The Reynolds number (Re) is the most important dimensionless “flow regime” indicator in fluid mechanics. It compares inertial transport to viscous damping. Large Re tends to indicate inertia-dominated flow and increased likelihood of turbulence; small Re indicates viscosity-dominated (creeping/laminar) behavior.

Even though Re is dimensionless (sharing a dimension key with the scalar unit), it is not “just a number” in practice. It is a navigation coordinate for fluid physics: it predicts which governing simplifications apply, which correlations to use, and what flow features to expect. Fundamap keeps it as its own node (no aliasing) because it is a top-level map waypoint.

Dimensional Structure

Re = (ρ · v · L) / μ
ρ: density (kg/m³)
v: velocity (m/s)
L: characteristic length (m)
μ: dynamic viscosity (Pa·s)
    

Interpretation

• Low Re: viscous forces dominate; flow is smooth and predictable.
• High Re: inertia dominates; flow can transition to turbulence depending on geometry.
• Why it matters: it selects the right physics model and the right empirical correlations.

Summary

Reynolds number is the “phase diagram axis” for flow behavior. Adding it greatly increases Fundamap coverage in fluid mechanics and transport.

1) Core definition

Re = (ρ · v · L) / μ
    

2) Pipe flow intuition (common engineering heuristic)

• Laminar flow often occurs at lower Re; turbulent flow becomes more likely at higher Re.
• The exact thresholds depend on geometry, roughness, and disturbances (so treat thresholds as heuristics, not laws).

3) Where it appears

• Flow regime selection (laminar vs transitional vs turbulent)
• Drag and friction correlations
• Heat and mass transfer correlations (often combined with Prandtl)
• Scaling analysis for experiments and model similarity

4) Map edges (recommended)

reynolds_number = density ⊗ velocity ⊗ meter ⊗ (1/viscosity)
    

This edge connects your existing density/velocity/viscosity nodes into a single “flow regime” coordinate.