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 $B$?

Select the $WRONG$ statement from the following. In a streamline flow,

$A$ shower head has $25$ circular openings, each with radius $1 \,mm$. The shower head is connected to a pipe with radius $2 \,cm$. If the speed of the water in the pipe is $25 \,cm/s$, what is its speed as it exits the shower head openings (in $\,m/s$)?

The surface of water in a water tank of cross-sectional area $750 \,cm^2$ on the top of a house is '$h$' $m$ above the tap level. The speed of water coming out through the tap of cross-sectional area $500 \,mm^2$ is $30 \,cm/s$. At that instant, $\frac{dh}{dt}$ is $x \times 10^{-3} \,m/s$. The value of '$x$' will be:

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipe are $6.4 \; cm$ and $4.8 \; cm,$ respectively. The ratio of the minimum and the maximum velocities of the fluid in this pipe is: