Question

An ideal fluid flows through a pipe of circular cross section with diameters $5cm$ and $10cm$ as shown. The ratio of velocities of fluid at $A$ and $B$ is

• A. 4 : 1
• B. 1 : 4
• C. 2 : 1
• D. 1 : 2

Answer 1

Answer: (A)

From continuity equation,
$a_1{u}_1=a_2{v}_2$
$\frac{v_1}{v_2}=\frac{a_2}{a_1}$
$a_1=\pi {\left(\frac{d_1}{2}\right)}^2$
$a_2=\pi {\left(\frac{d_2}{2}\right)}^2$
where, $d_1$ and $d_2$ are the diameters of the openings.
$\Rightarrow \frac{v_1}{v_2}=\frac{\left(\pi d_2^2/4\right)}{\left(\pi d_1^2/4\right)}$
$=\frac{d_2^2}{d_1^2}={\left(\frac{10cm}{5cm}\right)}^2$
$=\frac{10\times 10}{5\times 5}=\frac{4}{1}$ or $4:1$