$A$ wide cylindrical vessel $50 \ cm$ in height is filled with water and rests on a table. Assuming the viscosity to be negligible,find at what height from the bottom of the vessel a small hole should be made for the water jet coming out of it to hit the surface of the table at the maximum horizontal distance from the vessel. (in $cm$)

$A$ large vessel with a small hole at the bottom is filled with water and kerosene, with kerosene floating on water. The length of the water column is $20 \,cm$ and that of the kerosene is $25 \,cm$. The velocity with which water flows out of the hole is (density of kerosene $= 0.8 \,g/cm^3$, density of water $= 1.0 \,g/cm^3$, neglect viscous force). (in $\,m/s$)

$A$ water tank kept on the ground has an orifice of $2 \,mm$ diameter on the vertical side. What is the minimum height of the water above the orifice for which the output flow of water is found to be turbulent (in $\,cm$)? (Assume, $g=10 \,m/s^2, \rho_{\text{water}}=10^3 \,kg/m^3$, viscosity $=1$ centi-poise)

$A$ large open tank containing water has two holes in its wall. $A$ square hole of side $a$ is made at a depth $y$ and a circular hole of radius $r$ is made at a depth $16y$ from the surface of the water. If an equal amount of water comes out through both the holes per second,then the relation between $r$ and $a$ will be:

In a cylindrical water tank,there are two small holes $A$ and $B$ on the wall. Hole $A$ is at a depth of $h_1$ from the water surface,and hole $B$ is at a height of $h_2$ from the bottom of the tank. The total height of the water surface from the bottom of the tank is $H$. Water coming out from both holes strikes the ground at the same point $S$. Find the ratio of $h_1$ and $h_2$.

$A$ water barrel having water up to a depth $d$ is placed on a table of height $h$. $A$ small hole is made on the wall of the barrel at its bottom. If the stream of water coming out of the hole falls on the ground at a horizontal distance $R$ from the barrel,then the value of $d$ is