

Image courtesy: Google

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