Forced Vortex Motion

Another type of relative equilibrium. If a fluid-contained vessel is rotating at a constant angular velocity, the fluid will reach a relative equilibrium position and rotate with the vessel. Under this condition, the fluid is said to be in Forced Vortex Motion.

Note

For S1, forced vortex motion, only about vertical axis, is required.

TODO

Explain how to derive the above equation.

Equation of the free surface

On the free surface .

The free surface is parabolic. The constant part can be found by a known point of the free surface. For simplicity we can choose the axes so that the free surface passes through .
In that case, equation of the free surface is:

Vertical Pressure Distribution

Pressure increases with height. Isobars are parabolic.

Volume of the fluid

Total volume of the fluid is: