$A$ rectangular vessel,when full of water,takes $10 \text{ minutes}$ to be emptied through an orifice in its bottom. How many minutes will it take to be emptied when half-filled with water?

$A$ 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 vessel of cross-sectional area $1000 \ cm^2$ is fitted with a frictionless piston of mass $10 \ kg$ and filled with water completely. $A$ small hole of cross-sectional area $10 \ mm^2$ is opened at a point $50 \ cm$ deep from the lower surface of the piston. The velocity of efflux from the hole will be ........... $m/s$.

$A$ large vessel completely filled with water has two holes '$A$' and '$B$' at depths '$h$' and '$4h$' from the top. Hole '$A$' is a square of side '$L$' and hole '$B$' is a circle of radius '$R$'. If the same quantity of water is flowing per second from both holes,then the side of the square hole is:

$A$ cylindrical vessel of $40 \text{ cm}$ radius is completely filled with water and its capacity is $528 \text{ dm}^3$. The vessel is placed on a solid block of exactly the same height as the vessel. If a small hole is made at $70 \text{ cm}$ below the top of the water level, then the horizontal range of water falling on the ground in the beginning is . . . . . . $\text{cm}$.

There are two holes, one each along the opposite sides of a wide rectangular tank. The cross-section of each hole is $0.01 \,m^2$ and the vertical distance between the holes is $1 \,m$. The tank is filled with water. The net force on the tank in newton when the water flows out of the holes is (Density of water $= 1000 \,kg/m^3$, $g = 10 \,m/s^2$)