Test on Mechanical Properties of Fluids

A spherical solid ball of volume V is made of a material of density ρ₁. It is falling through a liquid of density ρ₂ (ρ₂ < ρ₁). Assume that the liquid applied a viscous force on the ball that is proportional to the square of its speed v, i.e., F_viscous = - kv² (k > 0). The terminal speed of the ball is

Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is T, density of liquid is ρ and L is its latent heat of vaporization.

Water is flowing continuously from a tap having an internal diameter 8 × 10^–3 m. the water velocity as it leaves the tap is 0.4 ms^–1. The diameter of the water stream at a distance 2 × 10^–1 m below the tap is close to

There is a circular rube in a vertical plane. Two liquids which do not mix and of densities d₁ and d₂ are filled in the tube. Each liquid subtends 90 ° angle at centre. Radius joining their interface makes an angle α with vertical, ratio d₁/d₂ is

A 20 cm long capillary tube is clipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be