A cylindrical bucket of liquid (density [itex]\rho[/itex]) is rotated about its symmetry axis, which is vertical. If the angular velocity is [itex]\omega[/itex], show that the pressure at a distance r from the rotation axis is [tex]P = P_0 + 1/2\rho \omega ^2 r^2[/tex] where [itex]P_0[/itex] is the pressure at r = 0. Isn't depth supposed to play a role here!? Am I supposed to use Bernoulli's equation to solve this (although I don't see how)? It seems the presure increases as we move away from the rotation axis but this doesn't make any sense to me because the velocity of the fluid is (in my opinion) faster the farther away we are from the rotation axis and by Bernoulli's principle the pressure should be lower. Am I missing something?