$A$ vertical $U-$tube of uniform inner cross-section contains mercury in both sides of its arms. $A$ glycerin (density = $1.3 \text{ g/cm}^3$) column of length $10 \text{ cm}$ is introduced into one of its arms. Oil of density $0.8 \text{ g/cm}^3$ is poured into the other arm until the upper surfaces of the oil and glycerin are in the same horizontal level. Find the length of the oil column in $\text{cm}$. (Density of mercury = $13.6 \text{ g/cm}^3$)

Water coming out of a horizontal tube at a speed $v$ strikes a vertical wall normally,close to the mouth of the tube,and falls down vertically after impact. When the speed of water is increased to $2v$:

An incompressible liquid is kept in a container having a weightless piston with a hole. $A$ capillary tube of inner radius $0.1 \,mm$ is dipped vertically into the liquid through the airtight piston hole,as shown in the figure. The air in the container is isothermally compressed from its original volume $V_0$ to $\frac{100}{101} V_0$ with the movable piston. Considering air as an ideal gas,the height $(h)$ of the liquid column in the capillary above the liquid level in $cm$ is. . . . . . .
[Given: Surface tension of the liquid is $0.075 \,N \,m^{-1}$,atmospheric pressure is $10^5 \,N \,m^{-2}$,acceleration due to gravity $(g)$ is $10 \,m \,s^{-2}$,density of the liquid is $10^3 \,kg \,m^{-3}$ and contact angle of capillary surface with the liquid is zero]

The figure shows a three-arm tube in which a liquid is filled up to a height $l$. It is now rotated at an angular frequency $\omega$ about an axis passing through arm $B$. Find the angular frequency $\omega$ at which the level of liquid in arm $B$ becomes zero.

Why can liquids flow?

At a speed of .......... $m/s$,the velocity head of water is equal to the pressure head of $40\, cm$ of $Hg$.