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:

$A$ liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid rises at the sides. If the radius of the vessel is $0.05\,m$ and the speed of rotation is $2\,rev/s$,the difference in the height of the liquid at the center of the vessel and its sides will be .............. $cm$ $(\pi^2 = 10)$.

An air bubble of volume $V_0$ is released by a fish at a depth $h$ in a lake. The bubble rises to the surface. Assume constant temperature and standard atmospheric pressure $P$ above the lake. The volume of the bubble just before touching the surface will be (density of water is $\rho$):

$A$ drum of radius $R$ full of liquid of density $d$ is rotated at angular velocity $\omega \ rad/s$. The increase in pressure at the centre of the drum will be

Give the limitations and uses of turbulence.

$A$ uniform meter scale is supported at its $20 \ cm$ mark. $A$ body suspended from the $10 \ cm$ mark keeps the scale horizontal. However,the scale becomes unbalanced if the body is completely immersed in water. To regain the balance,the body is shifted to the $8 \ cm$ mark. Therefore,the specific gravity of the material of the body is