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Kozeny-Carman Equation Calculator

Relationship between permeability and porosity.

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Permeability

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Overview

The Kozeny-Carman equation is a semi-empirical relationship used to estimate the intrinsic permeability of granular porous media like sand and gravel. It relates the flow capacity of the medium to its porosity and the average diameter of the constituent particles, modeling the pores as a network of tortuous channels.

Symbols

Variables

k = Permeability, \phi = Porosity, d_p = Grain Size

Permeability
Porosity
Grain Size

Apply it well

When To Use

When to use: This equation is best applied to laminar flow conditions in well-sorted, non-cohesive soils or packed beds of uniform particles. It is particularly useful when laboratory permeability tests are unavailable but grain size distribution and porosity data are known.

Why it matters: Accurate permeability estimates are vital for modeling groundwater aquifers, predicting the movement of subsurface contaminants, and optimizing drainage in civil engineering. It provides a theoretical bridge between measurable physical geometry and hydraulic performance.

Avoid these traps

Common Mistakes

  • Applying it to fractured rocks (it only works for granular media).

One free problem

Practice Problem

A sand sample from a coastal aquifer has a porosity of 0.30 and an average grain diameter of 0.2 mm. Assuming a sphericity of 1.0, calculate the intrinsic permeability k in m².

Porosity0.3
Grain Size0.0002 m

Solve for:

Hint: Convert the diameter from 0.2 mm to 0.0002 meters before plugging it into the equation.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Bird, R. B., Stewart, W. E., & Lightfoot, E. N. (2007). Transport Phenomena (2nd ed.). John Wiley & Sons.
  2. Incropera, F. P., DeWitt, D. P., Bergman, T. L., & Lavine, A. S. (2007). Fundamentals of Heat and Mass Transfer (6th ed.).
  3. Wikipedia: Kozeny-Carman equation
  4. Bird, R. Byron, Stewart, Warren E., Lightfoot, Edwin N. (2007). Transport Phenomena (2nd ed.). John Wiley & Sons.
  5. Incropera, Frank P., DeWitt, David P., Bergman, Theodore L., Lavine, Adrienne S. (2007). Fundamentals of Heat and Mass Transfer (6th ed.).
  6. Bird, Stewart, and Lightfoot, Transport Phenomena, 2nd Edition
  7. Incropera, DeWitt, Bergman, Lavine, Fundamentals of Heat and Mass Transfer, 7th Edition
  8. Fetter, Applied Hydrogeology, 4th Edition