Studying the force on a plate from an air jet

[skaboy607]

Hi,

I have been carrying out a lab experiment where I am studying the force on a plate from an air jet. I need to come up with a theoretical derivation of an equation for the force on the plate and I was wondering if anyone had any ideas about how to go about this?

Thanks

 

[stewartcs]

Hi,

I have been carrying out a lab experiment where I am studying the force on a plate from an air jet. I need to come up with a theoretical derivation of an equation for the force on the plate and I was wondering if anyone had any ideas about how to go about this?

Thanks

Use the momentum equation to find the reaction force of the jet impinging on the flat plate.

CS

 

[skaboy607]

Thanks for replying, the momentum equation that I have is F=m(dot)(v2-v1), however I only have a value for the velocity leaveing the nozzle (v1). Given also is an equation that says the force of the jet on the plate is = m(dot)v(nozzle). Is this correct as what has confused me is that the plate height varies so this would make the force less the further away it got from the jet.

Thanks

 

[stewartcs]

...Given also is an equation that says the force of the jet on the plate is = m(dot)v(nozzle). Is this correct as what has confused me is that the plate height varies so this would make the force less the further away it got from the jet.

Thanks

Yes that is the correct equation. Perhaps a little rearrangement would help:

$$F = \rho Q_0 V_0 \sin{\theta}$$

and since $Q = VA$ we can substitue and get:

$$F = \rho A V_0^2 \sin{\theta}$$

where,

A is the area of the jet striking the plate
V_0 is the initial velocity of the fluid
$\rho$ is the fluid density
$\theta$ is the angle the plate makes with the horizontal

If perpendicular it will be $\sin{\theta} = 1$ and will reduce further to:

$$F = \rho A V_0^2$$, which is the equation you were given for the lab.

Hope this helps.

CS

 

[Prasannak]

U can also calculate the forcce by using,

F=PxA

F=force applied
P=Pressure of the air jet
A=Area of the tube

 

[LDransfield]

I know this is from a while back, but still: if anyone gets this: I'm doing a similar problem at the moment, but I also have real values measured in the Lab, is it likely the theoretical values would be higher or lower than the actual values?

Just want to check I'm on the right lines before I go and write an entire report on the wrong thing...

Thanks very much,
Lauren

 

[JaredJames]

Well it depends, were the theoretical value calculations negating any values (for example, sometimes you ignore air resistance when doing projectile motion)?

If not, and the equations used detail all required variables, the theoretical values shouldn't be that far off the real values.

 

[LDransfield]

Air resistance is neglected.
Well I have values of 10.104 - 10.202 for the practical measurements and 7.167 for the theoretical value. I think the calculations are all right, but will go over the numbers again to check

 

[JaredJames]

Air resistance is neglected?

But you're measuring air resistance with this experiment (force of air jet on a plate)?

 

[LDransfield]

Ah, good point, well yeah.
Guess it isn't then.
I meant more that I don't know if we're supposed to be including whether the air jet slows down due to the other air particles in the room...It isn't mentioned so I assumed not.