Question

An ideal fluid flows through a pipe of circular cross-section made of two sections with diameters 2. 5 cm and 3. 75 cm. The ratio of the velocities in the two pipes is

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

Answer 1

The correct option is D 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: (a)