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

Step 1. Setup. A U-shaped glass tube has two open vertical arms of uniform cross-sectional area $A$, filled with a non-viscous, incompressible liquid of density $\rho$ up to a common equilibrium level in both arms.

Step 2. Equilibrium. Undisturbed, the liquid level is the same in both arms, since atmospheric pressure balances equally on both open surfaces, and the pressure at any point in the liquid depends only on depth.

Step 3. Disturbance. Blowing gently down one arm raises the pressure there, pushing the liquid level down in that arm and correspondingly up in the other by the same amount; once released, the resulting pressure imbalance provides a restoring force driving the liquid back towards the common level. …

Describe the equilibrium (equal levels, balanced pressure), the disturbance mechanism (unequal levels give a net restoring press …

• Forgetting the factor of 2 under the g in the final formula (writing T = 2 pi sqrt(l/g) instead of sqrt(l/2g)). …