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Eddy Viscosity Definition Calculator

Eddy viscosity is a parameter used in turbulence modeling to represent the enhanced momentum transfer caused by turbulent eddies in a fluid flow.

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Eddy Viscosity

Formula first

Overview

This concept models the effect of turbulent fluctuations on the mean flow by treating them as an additional viscous stress, analogous to molecular viscosity. It is defined as the ratio of the turbulent shear stress to the mean velocity gradient, effectively acting as an 'apparent' viscosity that accounts for the increased mixing in turbulent regimes. Because it depends on the flow state rather than just the fluid properties, it is not a physical constant but a flow-dependent variable.

Symbols

Variables

= Eddy Viscosity, |_{yz}^{}| = Total Shear Stress Magnitude, = Velocity Gradient, = Molecular Viscosity, \frac{\mathcal{P}_0 - _1}{L} = Pressure Gradient

Eddy Viscosity
Total Shear Stress Magnitude
Pa
Velocity Gradient
Molecular Viscosity
Pressure Gradient
Pa/m
Radial Position

Apply it well

When To Use

When to use: Apply this when modeling turbulent flow using the Boussinesq hypothesis to relate turbulent shear stress to the mean velocity gradient.

Why it matters: It allows engineers to simplify complex turbulent flow calculations by using existing laminar flow equations with an adjusted, effective viscosity.

Avoid these traps

Common Mistakes

  • Confusing eddy viscosity with molecular (dynamic) viscosity.
  • Assuming eddy viscosity is constant throughout the entire flow field.
  • Neglecting the negative sign in the definition when calculating turbulent shear stress.

One free problem

Practice Problem

In a turbulent pipe flow, the total shear stress is 10 Pa, the velocity gradient is 50 s^-1, and the molecular viscosity is 0.001 Pa·s. Calculate the eddy viscosity.

Total Shear Stress Magnitude10 Pa
Velocity Gradient50 s^{-1}
Molecular Viscosity0.001 Pa·s

Solve for:

Hint: Use the shear-stress magnitude form mu_t = (tau_total / dv_dy) - mu.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. White, F. M. (2011). Fluid Mechanics (7th ed.). McGraw-Hill.
  2. Pope, S. B. (2000). Turbulent Flows. Cambridge University Press.
  3. Wikipedia: Eddy viscosity
  4. NIST: CODATA Recommended Values of the Fundamental Physical Constants
  5. White, Frank M. Fluid Mechanics. McGraw-Hill, 2011.
  6. Pope, Stephen B. Turbulent Flows. Cambridge University Press, 2000.