$A$ 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 liquid, the rate of liquid flow is:

The cylindrical tube of a spray pump has a cross-section of $8.0 \; cm^{2}$,one end of which has $40$ fine holes each of diameter $1.0 \; mm$. If the liquid flow speed inside the tube is $1.5 \; m \, min^{-1}$,what is the speed (in $m/s$) of ejection of the liquid through the holes?

Fountains usually seen in gardens are generated by a wide pipe with an enclosure at one end having many small holes. Consider one such fountain which is produced by a pipe of internal diameter $2 \ cm$ in which water flows at a rate $3 \ ms^{-1}$. The enclosure has $100$ holes each of diameter $0.05 \ cm$. The velocity of water coming out of the holes is (in $ms^{-1}$):

What is a tube of flow?

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 $0.4 \ m/s$. The diameter of the water stream at a distance $2 \times 10^{-1} \ m$ below the tap is close to .......$\times 10^{-3} \ m$.

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