First slide

Fluid dynamics

Question

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

Easy

A

$\frac{81}{256}$
B

$\frac{9}{16}$
C

$\frac{3}{4}$
D

$\frac{\sqrt{3}}{2}$

Solution

Using equation of continuity
$A_{1} V_{1} = A_{2} V_{2} \Rightarrow \frac{V_{1}}{V_{2}} = \frac{A_{2}}{A_{1}} \Rightarrow \frac{V_{1}}{V_{2}} = (\frac{d_{2}}{d_{1}}) = {(\frac{4.8}{6.4})}^{2} = \frac{9}{16}$

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