The Reynolds Number

The Reynolds number $Re$ is a dimensionless ratio of inertial forces to viscous forces in a flow:

$Re = \frac{\rho v L}{\mu} = \frac{v L}{\nu}$

where:

• $\rho$ — fluid density (kg/m³)
• $v$ — flow velocity (m/s)
• $L$ — characteristic length (m); for a pipe, use the inner diameter
• $\mu$ — dynamic viscosity (Pa·s)
• $\nu = \mu / \rho$ — kinematic viscosity (m²/s)

Flow Regimes

The Reynolds number predicts whether flow is orderly or chaotic:

Reference Viscosities

For water in a 50 mm pipe at 0.1 m/s: $Re = (1000)(0.1)(0.05) / 1.002 \times 10^{-3} \approx 4990$ — turbulent.

Your Task

Implement:

• reynolds_number(rho, v, L, mu) — returns the Reynolds number (dimensionless)
• flow_regime(Re) — returns "laminar", "transitional", or "turbulent"