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 :

• A. $\frac{\sqrt{3}}{2}$
• B. $\frac{3}{4}$
• C. $\frac{81}{256}$
• D. $\frac{9}{16}$

Answer 1

Answer: (D)

$\frac{9}{16}$

Answer 2

$A_{1}V_{1} = A_{2}V_{2}$
$\frac{V_{min}}{V_{max}} = \frac{A_{min}}{A_{max}}$
$\frac{V_{min}}{V_{max}} = \left(\frac{4.8}{6.4}\right)^{2}$
$\frac{V_{min}}{V_{max}} = \frac{9}{16}$