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

$A$ pipe having an internal diameter $D$ is connected to another pipe of the same size. Water flows into the second pipe through $n$ holes, each of diameter $d$. If the water in the first pipe has speed $v$, what is the speed of water leaving the second pipe?

Two water pipes $P$ and $Q$ having diameters $2 \times 10^{-2} \ m$ and $4 \times 10^{-2} \ m$,respectively,are joined in series with the main supply line of water. The velocity of water flowing in pipe $P$ is

An incompressible fluid (ideal fluid) is flowing through a non-uniform cross-sectional tube $PQ$ from end $P$ to end $Q$. If $K_P$ and $K_Q$ are the kinetic energy per unit volume of the fluid at end $P$ and end $Q$ respectively, then

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: