Question

An ideal fluid flows through a pipe of circular cross-section made of two sections with diameters $2.5cm$ and $3.75cm$. The ratio of the velocities in the two pipes is

• A. $9:4$
• B. $3:2$
• C. $\sqrt{3}:\sqrt{2}$
• D. $\sqrt{2}:\sqrt{3}$

Answer 1

Answer: (A)

$9:4$

According to equation of continuity $A_1{v}_1=A_2{v}_2$

$\frac{v_1}{v_2}=\frac{A_1}{A_2}=\frac{\pi D_2^2/4}{\pi D_1^2/4}={\left(\frac{D_2}{D_1}\right)}^2$

Here, $D_1=2.5cm,D_2=3.75cm$

$\therefore \frac{v_1}{v_2}={\left(\frac{3.75}{2.5}\right)}^2={\left(\frac{3}{2}\right)}^2=\frac{9}{4}$