An incompressible fluid flows steadily through a cylindrical pipe… - Vidyadip

MCQ

An incompressible fluid flows steadily through a cylindrical pipe which has radius $2r$ at point $A $ and radius $r $ at $B $ further along the flow direction. If the velocity at point $A$ is $v, $ its velocity at point $B$ is

A
$2v$
B
$v$
C
$v/2$
✓
$4v$

✓

Answer

Correct option: D.

$4v$

d
(d) From equation of continuity volume of water entering per second at $\mathrm{A}=$ volume of water exiting per second from $B$

Let $v$ be the velocity at point $B$, then

$\pi(2 R)^{2} v=\pi\left(R^{2}\right) v^{\prime}$

$v^{\prime}=4 v$

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