When an air bubble rises from the bottom of a lake to the surface,its radius is doubled. The atmospheric pressure is equal to that of a column of water of height $H$. The depth of the lake is:

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:

$A$ large number of droplets,each of radius $r$,coalesce to form a bigger drop of radius $R$. An engineer designs a machine so that the energy released in this process is converted into the kinetic energy of the drop. The velocity of the drop is ($T=$ surface tension,$\rho =$ density)

When a large bubble rises from the bottom of a lake to the surface, the volume of the bubble becomes $5$ times its volume at the bottom of the lake. If $H$ is the atmospheric pressure expressed in terms of water column height, then the depth of the lake is (The temperature of the water in the lake is same at all points). (in $H$)

$A$ river of salty water is flowing with a velocity $2 \,m/s$. If the density of the water is $1.2 \,g/cc$, then the kinetic energy of each cubic metre of water is

$A$ vessel containing a liquid has a constant acceleration of $19.6 \, m/s^2$ in the horizontal direction. The free surface of the water gets sloped with the horizontal at an angle of ..........