$A$ tank filled with fresh water has a hole in its bottom and water is flowing out of it. If the size of the hole is increased,then

$A$ large tank is filled with water to a height $H$. $A$ small hole is made at the base of the tank. It takes $T_1$ time to decrease the height of water to $H/\eta$ (where $\eta > 1$),and it takes $T_2$ time to drain the rest of the water. If $T_1 = T_2$,then the value of $\eta$ is:

Equal volumes of two immiscible liquids of densities $\rho$ and $2\rho$ are filled in a vessel as shown in the figure. Two small holes are punched at depths $h/2$ and $3h/2$ from the surface of the lighter liquid. If $v_1$ and $v_2$ are the velocities of efflux at these two holes,then $v_1/v_2$ is:

$A$ tube is attached as shown in a closed vessel containing water. The velocity of water coming out from a small hole is:

$A$ cylindrical vessel open at the top is $20 \ cm$ high and $10 \ cm$ in diameter. $A$ circular hole whose cross-sectional area is $1 \ cm^2$ is cut at the centre of the bottom of the vessel. Water flows from a tube above it into the vessel at the rate of $100 \ cm^3 s^{-1}$. The height of water in the vessel under steady state is ....... $cm$ (Take $g = 1000 \ cm s^{-2}$)

$A$ 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: