Water flows through a frictionless duct with a cross-section varying as shown in the figure. Pressure $p$ at points along the axis is represented by:

Write two parts of fluid mechanics and what studies are made in them?

Different processes are given in Column-$I$ and their reasons are given in Column-$II$. Match them appropriately.

Column-$I$	Column-$II$
$(a)$ Rain drops move downwards with constant velocity.	$(i)$ Viscous liquids
$(b)$ Floating clouds at a height in air.	$(ii)$ Viscosity
	$(iii)$ Less density

An air bubble of volume $50\, cm^3$ is formed at the bottom of a lake $47.6\, m$ deep. What will be its volume when it reaches the surface? (Atmospheric pressure $= 70\, cm$ of $Hg$ and density of $Hg = 13.6\, g/cm^3$)

The rate of diffusion is

$A$ bubble of radius $R$ in water of density $\rho$ is expanding uniformly at speed $v$. Given that water is incompressible,the kinetic energy of water being pushed is