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Reynolds Number (Porous Flow) Calculator

Determines if flow is laminar or turbulent in rock pores.

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Reynolds Num.

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Overview

In geological fluid dynamics, the Reynolds number for porous media characterizes the ratio of inertial forces to viscous forces within the small spaces of a soil or rock matrix. It is a critical dimensionless quantity used to determine the transition from linear Darcian flow to non-linear turbulent flow in subsurface environments.

Symbols

Variables

Re = Reynolds Num., ho = Density, v = Velocity, d = Grain Diameter, mu = Dynamic Viscosity

Reynolds Num.
Density
Velocity
Grain Diameter
Dynamic Viscosity

Apply it well

When To Use

When to use: This equation is applied when analyzing groundwater movement, petroleum reservoir drainage, or contaminant transport through aquifers. Use it specifically to verify if Darcy's Law is valid, which typically requires a Reynolds number less than 1 to 10 in porous media.

Why it matters: It identifies the limit where the linear relationship between pressure gradient and flow rate breaks down due to inertial effects. Understanding this transition is essential for accurate modeling of high-velocity scenarios like pumping near a well screen or flow through coarse gravel.

Avoid these traps

Common Mistakes

  • Using diameter in cm instead of meters.

One free problem

Practice Problem

A hydrologist is studying water flow through a coarse sand layer. The water has a density of 1000 kg/m³ and a dynamic viscosity of 0.001 Pa·s. If the average grain diameter of the sand is 0.001 m and the seepage velocity is 0.002 m/s, calculate the Reynolds Number.

Density1000 kg/m³
Velocity0.002 m/s
Grain Diameter0.001 m
Dynamic Viscosity0.001 Pa·s

Solve for:

Hint: Multiply density, velocity, and diameter, then divide by the dynamic viscosity.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Bird, R. Byron; Stewart, Warren E.; Lightfoot, Edwin N. Transport Phenomena. John Wiley & Sons.
  2. Incropera, Frank P.; DeWitt, David P.; Bergman, Theodore L.; Lavine, Adrienne S. Fundamentals of Heat and Mass Transfer. John Wiley & Sons.
  3. Wikipedia: Reynolds number
  4. Freeze & Cherry, Groundwater
  5. Fetter, Applied Hydrogeology
  6. Bear, Dynamics of Fluids in Porous Media
  7. Incropera, Fundamentals of Heat and Mass Transfer
  8. Freeze, R. A., & Cherry, J. A. (1979). Groundwater. Prentice Hall.