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

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.

Water is flowing continuously from a tap having an internal diameter $8 \times 10^{-3}\, m$. The water velocity as it leaves the tap is $0.04\, ms^{-1}$. The diameter of the water stream at a distance $8 \times 10^{-1}\, m$ below the tap is close to

Water flows through a horizontal pipe of variable cross-section at the rate of $12 \pi$ litre per minute. The velocity of the water at the point where the diameter of the pipe becomes $2 \text{ cm}$ is (in $\text{ m/s}$)

An incompressible fluid flows steadily through a cylindrical pipe having radius $R$ at point $A$ and $\frac{R}{3}$ at point $B$ further along the direction of flow of liquid. If the velocity at point $A$ is $V$,then the velocity at point $B$ is:

The cylindrical tube of a spray pump has a cross-section of $8 \,cm^{2}$, one end of which has $40$ fine holes each of area $10^{-8} \,m^{2}$. If the liquid flows inside the tube with a speed of $0.15 \,m \,min^{-1}$, the speed with which the liquid is ejected through the holes is (in $\,ms^{-1}$)