Water flows into a large tank with a flat bottom at the rate of $10^{-4} \, m^3 s^{-1}$. Water is also leaking out of a hole of area $1 \, cm^2$ at its bottom. If the height of the water in the tank remains steady, then this height is ........ $cm$.

Water is filled in a container up to a height of $3\,m$. $A$ small hole of area $A_0$ is punched in the wall of the container at a height of $52.5\,cm$ from the bottom. The cross-sectional area of the container is $A$. If $A_0/A = 0.1$,then $v^2$ is......... $m^2/s^2$ (where $v$ is the velocity of water coming out of the hole).

$A$ cylindrical vessel is filled with a liquid up to height $H$. $A$ small hole is made in the vessel at a distance $y$ below the liquid surface as shown in the figure. The liquid emerging from the hole strikes the ground at a distance $x$.

The height of water in a tank is $H$. The range of the liquid emerging out from a hole in the wall of the tank at a depth $\frac{3H}{4}$ from the upper surface of water will be:

$A$ tank is filled with water of density $1 \, g/cm^3$ and oil of density $0.9 \, g/cm^3$. The height of the water layer is $100 \, cm$ and the height of the oil layer is $400 \, cm$. If $g = 980 \, cm/s^2$,then the velocity of efflux from an opening in the bottom of the tank is

$A$ cylinder containing water stands on a table of height $H$. $A$ small hole is punched in the side of the cylinder at its base. The stream of water strikes the ground at a horizontal distance $R$ from the table. Then the depth of water in the cylinder is ............