Mechanical Engineering-Fluid mechanics-impact of jets

PDF on topic of Impact of Jets from Subject of Fluid Mechanics. Next PDF will have topics when jets strike a moving plate/vane.

1. Fluid Mechanics - Impact of
Jets
Er. Himanshu Vasistha

2. Topics to be covered
1.Force exerted by liquid jet on a stationary vertical & inclined vertical plate.
2.Force exerted by liquid jet on a stationary curved vane.
3.Force exerted by liquid jet on a hinged plate.

3. Impact of jets
For liquid coming out of a pipe, a nozzle fitted at the end of the pipe increases the velocity of the liquid.
The liquid coming out of the nozzle is in the form of a jet.
If a flat plate or a vane is placed in jet’s path, it will exert a force on the plate or vane.

4. Force exerted on stationary vertical flat plate
V = velocity with which jet strikes the stationary
flat plate
D = diameter of the jet
*Jet deflects 90 degree tangentially after striking
the plate.
*Assuming no friction & loss energy upon impact

5. Force exerted on stationary vertical flat plate

*As the pressure at inlet & outlet is atmospheric, the velocities at inlet & outlet are also same.

*Mass flow rate of the liquid striking the plate is given by:


= Mass flow rate of the liquid

= Density of the liquid
= Cross sectional area of the jet

6. Force exerted on stationary vertical flat plate

Force exerted can be calculated by using the Impulse Momentum Equation
= rate of change of momentum in the direction of force
Change of momentum:
●Initial momentum =
●Final momentum = 0
Rate of change of momentum = = =

7. Point to remember
As per Newton’s third law of motion:
Force exerted by the plate on the jet is in the negative x-axis direction.

8. Force exerted on stationary inclined flat plate

Flat plate is inclined at an angle to the direction
of the moving jet.
*Mass flow rate of the liquid striking the plate is given by:

9. Force exerted on stationary inclined flat plate

Let, = force component exerted in the tangential direction by the jet on the plate & = force
component exerted in the normal direction by the jet on the plate.
The component of velocity in the direction normal to plate =
As the jet leaves tangentially, the final velocity in the direction normal to plate = 0

10. Force exerted on stationary inclined flat plate

Using Impulse Momentum principle, the force exerted by the jet in the direction normal to the plate is
given by:

11. Force exerted on stationary inclined flat plate

Resolving normal force into two components:
Along x-axis:

Along y-axis:

12. Force exerted on stationary inclined flat plate

Let and be discharge in the two directions as shown in the figure.


The above equation is zero as we have assumed there is no friction.

13. Force exerted on stationary inclined flat plate

14. Question
A 75 mm diameter jet of an oil
having specific gravity 0.8
strikes normally a stationary
flat plate. If the force exerted by
the jet on the plate is 1200 N,
find the volume flow rate of the
oil.
Answer:

15. Jet striking a symmetrical curved vane at the centre

Liquid jet after striking the curved vane glides
over the vane surface and comes out at the same
velocity V.
We are neglecting friction on the vane surface and
any energy losses.

16. Jet striking a symmetrical curved vane at the centre

The component of velocity of jet after striking the vane in the direction of jet =

The component of velocity of jet after striking the vane in the direction of jet =

17. Jet striking a symmetrical curved vane at the centre

Refer Impulse Momentum equation,
The force component in the direction of the jet,


The force component in the y-axis direction, i.e. normal to the direction of the jet,

18. Jet striking a symmetrical curved vane tangentially at one tip

●Inlet & outlet velocity is same.
●No friction over the vane surface.
●No loss of energy.
●No difference in the elevation levels.

19. Jet striking a symmetrical curved vane tangentially at one tip

As per the impulse momentum equation:
Force exerted by the jet in x-axis direction:


Force exerted by the jet in y-axis direction:

20. Jet striking an unsymmetrical curved vane tangentially at one tip

= angle made by tangent at inlet
= angle made by tangent at outlet

21. Jet striking an unsymmetrical curved vane tangentially at one tip

As per impulse momentum equation:
Force exerted by jet in the x-axis direction:


Force exerted by jet in the y-axis direction:

22. Question
A jet of water 50 mm in diameter and
having a velocity of 25 m/s enters
tangentially a stationary curved vane
without shock and is deflected through
an angle of 45 degrees. Because of the
friction over the surface, the exit velocity
is 80% of the inlet velocity. Find the
magnitude and direction of the resultant
force on the vane.
Answer:
873. 63 N and 52.47 degrees

23. Jet striking a hinged flat plate

As jet strikes the hinged plate, the plate swings by
an angle
W = weight of the plate acting at its CG
CG is at a distance x from the hinge O.
After swinging, the plate comes under quilibrium.

24. Jet striking a hinged flat plate

The moment of all forces about the hinge, O will be zero.
Force exerted by the jet normal to the plate:


Taking moment of forces about O and equating to zero.

25. Jet striking a hinged flat plate

26. For queries
Email: [email protected]