How Does a Rotating Pail Affect Water Surface Shape?

[Fusilli_Jerry89]

Homework Statement

A rotating pail of water with an angular velocity w has a surface curving up from the centre to the outer edge. Find the shape of the surface. The slope of the surface is dy/dx = tan(theta) at position x is y (= function of x) is the shape of the surface. You must resolve forces to find tan(theta) as a function of x, and then solve for the height, y, as a function of x.

If the pail rotates once per second, and has a diameter of 0.45 m, how high above the centre is the outer edge?

Homework Equations

The Attempt at a Solution

All I see is that w = 2pi rad/sec and r = 0.225 m.

 

[saket]

Method I:
Ideal Fluid, by definition, can not tolerate any shear force. Use this fact.
Assume the centre of the water surface to be origin. Let P(x,y) be a point on the water surface. Consider forces on it. Impose the condition that tangential force will be zero.
I hope you can proceed now.

 

[ogb p]

I am not sure what the rest of the information is asking for. I would need more information about the pail and the forces acting on it to accurately determine the shape of the surface. Additionally, the given equations and attempt at a solution are not applicable to this problem as they do not provide enough information. Can you please provide more details about the pail and the forces involved?