# How can I determine the air pressure in a wind tunnel for an airplane drag test?

• yuukichi
In summary, the conversation discusses a problem with understanding a drag force equation for an airplane and a request for assistance. The problem involves dimensional analysis and a need for the function f to be determined through experimentation. The conversation also mentions the use of a scale model and a pressurized wind tunnel to minimize compressibility effects.
yuukichi
Hi guys, have been reading these forums for a very long time, have always found it very helpful and informative.

There's this problem which I can't seem to get my head around, it seems very straight forward, but every time I try to do it, I always end up doing it wrong. I would greatly appreciate it if anyone could point me in the right direction.

The problem is:

Dimensional analysis showed that the following relation describes the drag force F on an airplane

$$\frac{F}{\rho d^{2}u^{2}}$$ = f$$\left(\frac{\mu}{\rho l u}\right)$$

Where u the airplane velocity, l is the characteristic length of the airplane, $$\rho$$ is the surrounding air density and $$\mu$$ is the viscosity of the air.
The drag on an airplane cruising at 390km/h in air at atmospheric pressure and temperature is to be determined from tests on a 1:10 scale model placed in a pressurised wind tunnel. To minimise compressibility effect the air speed in the wind tunnel is also to be 390km/h. Determine the air pressure in the wind tunnel, assuming the air temperature for the model and prototype.

I've tried separating F on the LHS by introducing a constant in the RHS, but that ends up totally wrong

Any help would be greatly appreciated!

Thanks :)

The only unknown thing is the function f: one must measure it experimentaly. If you only care about one particular real life problem, then you only need the value of f for that problem: you get this value by one experiment on the model that gives the same argument for f as the real life problem.

hey thread what answer did u get fir this question. pliz help me everyone.

## 1. What is dimensional analysis?

Dimensional analysis is a mathematical technique used to convert between different units of measurement. It involves using conversion factors and dimensional equations to ensure the units cancel out and the final result is in the desired unit.

## 2. Why is dimensional analysis important?

Dimensional analysis is important because it allows scientists to convert between different units of measurement, which is crucial for accurate and consistent measurements in experiments. It also helps to identify and correct errors in calculations and equations.

## 3. How do you perform dimensional analysis?

To perform dimensional analysis, you must first identify the given quantity and the desired unit of measurement. Then, list out all the conversion factors needed to convert between the two units. Finally, set up the dimensional equation, making sure to cancel out the unwanted units, and solve for the desired unit.

## 4. Can dimensional analysis be used for any type of unit conversion?

Yes, dimensional analysis can be used for any type of unit conversion, as long as the given and desired units are related by a conversion factor. This includes conversions between different systems of measurement, such as metric and imperial units.

## 5. What are some common mistakes to avoid in dimensional analysis?

Some common mistakes to avoid in dimensional analysis include using incorrect conversion factors, not canceling out units properly, and mixing up the order of the units in the dimensional equation. It is important to double check all units and equations to ensure accurate and consistent results.

• Aerospace Engineering
Replies
9
Views
2K
• Engineering and Comp Sci Homework Help
Replies
4
Views
1K
• Mechanics
Replies
4
Views
2K
• Engineering and Comp Sci Homework Help
Replies
1
Views
3K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Engineering and Comp Sci Homework Help
Replies
1
Views
2K
Replies
7
Views
5K
• Engineering and Comp Sci Homework Help
Replies
5
Views
5K
• Aerospace Engineering
Replies
2
Views
4K
• Introductory Physics Homework Help
Replies
1
Views
4K