Water flows through a hose pipe whose internal diameter is $4 \,cm$ at a speed of $1 \,ms^{-1}$. If water has to emerge at a speed of $4 \,ms^{-1}$, then the diameter of the nozzle should be (in $\,cm$)

Assertion $(A):$ The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up but tends to narrow down when held vertically down.
Reason $(R):$ In any steady flow of an incompressible fluid,the volume flow rate of the fluid remains constant.

$A$ water spray gun is attached to a hose of cross-sectional area $30 \text{ cm}^2$. The gun comprises $10$ perforations,each of cross-sectional area $15 \text{ mm}^2$. If the water flows in the hose with a speed of $50 \text{ cm/s}$,calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)

Two pipes of radii $2 \, cm$ and $4 \, cm$ are connected in series. What is the ratio of the flow velocities of the fluid in these pipes?

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

Water is flowing through a tube of non-uniform cross-section. The ratio of the radius at the entry and exit end of the pipe is $3:2$. Then the ratio of velocities at the entry and exit of the liquid is: