An open glass tube of uniform cross-section is bent into the shape of an L. One arm is immersed in...

An open glass tube of uniform cross-section is bent into the shape of an L. One arm is immersed in a liquid of density p, and the other arm of length I remains in the air in a horizontal position. The tube is rotated with constant angular speed w about the axis of the vertical arm. Prove that the height y to which the liquid rises in the vertical arm is equal to

Where Po is atmospheric pressure, M is the molar mass of air, and g is the acceleration of gravity.