How to calculate Reynold's number for the wind tunnel

[Forman]

Hi guys. I have successfully constructed a wind tunnel following the blueprints here on science buddies. I have also checked the Reynold's number equation, which according to wikipedia and some other sites is: pVL/M, where p is the density of the fluid, V is the velocity of the fluid, L is a "characteristic linear dimension", which according to this site: http://www.ajdesigner.com/reynoldsnumber/reynoldsre.php is the same as pipe diameter, and M is the dynamic viscocity of the fluid. According to wikipedia, the viscosity of air mainly depends on temperature, so I checked out what it was at 21 degrees Celsius (room temperature) using the converter on this site: http://www.lmnoeng.com/Flow/GasViscosity.htm and I got it to be: 1.841875*10^-5 Ns/m^2. Since the test section in the wind tunnel I built is rectangularly shaped and not circular, I suppose L would be equal to the (root of the cross-sectional area divided by pi) * 2, giving me 33.5 cm=0.0335 m?
Now the thing is, the blueprints recommended a fan with a CFM rating of 2000. My fan sucks in 947 L/s, which is slightly above that, so it should be perfect. My physics teacher told me that there still has to go 947 L of air through the cross-sectional area of the test section every second, so if I divide 0.947 m^3 by my cross-sectional area (30.5 cm * 28.9 cm), I get it to be 10.744 m/s. In other words, this is the speed of air when I have my fan on max. speed.
So if I plug in the numbers into the Reynold's number equation, I get: pvL/M= (1.204 kg/m^3*10.744m/s*0.0335m)/(1.841875*10^-5 Ns/m^2)= 23528 as my Reynold's number, which means the air flow is extremely turbulent, as Britannica online says that air flow is laminar as long as Reynold's number is under 2000.
So my question is: Have I done the calculations correctly? I also wonder whether the wind speed will be the same if I have a model inside the test section (I am guessing it will, but I want to make sure.)
I would greatly appreciate a quick response since I am going to be doing testing at 9 o' clock Swedish time (GMT+1). Thank you for this great site!

By the way, there was absolutely no problem in having plywood for the contraction cone. There are no vibrations or anything, and the wind tunnel seems to be working very well.

[deleted-71495]

Hi Forman,

I haven't checked your numbers, but I would take a guess the mere fact that your tunnel has rectangular cross section can cause turbulence, at the corners, and you have four of them. You can test this very quickly on a qualitative level by sticking a probe in there with small cross section and a streamer attached. For example, a long needle with a long but narrow piece of lightweight paper (lametta from a christmas tree works really well). As you can guess, if you really have laminar flow the streamer is going to be mostly straight along the direction of airflow. Move the needle closer to a corner and you'll see more lateral movement, if my hypothesis is correct.

Cheers, Ivo

[deleted-71709]

Good input from Ivo.

One thing you wondered was, "I also wonder whether the wind speed will be the same if I have a model inside the test section (I am guessing it will, but I want to make sure.)"

The answer is, no. Whenever you put a test model in your wind tunnel, it present an air resistance to the system. This will cause the flow through the fan to decrease, as long as the power you are putting into the fan remains constant.

Does your wind tunnel have a flow measurement capability? If not, can you measure the "static" pressure behind your test model, and in front of the fan? If you can do that, you should see a change in that static pressure measurement with and without your test model.

Does your fan have the capability to run at lower speed? If so, you could just slow it down to reduce the Reynolds number.

Ivo's idea of introducing a streamer of some kind, knitting yarn works well, is a very good one. Looking at the plans on how to build your wind tunnel that is on the Science Buddies site tells me you will indeed have highly turbulent flow at your test model. Also, you will probably notice the flow is not very straight. I suspect you would see the streamers bowing towards the center of the test section and, perhaps, back out a bit before reaching your model. That's just because this is such a simple wind tunnel design.

You've done a very good job researching the Reynolds number. I commend you.

Keep up the good work, and have fun.

