$A$ tank of height $5\, m$ is full of water. There is a hole of cross-sectional area $1\, cm^2$ in its bottom. The initial volume of water that will come out from this hole per second is

$A$ 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 $\,m/s$)

$A$ 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

$A$ square hole of side length $l$ is made at a depth of $h$ and a circular hole of radius $r$ is made at a depth of $4h$ from the surface of water in a water tank kept on a horizontal surface. If $l << h$ and $r << h$,and the rate of water flow from the holes is the same,then $r$ is equal to:

$A$ water tank kept on the ground has an orifice of $2 \,mm$ diameter on the vertical side. What is the minimum height of the water above the orifice for which the output flow of water is found to be turbulent (in $\,cm$)? (Assume, $g=10 \,m/s^2, \rho_{\text{water}}=10^3 \,kg/m^3$, viscosity $=1$ centi-poise)

Water $(\rho_1=1000 \, kg/m^3)$ and kerosene $(\rho_2=800 \, kg/m^3)$ are filled to the same height in two identical cylindrical vessels. Both vessels have small holes at their bottom. The speeds of the water and kerosene coming out of their holes are $v_1$ and $v_2$ respectively. Select the correct alternative.