Pressure and flow speed relationship in wind tunnel

[FQVBSina]

I need 250 m/s of airflow speed in a wind tunnel. I can assume for this purpose, the test section of the wind tunnel has uniform flow.

However, the wind tunnel can only generate a flow rate of 100 m/s but the pressure can be increased.

I am drawing a blank on how could a generic boundary layer wind tunnel increase pressure, and how do I relate that to the air speed?

I have considered the following but I am not sure if I am thinking in the right direction:
To increase pressure, design a test section to be a pipe that restricts flow in the wind tunnel near the part that has the full 100 m/s speed.
This way, I can set the Bernoulli equation with initial speed 100 m/s and at atmospheric pressure, and the final speed of 250 m/s at test section absolute pressure.

Thank you in advance for your help!

 

[boneh3ad]

I am not clear about what you are saying. You said that that the pressure can be increased but then asked how you could increase the pressure. These ideas seem to conflict to me.

 

[FQVBSina]

I am not clear about what you are saying. You said that that the pressure can be increased but then asked how you could increase the pressure. These ideas seem to conflict to me.

The problem statement says the pressure in the wind tunnel can be changed to compensate for the limited speed from the fans, but it doesn't say how does it change the pressure.

Depending on different ways to change pressure, the equation is different.

If I assume the normal stuff like incompressible flow etc. I can use Bernoulli's to get the pressure, but I am not sure if that is the way to go.

 

[russ_watters]

So this is homework? Or some sort of open-ended project/problem?

You can use the compressible form of Bernoulli's equation to relate changes between pressure and velocity if you restrict the size of a test section (or any duct). But real world fans follow performance curves, so it would be very wrong to assume the fan could put out the same volume of air at a much higher pressure (even without considering the compressibility issue...). So unless something else is changed about the fan you would have to account for the drop in flow.

So I would agree that we need more information to get a meaningful answer.

 

[boneh3ad]

First of all, I agree that we need to know if this is homework before taking it too much further.

Second, @russ_watters is correct in that a fan is not going to just be able to arbitrarily operate at a wide range of pressures (or more importantly, pressure ratios). I will also point out that 250 m/s is about Mach 0.73 at sea level conditions, so this flow is absolutely compressible in any region where the Mach number is greater than about 0.3. You will have to account for that. If you go much faster (say, 275 m/s) then you will be in the realm of transonic effects and will have much more to deal with.