Variation in pressure in a rotating tube?

[Ravija]

What is the pressure experienced by any point at different locations inside a rotating tube filled with water?
The axis of rotation is through the center of the tube.

 

[kuruman]

Hi Ravija and welcome to PF.

Perhaps the easiest way to see this is in the rotating frame of the tube. Assuming that the rotation is in a horizontal plane, so that we don't have to worry about gravity, the centripetal acceleration points towards the center and is $\omega^2 r$ where $r$ is the distance from the center. In the reference frame of the rotating tube, this is seen as a centrifugal acceleration that has the same magnitude but points away from the center. The effective acceleration of gravity then is is $g_{eff}=\omega^2 r$ and becomes larger the more one moves away from the center. At the center the pressure is zero. At a point away from the center, the pressure is $p = \rho g_{eff} r = \rho \omega^2 r^2$.

On edit: Here, $\omega$ is the angular speed of the tube and $\rho$ is the density of water.