# Parabolic surface shape of a tank of water in solid body rotation

One of the first exercises Torge and I plan on doing with the students in our “dry theory to juicy reality” project is to bring a water-filled tank to solid body rotation and measure rotation, surface height at the center of the tank and the sides, as well as water depth before rotation, and then have them put those together according to theory.

Setup of the experiment as we did it using a glass vase my mom gave me as tank (diameter 24.5 cm). The non-rotating water depth was 9.2 cm. Once we rotated the tank with 10 rotations per 8.6 seconds, the maximum water level at the outside edge of the tank was approximately 10.8 cm, and the minimum 7.9 cm.

Seeing how difficult it is to “measure” the surface heights while the tank is rotating (we chose to draw circles on the outside of the tank at the heights where we thought the water levels were, in order to measure them later on a non-rotating tank), we were quite pleased with those results once we plugged them into the equations.

Calculating the resting water level as arithmetic mean between the rotating maximum value at the rim and the minimum value in the center, we are only off by 0.1 cm, so not too shabby!

And calculating the height difference between resting water level and rotating maximum level from the tangential velocity and radius of the tank, we are only off by 0.4 cm. So all in all, that’s working well!

Btw, below you see the resting water level and above the mark for the rotating maximum value. Quite impressive difference, isn’t it?

Anyway, looking at rotational surfaces and volumes and stuff this way is a lot more fun than doing it the dry theoretical way only! At least that’s what I think ;-)