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.

An incompressible fluid flows steadily through a cylindrical pipe which has radius $2r$ at point $A$ and radius $r$ at point $B$ further along the flow direction. If the velocity at point $A$ is $v$,what is its velocity at point $B$?

Can two streamlines cross each other? Why?

$A$ 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 $v$,the speed of water leaving the second pipe is

What is the effect on the velocity of a fluid if streamlines are closely spaced?