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 .......$\times 10^{-3} \ m$.

Water coming out of the mouth of a tap and falling vertically in streamline flow forms a tapering column,i.e.,the area of cross-section of the liquid column decreases as it moves down. Which of the following is the most accurate explanation for this?

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

$A$ pipe having an internal diameter $D$ is connected to another pipe of the same size. Water flows into the second pipe through $n$ holes,each of diameter $d$. If the water in the first pipe has speed $v$,the speed of water leaving the second pipe is

In the figure shown,a liquid is flowing through a tube at the rate of $0.1\, m^3/sec$. The tube is branched into two semicircular tubes of cross-sectional area $A/3$ and $2A/3$. The velocity of liquid at $Q$ is ......... $m/sec$. (The cross-section of the main tube $= A = 10^{-2}\, m^2$ and $v_p = 20\, m/sec$)

Derive the equation of continuity for the steady flow of an incompressible fluid.