# Reynolds Number Calculator

Calculate the Reynolds number and determine if fluid flow is laminar, transitional, or turbulent. Supports water, air, and oil.

## What this calculates

The Reynolds number (Re) is a dimensionless quantity that predicts whether fluid flow will be laminar or turbulent. It is defined as Re = vL/nu, where v is flow velocity, L is a characteristic length (such as pipe diameter), and nu is kinematic viscosity. This calculator computes Re and classifies the flow regime.

## Inputs

- **Flow Velocity** (m/s) — min 0 — Average velocity of the fluid.
- **Characteristic Length** (m) — min 0 — Pipe diameter or object length scale.
- **Fluid** — options: Water (20°C), Air (20°C), Engine Oil (SAE 30, 20°C), Custom — Select fluid or enter custom kinematic viscosity.
- **Kinematic Viscosity** (m²/s) — min 0 — Kinematic viscosity (ν). Used when 'Custom' is selected.

## Outputs

- **Reynolds Number** — Dimensionless Reynolds number (Re = vL/ν).
- **Flow Regime** — formatted as text — Laminar (Re < 2300), Transitional (2300-4000), or Turbulent (Re > 4000).
- **Critical Velocity (turbulence onset)** (m/s) — Velocity at which flow transitions to turbulent (Re = 4000).

## Details

The Reynolds number represents the ratio of inertial forces to viscous forces in a fluid. Low Re (below 2300 for pipe flow) indicates laminar flow, with smooth, orderly layers of fluid sliding past each other. High Re (above 4000) indicates turbulent flow, with chaotic, swirling motion with eddies and mixing. The range 2300-4000 is the transitional zone where flow can switch between regimes.

The characteristic length depends on the geometry: for pipe flow, it is the internal diameter; for flow over a flat plate, it is the distance from the leading edge; for a sphere, it is the diameter. The kinematic viscosity ν = μ/ρ depends on the fluid and temperature.

Reynolds number is critical in engineering design. Laminar flow has lower friction losses but poor mixing. Turbulent flow has higher drag but better heat and mass transfer. Pipe sizing, pump selection, heat exchanger design, and aerodynamic analysis all rely on Reynolds number calculations.

## Frequently Asked Questions

**Q: What is the critical Reynolds number?**

A: For flow in a circular pipe, the critical Reynolds number is approximately 2300 (onset of transition from laminar to turbulent). Above ~4000, flow is fully turbulent. These values can vary with pipe roughness and entrance conditions.

**Q: What is kinematic viscosity?**

A: Kinematic viscosity (ν) is the ratio of dynamic viscosity to fluid density: ν = μ/ρ. It measures a fluid's resistance to flow under gravity. Water at 20°C has ν ≈ 1.0 × 10⁻⁶ m²/s; air has ν ≈ 1.5 × 10⁻⁵ m²/s.

**Q: Why does temperature affect the Reynolds number?**

A: Temperature changes the fluid's viscosity. For liquids, viscosity decreases with temperature (making turbulence more likely). For gases, viscosity increases with temperature. Both effects change the Reynolds number.

**Q: Who was Osborne Reynolds?**

A: Osborne Reynolds (1842-1912) was a British-Irish engineer who demonstrated in 1883 that the transition from laminar to turbulent pipe flow occurs at a characteristic ratio of inertial to viscous forces, now called the Reynolds number.

---

Source: https://vastcalc.com/calculators/physics/reynolds-number
Category: Physics
Last updated: 2026-04-21