Write shorts notes on the oscillations of liquid column in U-tube.

Explanation

Let us consider a U-shaped glass tube which consists of two open arsm with uniform cross-sectional area A. Let us pour a non-viscous uniform incompressible liquid of density `rho` in the U-shaped tube to a height h as shown in the figure. It the liquid and tube are not disturbed then the liquid surface will be in equilibrium position O.

It measn the pressure as measured at any point on the liquid is the same and also at the surface on the arm (edge of the tube on either side), that balance the atmospheric pressure. Hence, the level of liquid in each earm will be the same. By blowing air one can provide sufficient force in on arm, and the liquid gets disturbed from equilibrium position O, It is meant , that pressure blown are is higher than the other arm. A difference in pressure is created that will cause the liquid to oscillate for very short duration of time about the mean or equilibrium position. Finally it comes to rest.
Time period of the oscillations is
`T=2pi sqrt((l)/(g))` second