Just to clarify, the tunnel on the site is not my design. I haven’t worked with this particular tunnel design. However, I’ve worked with quite a few low and high speed tunnels before…one of which was very similar to the one depicted in Figure E on the first page of the Science Buddies design.
Both the 15 degrees, noted by the engineering forum and the one I pointed out are “rules of thumb”. That being said, that means they are ballpark figures designed to give decent results without an intensive flow analysis that would be required for a professional wind tunnel (very expensive, and something not done by hand).
Ideally you’d like to have the angle as small as possible. The “rule of thumb” (i.e. length approximately equal to inlet height) I mentioned earlier gets you close to a 15 degree angle (~17 deg). However, for the design I mentioned, the height and length of the contraction cone is constrained by standard materials available at most hardware stores. Sheets of wood typically come in 2’ X 4’ rectangles. For an area ratio of 7 and a test section opening of 12x12 inches, the inlet of the tunnel must be ~32 in. One can make a side out of a single sheet of commercially available wood if you “cheat” a bit on the contraction cone length and angle. Again, for slow speed flows, this is unlikely to be an issue.
In order to get closer to a 15 degree turn, you’d have to find a non-standard size piece of wood, or make each wall of the cone out of two pieces, which would create a seam somewhere in the middle of the cone that could “trip” your boundary layer flow prior to entering your test section, causing unpredictable turbulent regions in your upstream flow (Ux). This is very undesirable, much better to make your flow turn an extra 5-7 degrees to get into the test section. Think of a skate boarder rolling down a sidewalk, then suddenly there is a slight lip where the sections of two pieces of the sidewalk don’t match up. If this lip is significant enough, the skater is unlikely to remain on his board.
Ok, bottom line: If you are looking for a simple equation that tells you the optimum geometry, there really isn’t one…There is a paper by Bell and Mehta (April 1988) that has a good description of the considerations required to optimize the design of this component of a wind tunnel, at the following link:https://moodle.polymtl.ca/file.php/1047 ... l_1988.pdf
I hope this helps.
"As the circle of light increases, so does the circumference of darkness around it."
~ Albert Einstein