Created By : Naaz Fatima

Reviewed By : Phani Ponnapalli

Last Updated : May 18, 2023

Knudsen Number Calculator: Our Knudsen Number Calculator is an easy tool for calculating the Knudsen number, which is one of fluid mechanics' dimensionless characteristic values. Its value is used as the key criterion for determining if fluid mechanics equations are applicable. We shall explain what a Knudsen number is and how to calculate it using the Knudsen number definition in the following text.

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Mean free path:
Characteristic linear dimension:

Knudsen Number - Definition

Fluid dynamics is an area of physics that explains how liquids and gases flow. Two types of fluid dynamics formulas can be utilised in general

  • Statistical Mechanics - The microscopic structure of matter - each particle individually - is taken into account by statistical mechanics. Statistical approaches, probability theory, and microscopic physical laws are used in this approach.
  • Continuum Mechanics - In contrast to statistical mechanics, continuum mechanics does not include a microscopic description. It fails to recognise that matter is made up of atoms. The Bernoulli equation and Stoke's law are two examples.

The Knudsen number aids in determining which of the above-mentioned fluid dynamics formulations should be used in a given situation. The continuity assumption of fluid mechanics is no longer a good approximation when the mean free path of the fluid molecules is larger than the size of the chamber or pipe. We'll need to employ statistical mechanics.

The typical free path of air molecules under normal conditions is roughly 6.21 * 10^(-8) m, hence the Knudsen number is usually relatively low. As a result, we can employ a continuum mechanics strategy. The scenario is different in highly rarefied fluids like outer space or the Earth's exosphere, where the density of molecules is too low for them to collide (like in gases). Gases at extremely low pressures, such as those encountered in high vacuum, behave similarly.

How to find Knudsen Number?

The particle's mean free path and characteristic linear dimension determine the Knudsen number, which is a dimensionless quantity. The following is the Knudsen number formula that we use in our Knudsen number calculator is Kn = λ / L

  • Kn = Knudsen number (dimensionless)
  • λ = mean free path (expressed in length units)
  • L = characteristic linear dimension (expressed in length units)

The linear dimension that is distinctive The letter L (or characteristic length) is a convention. It determines the smallest length scale at which significant variations in macroscopic flow characteristics can be noticed by definition. For example, if you want to calculate the flow through a pipe, you can use the diameter (or radius) of the pipe as L.

It should be noted that, especially for flows in complex geometries, different authors may use slightly different definitions of L. As a result, the value of the typical linear dimension cannot be calculated with certainty. The Knudsen number is significant because when Kn < 1, the fluid acts as a continuous fluid. When Kn >1, however, statistical mechanics should be used.

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FAQs on Knudsen Number Calculator

1. When the Knudsen number is greater than 0.5 the flow is of the type?

At Knudsen numbers greater than 0.5, molecular interaction is non-existent. The molecular flow takes precedence. The mean free path in this situation is much larger than the flow channel's diameter.

2. What is the Knudsen effect, and how does it work?

The Knudsen Effect occurs when a material's pore width is less than the average free length of a gas molecule's journey.

3. What is the Knudsen diffusion's main assumption?

When the mean pore diameter of the porous material is lower than the mean free route of the gas particles, Knudsen diffusion, or Knudsen flux, occurs. When the mean free path gets large in low permeability porous media with small pore radii and low gas pressures, this form of diffusion occurs.

4. What is the characteristic length in the Knudsen Number?

The Knudsen number is a dimensionless parameter with the formula K n = / L, where L is the characteristic length and M is the mean free path. It expresses the degree to which something deviates from the norm. When K n> 0.01, the concept of continuity usually fails to hold.