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

Answer 1

The correct option is C $9:4$

Given:
Diameter of section $1,d_1=2.5cm$
Diameter of section $2,d_2=3.75cm$
Using continuity equation for an ideal fluid,
$Av=constant$
$\therefore A_1{v}_1=A_2{v}_2$

$\therefore \pi r_1^2{v}_1=\pi r_2^2{v}_2$

$\therefore \frac{\pi d_1^2{v}_1}{4}=\frac{\pi d_2^2{v}_2}{4}$

$\therefore \frac{v_1}{v_2}=\frac{d_2^2}{d_1^2}=\frac{(3.75{)}^2}{(2.5{)}^2}=\frac{9}{4}$

Final Answer:$\left(A\right)$