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 ______.

Options

• 9:4

• 3:2

• `sqrt(3) : sqrt(2)`

• `sqrt(2) : sqrt(3)`

Answer 1

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 9:4.

Explanation:

According to the continuity equation (Law of Conservation of mass)

`a_1v_1 = a_2v_2`

`v_1/v_2 = a_2/a_1`

= `(pi(d_2/2)^2)/(pi(d_1/2)^2)`

= `d_2^2/4 * 4/d_1^2`

= `d_2^2/d_1^2`

`v_1/v_2 = (3.75)^2/(2.50)^2 = [3/2]^2`

⇒ `v_1/v_2 = 9/4`

Or `v_1 : v_2 :: 9:4`