How to calculate the force in water tunnel

[derekteo0710]

I am tasked to design an orifice plate to be inserted into a water tunnel in an experiment. I am having some problem with the force calculation.

To understand the amount of pressure being applied onto the plate, the dimensions of the orifice is known. P = F/A

A is known therefore I need to calculate what is F.

F = ma

I am not sure can I use m = density x area x velocity

If it is correct, how do I determine what is the acceleration?

Once the velocity of the water is being regulated and remain constant, it will means that the acceleration is = 0.

Will need some help here. Thanks alot!

 

[boneh3ad]

Have you taken a fluid mechanics course before? Since it is a water tunnel, you likely only need to use Bernoulli's equation:

$$\frac{v^{2}}{2} + gz + \frac{p}{\rho} = Const.$$

Where:
$$v$$ = velocity
$$g$$ = acceleration due to gravity (safely ignore this)
$$z$$ = elevation
$$p$$ = pressure
$$\rho$$ = density

You know all the values (or you should) for the free stream, so then you just need to set the free stream version of the equation equal to the stagnation version (where there is no velocity) and you will get the pressure on the plate.

$$\frac{v_{1}^{2}}{2} + \frac{p_{1}}{\rho} = \frac{p_{2}}{\rho}$$

So:

$$p_{2} = \frac{\rho v_{1}^{2}}{2} + p_{1}$$

That should give you the pressure on the front of the plate. Depending on the design of your plate, you could have any value of total force because the pressure on the back of the plate depends on the shape and if there is a separation bubble or not. This will give you the worst-case scenario.