$A$ horizontal tube of non-uniform cross-section has radii of $0.1 \,m$ and $0.05 \,m$ respectively at $M$ and $N$. For a streamline flow of an incompressible liquid, the rate of liquid flow is

$A$ 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 ......... $m/s$.

Water is flowing through two horizontal pipes of different diameters which are connected together. The diameters of the two pipes are $3\, cm$ and $6\, cm$ respectively. If the speed of water in the narrower pipe is $4\, m/s$ and the pressure is $2.0 \times 10^4\, Pa$,then the speed of water in the wider pipe is ........ $m/s$.

What is steady flow?

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.

An ideal fluid flows through a pipe of circular cross-section with diameters $5 \ cm$ and $10 \ cm$ as shown. The ratio of velocities of the fluid at $A$ and $B$ is