Knudsen Number Calculator

Enter value and click on calculate. Result will be displayed.
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Mean Free Path (λ) :
m
Representative Physical Length Scale (L) :
m
Result:

A Knudsen Number Calculator is a tool used to determine the Knudsen number (Kn), which is a dimensionless quantity in fluid dynamics and gas dynamics. It describes the relative importance of molecular mean free path to a characteristic length scale of the system, helping to determine whether a gas behaves as a continuum or if rarefied gas effects become significant.

Why use a Knudsen Number Calculator?

The Knudsen number is crucial in:

  • Aerospace engineering: For analyzing gas flows at high altitudes where the air is rarefied.
  • Vacuum technology: To determine whether gases in vacuum systems behave as a continuum or as free molecular flow.
  • Microfluidics & nanotechnology: Used in designing devices where gas flow occurs in very small channels.
  • Heat transfer & semiconductor manufacturing: Helps in modeling gas interactions in extremely small spaces.

How does a Knudsen Number Calculator work?

The Knudsen Number (Kn) is defined as:

Where:

  • λ is the mean free path of gas molecules (average distance a molecule travels before colliding with another molecule),
  • L is a characteristic length scale of the system (such as pipe diameter or channel width).

The calculator computes Kn by taking the values of λ and L and performing the division.

When to use a Knudsen Number Calculator?

  • Determining flow regimes: Used to classify the flow as:
    • Continuum flow (Kn<0.01) → Normal fluid mechanics apply (Navier-Stokes equations valid).
    • Slip flow (0.01≤Kn<0.1) → Slight deviation from classical fluid dynamics; slip conditions may apply.
    • Transitional flow (0.1≤Kn<10) → Neither continuum nor free molecular assumptions hold well.
    • Free molecular flow (Kn≥10) → Gas molecules move independently, requiring statistical mechanics for analysis.
  • Designing vacuum systems: In ultra-high vacuum (UHV) systems, Knudsen number helps predict gas behavior.
  • Aerospace & space exploration: Helps in studying rarefied gas dynamics for spacecraft moving through upper atmospheric layers.
  • Microfluidics: Assists in determining gas flow properties in microscale devices like lab-on-a-chip systems.

Example Calculation

If a gas has:

  • A mean free path λ = 0.1 mm,
  • A characteristic length L = 10 mm,

Then,

Since Kn=0.01, this indicates continuum flow with slip conditions.