Water falls from a tap,down the streamline. What happens to the cross-sectional area of the water stream?

Which fundamental law forms the basis of the equation of continuity?

Water enters through end $A$ with speed $v_1$ and leaves through end $B$ with speed $v_2$ of a cylindrical tube $AB$. The tube is always completely filled with water. In case $I$,the tube is horizontal; in case $II$,it is vertical with end $A$ upwards; and in case $III$,it is vertical with end $B$ upwards. We have $v_1 = v_2$ for:

$A$ river gradually deepens from a depth of $4 \ m$ to a depth of $8 \ m$ as shown. The width,$W$,of the river does not change. At the depth of $4 \ m$,the river's speed is $12 \ m/s$. Its velocity at the $8 \ m$ depth is ......... $m/s$.

The blades of a windmill sweep out a circle of area $A$. If the wind flows at a velocity $v$ perpendicular to the circle,then the mass of the air of density $\rho$ passing through it in time $t$ is

In the given figure,the velocity of the fluid $v = $ . . . . . . $m/s$.