$A$ small hole of area of cross-section $2 \; mm^{2}$ is present near the bottom of a fully filled open tank of height $2 \; m$. Taking $g = 10 \; m/s^{2}$,the rate of flow of water through the open hole would be nearly ......... $\times 10^{-6} \; m^{3}/s$.

For the shown diagram,find the ratio of $R_1: R_2$.

Water $(\rho_1=1000 \, kg/m^3)$ and kerosene $(\rho_2=800 \, kg/m^3)$ are filled to the same height in two identical cylindrical vessels. Both vessels have small holes at their bottom. The speeds of the water and kerosene coming out of their holes are $v_1$ and $v_2$ respectively. Select the correct alternative.

Tanks $A$ and $B$ open at the top contain two different liquids up to a certain height. $A$ hole is made in the wall of each tank at a depth $h$ from the surface of the liquid. The area of the hole in $B$ is twice that of the hole in $A$. If the liquid mass flux through each hole is equal,then the ratio of the densities of the liquids,$\rho_A / \rho_B$,is:

For a container open to the atmosphere,derive the velocity of the liquid exiting a narrow hole in the container wall using Bernoulli's equation and obtain Torricelli's law.

$A$ rectangular tank is placed on a horizontal ground and is filled with water to a height $H$ above the base. $A$ small hole is made on one vertical side at a depth $D$ below the level of the water in the tank. The distance $x$ from the bottom of the tank at which the water jet from the tank will hit the ground is