Water flows through a horizontal pipe of varying cross-section at a rate of $0.314 \,m^3 \,s^{-1}$. The velocity of water at a point where the radius of the pipe is $10 \,cm$ is (in $\,m/s$)

Two pipes of radii $2 \, cm$ and $4 \, cm$ are connected in series. What is the ratio of the flow velocities of the fluid in these pipes?

Water falls from a tap,down the streamline.

$A$ laminar stream is flowing vertically down from a tap of cross-section area $1 \ cm^2$. At a distance $10 \ cm$ below the tap,the cross-section area of the stream has reduced to $0.5 \ cm^2$. The volumetric flow rate of water from the tap is about ........ $litre/min$.

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:

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