$A$ small hole of area of cross-section $2 \; mm^{2}$ is present near the bottom of a fully filled open tank of height $2 \; m$. Taking $g = 10 \; m/s^{2}$,the rate of flow of water through the open hole would be nearly ......... $\times 10^{-6} \; m^{3}/s$.

If in a stationary lift,a man is standing with a bucket full of water,having a hole at its bottom. The rate of flow of water through this hole is $R_0$. If the lift starts to move up and down with the same acceleration $a$,and the rates of flow of water are $R_u$ and $R_d$ respectively,then:

$A$ 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 $\,m/s$)

$A$ cylindrical vessel, open at the top, contains $15 \text{ litres}$ of water. Water drains out through a small opening at the bottom. $5 \text{ litres}$ of water comes out in time $t_1$, the next $5 \text{ litres}$ in further time $t_2$, and the last $5 \text{ litres}$ in further time $t_3$. Then,

$A$ large tank filled with water to a height $h$ is to be emptied through a small hole at the bottom. The ratio of times taken for the level of water to fall from $h$ to $h/2$ and from $h/2$ to zero is

$A$ large tank is filled with water (density $= 10^3 \ kg/m^3$). $A$ small hole is made at a depth $10 \ m$ below the water surface. The range of water issuing out of the hole is $R$ on the ground. What extra pressure must be applied on the water surface so that the range becomes $2R$? (Take $1 \ atm = 10^5 \ Pa$ and $g = 10 \ m/s^2$)