Consider a symmetrical U-shaped tube, of circular section and internal diameter d<<R, containing an incompressible liquid of density ρ. Before starting the rotation of the system, the system is in equilibrium, where the rotating branch has an initial height of fluid equal to L, while at the other end of the tube there is a chamber of height h and filled with a gas at initial pressure P0. The top cap of the chamber is attached to the tube. However, the bottom cap can be moved vertically acting as a “piston”, as shown in the diagram. Both the mass of the lower lid and that of the gas contained in the chamber are negligible.
Suddenly the tube begins to rotate at constant
For the initial instant find a relationship between the pressure P0 of the gas, the height h, the properties fluid physics and Patm.
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