[Forman]

Thank you for your hypothesis, Ivo. I am thinking about taping small Swedish paper flags on the walls and corners of the test section, and then one in the middle, and we'll see what happens. Thanks also to edneu for your ideas.
No, unfortunately my wind tunnel does not have flow measurement capability. On the blueprints it said you should use a small pick-up fan, acting as a generator, to measure the voltage produced when you have your fan on max speed. I spoke with my physics teacher about this, and he taught me that Power=kv^3. so if I have my fan on a certain speed and I read off the voltage produced on the volt meter, and then turn the knob and read off the amps, I know that the product of this is proportional to the velocity cubed. Since I know that my fan blows 947 L/s on max. speed, and the speed in the test section then should then be about 10.744 m/s, I can calculate K. I got my Power on max. speed to be= 0.6 W, so K was then 4.84*10^-4. Then I used this K to calculate the wind speeds for other power readings. Of course, the wind speed is probably not very accurate if you use this way of calculating it, but I'm not sure if the school is willing to pay 400 kr (50 dollars) for an anemometer to my already very costly project. ^^
Regarding the static pressure measurement, doesn't that also require some expensive piece of equipment to measure it?
Yes, my fan can run on many different speeds, since I connected it to a variable AC adapter. However, according to what I have read about Reynold's number, if you have the same Reynold's number for a small 1:24 model as a full-size car, you can draw conclusions about how large the force would be on the big car in the same wind speed condition. Obviously, a smaller car should have a lower L in the equation pVL/M, but what exactly is my L on a small car model? I have tried to find information about this, but I couldn't. Anyway, if L is 24 times smaller, the velocity should be 24 times greater on the small model in order for the Reynold's numbers to match up. In this case, I can draw some conclusions about the drag force on full-scale models, right? (Even though i know they will probably be pretty inaccurate, but anyway)

Thanks for the help you guys have given me so far, and hopefully science buddies' experts can also answer these questions : )

[Forman]

Could someone please help me with this? I have my project fair on Friday so I am kind of running out of time... xD

[deleted-71588]

Reynold's number analysis in wind tunnels is complicated math involving fluid dynamics and interactions with surfaces. http://en.wikipedia.org/wiki/Reynolds_number

I'm not sure what you are really tring to accomplish by dragging Reynold's numbers for fluid flow boundary conditions into your project.

There are multiple Reynold's numbers involved with all of the different surfaces of the model and the tunnel. Since you are dealing with a presumably scale model car that has some modeled ground clearance, you have a problem with Reynold's number ratios to start with. If you sit the model car tires on the bottom of a square/rectangular wind tunnel, the space between the bottom of the model maybe proportional to the real world car; however, the space to the sides and top of the wind tunnel will NOT be proportional to the atmosphere except in a real world tunnel.

Wind tunnel models for buildings which meet the ground and for aircraft that are off the ground do not suffer these same modeling issues.

My recommendation would be to introduce a thin road surface (think sheet metal, thick enough and stiff enough to not bend) about three times the width of the model and twice the length of the model that is suspended from the top of the wind tunnel so that the bottom of the simulated road and top of the car are the same distance from the middle of the tunnel. If you use small diameter fishing line on all four corners, then you can use the angle they make to calculate the drag force (need to know the mass of the road + model car).

If your road surface is less than 1/3 of the width of the wind tunnel and the height of the road surface plus model is less than 1/3 of the height of the wind tunnel, then the wind tunnel surface effects shouldn't affect your drag angle.

The drag co-efficient is not dimensionless but it will be proportional and be the same for the model and the full scale car for the same wind velocity and be a lot simpler calculations.

With the above approach, the only thing you need to measure is the velocity of the air. Sorry, I don't have any inexpensive ideas on how to accomplish that.

Reynold's number mess (if you still care after reading the above):
If your wind tunnel is not a uniform circular cross section, then corners will affect the pressure gradient.

Take a look at Pitot tubes http://en.wikipedia.org/wiki/Pitot_tube
Take a look at the liquid column applications in http://en.wikipedia.org/wiki/Pressure_measurement. This is how I would attempt to measure static pressure at various points in your wind tunnel compared to the ambient room pressure. The only requirement is that the viscosity of the liquid is low enough (food coloring in water would be a good choice) used and the diameter of the tube large enough so that capillary forces are small enough (1/4" ID would be a good choice). In other words, you don't need anything vary expensive to make this measurement.