# Rotation of Fluid in a Cylinder

Question:

See what I tried below and verify if I'm wrong. I need help here.

You just need to get the height of the paraboloid (air) in the cylinder. Knowing that the volume of the paraboloid is half of the cylinder of the same height,

$$H_{paraboloid}=2*H_{cylinder}$$

where $H_{cylinder}$ is the height of air when it is not rotating, $0.2\ m$, therefore $$H_{paraboloid}=0.4m=y$$

substituting the value in the equation,

$$y=\frac{\omega^2x^2}{2g}$$

where $x=0.1\ m$, (radius of paraboloid) and $g=9.81\ m/s^2$, you will get

$$\omega=28.014\ rad/s = 267.51 rev/min$$