An incompressible liquid flows through a horizontal tube as shown in the following figure. Then the velocity $v$ of the fluid is ....... $m/s$.

$A$ 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:

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

The cylindrical tube of a spray pump has radius $R,$ one end of which has $n$ fine holes,each of radius $r.$ If the speed of the liquid in the tube is $v,$ the speed of the ejection of the liquid through the holes is

Two water pipes $P$ and $Q$ having diameters $2 \times 10^{-2} \, m$ and $4 \times 10^{-2} \, m$ respectively are joined in series with the main supply line of water. The velocity of water flowing in pipe $P$ is ........

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: