Water flows into a cylindrical vessel of large cross-sectional area at a rate of $10^{-4} \; m^3/s$. It flows out from a hole of area $10^{-4} \; m^2$, which has been punched through the base. How high does the water rise in the vessel (in $; m$)?

$A$ vessel is filled with water up to a height $h$. When a hole is made at the bottom,all the water drains out in time $t$. If the vessel is filled with water up to a height $4h$,how long will it take for the water to drain out completely when a hole is made at the bottom?

$A$ 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

$A$ cubical box of wine has a small spout located in one of the bottom corners. When the box is full and placed on a level surface,opening the spout results in a flow of wine with an initial speed of $v_0$ (see figure). When the box is half empty,someone tilts it at $45^{\circ}$ so that the spout is at the lowest point (see figure). When the spout is opened,the wine will flow out with a speed of

$A$ tank with a small hole at the bottom has been filled with water and kerosene (specific gravity $0.8$). The height of water is $3\,m$ and that of kerosene $2\,m$. When the hole is opened,the velocity of fluid coming out from it is nearly ........ $ms^{-1}$. (Take $g = 10\,ms^{-2}$ and density of water $= 10^3\,kg\,m^{-3}$)

$A$ vessel completely filled with water has two holes $P$ and $Q$ at depths $2h$ and $8h$ from the top,respectively. Hole $P$ is a square of side $a$ and hole $Q$ is a circle of radius $r$. If the volume of water flowing out per second from both holes is the same,then the side $a$ of hole $P$ is: