$A$ liquid flows through a horizontal tube. The velocities of the liquid in the two sections,which have areas of cross-section $A_1$ and $A_2$,are $v_1$ and $v_2$ respectively. The difference in the levels of the liquid in the two vertical tubes is $h$.

$A$ thin vertical uniform wooden rod is pivoted at the top and immersed in water as shown. The container is slowly raised. At a certain moment,the equilibrium becomes unstable. If the density of water is $9/5$ times the density of wood,then the ratio of the total length of the rod to the submerged length of the rod at that moment is:

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]

$A$ 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)

$A$ $U$-tube has a left limb with a cross-sectional area one-quarter that of the right limb. The tube contains mercury (density $13.6 \text{ g/cm}^3$). The level of mercury in the narrow (left) limb is at a distance of $36 \text{ cm}$ from the upper end of the tube. What will be the rise in the level of mercury in the right limb if the left limb is filled to the top with water (in $\text{ cm}$)? (Density of water = $1 \text{ g/cm}^3$)

Give the limitations and uses of turbulence.