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

$A$ liquid flows steadily through a cylindrical pipe having a radius $2R$ at point $A$ and radius $R$ at point $B$ farther along the flow direction. If the velocity at point $B$ is $4v$, what will be the velocity at point $A$?

The surface of water in a water tank of cross-sectional area $750 \,cm^2$ on the top of a house is '$h$' $m$ above the tap level. The speed of water coming out through the tap of cross-sectional area $500 \,mm^2$ is $30 \,cm/s$. At that instant, $\frac{dh}{dt}$ is $x \times 10^{-3} \,m/s$. The value of '$x$' will be:

Water flows through a horizontal pipe at a speed '$V$'. The internal diameter of the pipe is '$d$'. If the water is emerging from a nozzle at a speed '$V_1$',then the diameter of the nozzle is:

The radius of the cross-section of the cylindrical tube of a spray pump is $2 \,cm$. One end of the pump has $50$ fine holes, each of radius $0.4 \,mm$. If the speed of flow of the liquid inside the tube is $0.04 \,ms^{-1}$, what is the speed of ejection of the liquid from the holes (in $\,ms^{-1}$)?

$A$ 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?