Question

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

• A. $\frac{9}{16}$
• B. $\frac{81}{256}$
• C. $\frac{3}{2}$
• D. $\frac{\sqrt{3}}{2}$

Answer 1

The correct option is A $\frac{9}{16}$

Given, maximum and minimum diameter of the pipes $6.4cm$ and $4.8cm$

So, maximum and minimum radius of the pipes $3.2cm$ and $2.4cm$

Using equation of continuity

$A_1{v}_1=A_2{v}_2$

$\frac{v_{min}}{v_{max}}=\frac{A_{min}}{A_{max}}={\left(\frac{\pi r_{min}}{\pi r_{max}}\right)}^2$

$\frac{v_{min}}{v_{max}}={\left(\frac{2.4}{3.2}\right)}^2=\frac{9}{16}$