Question

An incompressible non viscous fluid flows steadily through a cylindrical pipe which has radius $2R$ at point $A$ and radius $R$ at point $B$ farther along the flow direction. If the velocity of the fluid at point $A$ is $V$, its velocity at the point $B$ will be

• A. $2V$
• B. $V$
• C. $V/2$
• D. $4V$

Answer 1

Answer: (D)

$4V$

Answer 2

We know that, from continuity equation,
$A_{1} V_{1}=A_{2} V_{2}$
(Symbols have usual meanings)
$\pi(2 R)^{2} V=\pi R^{2} V_{B}$
$\left(V_{B}=\right.$ Velocity of the fluid at point $B$ )
$\Rightarrow \pi(2 R)^{2} V =\pi R^{2} V_{B}$
$\Rightarrow \pi 4 R^{2} V=\pi R^{2} V_{B}$
$4 V=V_{B}$
$\therefore V_{B}=4 V$