Question

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is ______.

Options

• `9/16`

• `sqrt3/2`

• `3/4`

• `81/256`

Answer 1

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is `underlinebb(9/16).`

Explanation:

From the equation of continuity,

`A_1ν_1 = A_2ν_2`

Here, v₁ and v₂ are the velocities at two ends of the pipe. A₁ and A₂ are the areas of the pipe at two ends.

⇒ `ν_1/ν_2 = A_2/A_1 = (pi(4.8)^2)/(pi(6.4)^2) = 9/16`