$A$ large storage tank, open to the atmosphere at the top and filled with water, develops a small hole in its side at a point $20.0 \ m$ below the water level. If the rate of flow from the hole is $3.08 \times 10^{-5} \ m^3 s^{-1}$, then the diameter of the hole is (Take $g = 10 \ m s^{-2}$): (in $mm$)

Water is filled in a tank up to a height of $20 \ cm$ from the bottom of the tank. Water flows through a hole of area $1 \ mm^2$ at its bottom. The mass of the water coming out from the hole in a time of $0.6 \ s$ is (Density of water $= 1000 \ kg \ m^{-3}$ and acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $g$)

$A$ light cylindrical vessel is kept on a horizontal surface. The area of the base is $A$. $A$ hole of cross-sectional area $a$ is made just at its bottom side. The minimum coefficient of friction necessary to prevent the vessel from sliding due to the impact force of the emerging liquid is $(a \ll A)$.

$A$ 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?

The height of the water level in a tank of uniform cross-section is $5 \,m$. The volume of water leaked in $5 \,s$ through a hole of area $2.4 \,mm^2$ made at the bottom of the tank is (Assume the level of the water in the tank remains constant and acceleration due to gravity $= 10 \,ms^{-2}$).

$A$ 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