A spinning liquid of any sort forms a paraboloid; a three dimensional parabolic shape. Therefore, you can apply the physics principles relating to centripetal motion to any mass, *m,* on the surface of the liquid. Therefore, you may arrive at the conclusion that the position of the surface of the water, *f(x),* is equal to (2*Π^2*x^2)/(T^2*g) + c; where g = 9.81 m/s^2, T = the period of the spinning liquid, and c = a negative number in meters which is designated to the distance between the vertex of the resultant paraboloid and the initial surface of the water, which will be a function of T; x is measured in meters.

How does one go about finding this value, *c?*

Here is what I have so far, but I am not sure how close I am to finding it:

There are two points on the x axis which f(x) = 0, where the initial surface level of the liquid is also zero. The water is also displaced, which means the area between the curve and the x axis (indefinite integral) on the positive side of the positive x intercept and the negative area between the curve and the x axis between the vertex and the positive x intercept are equal to each other, no matter what T is.

This is my science fair project for 2018, and I'd like a little bump in the right direction, so I wish not for a complete solution and explanation, simply some ideas. Please help!

Matthew P.

12/26/16