$A$ 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 ......... $\times 10^{-6} \; m^{3}/s$.

$A$ cylindrical tank has a hole of $1 \ cm^2$ in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of $70 \ cm^3/s$,then the maximum height up to which water can rise in the tank is: $(g = 9.8 \ m/s^2)$ (in $cm$)

$A$ cylindrical vessel filled with water up to a height of $H$ stands on a horizontal plane. The side wall of the vessel has a plugged circular hole touching the bottom. The coefficient of friction between the bottom of the vessel and the plane is $\mu$ and the total mass of the water plus the vessel is $M$. What should be the minimum diameter of the hole so that the vessel begins to move on the floor if the plug is removed? (Here,the density of water is $\rho$)

$A$ 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,

$A$ 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

$A$ cylinder containing water up to a height of $25 \ cm$ has a hole of cross-section $\frac{1}{4} \ cm^2$ in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out?