Question

The continuum approach breaks down when the mean free path of the molecules is

• A. the same order of magnitude as the smallest significant length in the problem being investigated
• B. greater than the magnitude as the smallest significant length in the problem being investigated
• C. less than the magnitude as the smallest significant length in the problem being investigated
• D. less than one

Hint:

Use Knudsen number (Kn) to assess continuum validity.

Answer 1

The Correct Option is A

The continuum approach in fluid mechanics assumes that fluid properties such as density, pressure, and temperature vary smoothly and continuously throughout the flow. This approximation is valid when the mean free path of the molecules, which is the average distance a molecule travels before colliding with another molecule, is much smaller than the smallest significant length scale in the problem.

However, when the mean free path becomes comparable to the smallest significant length scale, the continuum assumption breaks down. This is because the fluid can no longer be accurately described as a continuous medium. In such cases, molecular effects become significant and must be accounted for using methods like statistical mechanics or molecular dynamics.

Therefore, the continuum approach breaks down when the mean free path of the molecules is:

• the same order of magnitude as the smallest significant length in the problem being investigated.