# Pressure and flow speed relationship in wind tunnel

• FQVBSina
In summary, a wind tunnel can only generate a flow rate of 100 m/s, but the pressure can be increased by creating a test section that restricts flow. This way, the equation for pressure can be derived.
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.

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.

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.

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.

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.

## What is the relationship between pressure and flow speed in a wind tunnel?

The pressure and flow speed in a wind tunnel are inversely related. This means that as the flow speed increases, the pressure decreases and vice versa.

## How does the shape of the wind tunnel affect the pressure and flow speed relationship?

The shape of the wind tunnel can greatly impact the pressure and flow speed relationship. A narrower wind tunnel will result in higher flow speeds and lower pressures, while a wider wind tunnel will have lower flow speeds and higher pressures.

## What is the significance of the pressure and flow speed relationship in wind tunnels?

The pressure and flow speed relationship is crucial in wind tunnels as it allows for the simulation of real-world conditions. By controlling the pressure and flow speed, researchers can accurately test the aerodynamic properties of objects such as airplanes or cars.

## How is pressure measured in a wind tunnel?

Pressure is typically measured using instruments called pressure gauges. These gauges use a diaphragm or a manometer to measure the force exerted by the air on a surface, which is then converted into a pressure reading.

## What factors can affect the pressure and flow speed relationship in a wind tunnel?

Several factors can affect the pressure and flow speed relationship in a wind tunnel, including the shape and size of the tunnel, the speed and density of the air, and the presence of any obstacles or walls. Additionally, changes in temperature or humidity can also impact the relationship.

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