Differential Rotation

[ErikaLinh]

Hello,
I am currently doing a science project which focuses on differential rotation (DR) of fluids, particularly water (liquid). I want to know what the cause of it is, how the angular velocity changes with radius from the axis of rotation and lastly, how this dependence changes with temperature. Do you think it is too much and/or too broad for a highschool student to do? Is it narrow and focused enough? Besides, do you recommend any relevant books that are related to DR?

My plan is to do experiments of water draining out of a hole because I think the spiral water formed has differential rotation characteristics (smaller radius has greater angular velocity). Could you please suggest me other relevant phenomena and books that are related to physics of tornadoes or spiral water?

In order to measure angular velocity, I’m using dye and then record the flow visualisation by a camera and then calculate the speed. Then I will repeat it with different water temperature. However, I find this difficult to measure the radius and the speeds through a camera, could you please suggest me some improvements on my experiments?

Thank you very much.
Erika Linh

[deleted-71417]

Hi,

I recommend a Google search on “differential rotation of draining water” and look at relevant pages in the first ten pages of search results. I think you will enough information to answer your questions. The project looks within the grasp of a good high school student to me, though I am not a credentialed teacher and high school is but a distant memory for me. It looks narrow enough to be a good project. Go for it!

Good luck and have fun!

Barrett L Tomlinson

[deleted-71712]

Hi Erika,

I agree that you should go ahead with this project -- it seems like you're really interested and have a hypothesis already!

In order to measure angular velocity, I’m using dye and then record the flow visualisation by a camera and then calculate the speed. Then I will repeat it with different water temperature. However, I find this difficult to measure the radius and the speeds through a camera, could you please suggest me some improvements on my experiments?

If the problem is that the dye disperses too quickly, you could try using small pieces of plastic that would float on the surface of the water, though this might have some effect on the water's motion. You could also try using a clear container and shining a light through the bottom if it's too dark. You might even get some ideas by searching youtube for videos of swirling/moving water.

If the problem is not knowing the relationship between location and distance in the videos you record, you'll need to calibrate your images in some way. First you'll want to mount your camera so that it's always at the same distance and angle from the image you're recording. (Note that if you're looking at the surface of the water, water at different heights will be a different distance away from the camera.) Then put something of known length in the image at the location where you're trying to measure distance (e.g. at the water's surface) and take some photos. Then you can calculate, for example, the number of pixels equivalent to 1 cm.

Amanda

[ErikaLinh]

Thanks very much for your reply

I'm still concerning about the literature, I am currently swimming in a sea of information and I don't know which textbooks and journals I should read. So could you suggest me some relevant textbooks and journal websites please ?

[deleted-71360]

A methode for measuring water that is hard to see would be to float something on the water and them measure the relative motions of those things.

As a measurement method, consider a video recording that you can analyze frame by frame with a video editor.

Robert Reavis