Water is moving with a speed of $5.18 \; ms^{-1}$ through a pipe with a cross-sectional area of $4.20 \; cm^2$. The water gradually descends $9.66 \; m$ as the pipe increases in area to $7.60 \; cm^2$. The speed of flow at the lower level is ....... $ms^{-1}$.

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 $\,ms^{-1}$)

Define line of flow and streamline.

Water enters through end $A$ with speed $v_1$ and leaves through end $B$ with speed $v_2$ of a cylindrical tube $AB$. The tube is always completely filled with water. In case $I$,the tube is horizontal; in case $II$,it is vertical with end $A$ upwards; and in case $III$,it is vertical with end $B$ upwards. We have $v_1 = v_2$ for:

In a streamlined flow,the velocity of a fluid at a given point

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 $ms^{-1}$):