Continuum Hypothesis

Definition

The Continuum Hypothesis assumes that a fluid can be treated as a continuous medium rather than a collection of discrete molecules. Properties such as density, velocity, and temperature are defined as continuously differentiable fields.

Conditions

This hypothesis is valid when the Knudsen number ($Kn$) is small: $Kn = \frac{\lambda}{L} \ll 1$ where $\lambda$ is the molecular mean free path and $L$ is the characteristic length scale.

Relationships

• Related: Fluid Dynamics