Question

A cylindrical vessel of area of cross-section A and filled with liquid to a height h₁ has a capillary tube of length l and radius r protruding horizontally at its bottom. If the viscosity of liquid is η , density ρ and g = 9.8 m/s², find the time in which the level of water in vessel falls to h₂.

Answer 1

Let h be the height of water level in the vessel at any instant t which decreases by dh in fine dt.

∴ Rate of flow of water through capillary tube,

Also, according to poiseuille formula, the rate of flow is given by