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 ........ $cm$.

$A$ tank with vertical walls is mounted so that its base is at a height $H$ above the horizontal ground. The tank is filled with water to a depth $h$. $A$ hole is punched in the side wall of the tank at a depth $x$ below the water surface. To have maximum range of the emerging stream,the value of $x$ is

Consider a water jar of radius $R$ that has water filled up to height $H$ and is kept on a stand of height $h$ (see figure). Through a hole of radius $r$ $(r << R)$ at its bottom,the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is $x$,then:

The water is filled up to a height of $12\, \text{m}$ in a tank having vertical sidewalls. $A$ hole is made in one of the walls at a depth $h$ below the water level. The value of $h$ for which the emerging stream of water strikes the ground at the maximum range is $.....\, \text{m}$.

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.

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: