Problem

The U-tube manometer lies in the vertical plane and contains a fluid of density ρ that has...

The U-tube manometer lies in the vertical plane and contains a fluid of density ρ that has been displaced a distance y and oscillates in the tube. If the cross-sectional area of the tube is A and the total length of the fluid in the tube is L, determine the natural period of oscillation of the fluid, using the energy method. Hint: As long as the curved portion of the tube is always filled with liquid (i.e., the oscillations don’t get large enough to empty part of it), the contribution of the liquid in the curved portion to the potential energy is constant.