What this calculator does
The Reynolds number decides whether a flow is smooth and layered or chaotic and mixing. It compares inertial forces, which want to keep the fluid moving and tumbling, against viscous forces, which want to damp everything down into orderly layers.
Below roughly 2,300 in a pipe the flow is laminar; above about 4,000 it is turbulent, with a transitional zone between. That single dimensionless number governs pressure drop, heat transfer and mixing behaviour across an enormous range of scales.
The formula
Multiply density by flow speed by the characteristic length, then divide by dynamic viscosity. The units cancel completely, which is what makes the result comparable across fluids and scales.
| Term | Meaning |
|---|---|
| Laminar flow | Smooth, layered flow where fluid moves in parallel sheets without mixing between them. |
| Turbulent flow | Chaotic flow with eddies and active mixing, which greatly increases both drag and heat transfer. |
| Characteristic length | The dimension that defines the scale of the flow, usually pipe diameter for internal flow. |
| Dynamic viscosity (μ) | A fluid's resistance to shearing. Water is about 0.001 Pa·s at room temperature. |
The inputs explained
| Field | What to enter |
|---|---|
| Fluid density (water = 1000) (kg/m³) | Fluid density in kilograms per cubic metre. |
| Flow speed (m/s) | Flow speed in metres per second. |
| Characteristic length (pipe diameter, etc.) (m) | The characteristic length in metres, typically the internal pipe diameter. |
| Dynamic viscosity (water at 20 °C ≈ 0.001002) (Pa·s) | Dynamic viscosity in pascal seconds. Water is about 0.001; air about 0.000018. |
When to use it
Predicting pressure drop in a pipe
Laminar and turbulent flow follow completely different pressure-drop relationships, so the regime has to be established first.
Scaling a model test
Matching the Reynolds number between a scale model and the full-size object is what makes wind tunnel results transferable.
Designing for mixing or for smoothness
Turbulence is wanted where mixing or heat transfer matters, and avoided where low drag matters.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does flow speed change the Reynolds number in a 50 mm pipe?
Water through a fixed pipe diameter at a range of speeds.
| Flow speed | Reynolds number | Flow regime |
|---|---|---|
| 0.5 m/s | 25,000 | Turbulent (pipe flow: laminar < 2300, turbulent > 4000) |
| 2 m/s | 100,000 | Turbulent (pipe flow: laminar < 2300, turbulent > 4000) |
| 5 m/s | 250,000 | Turbulent (pipe flow: laminar < 2300, turbulent > 4000) |
Questions
Why is the number dimensionless?
Because the units of density, speed, length and viscosity cancel exactly. That is the point: it allows a small model in a wind tunnel and a full-size aircraft to be compared directly, provided the numbers match.
Why 2,300 as the threshold?
It is an empirical figure for pipe flow rather than a derived constant, and the transition is gradual rather than sharp. Careful experiments can maintain laminar flow well above it, while disturbances can trigger turbulence below.
Does turbulence always increase drag?
For pipe flow, yes, substantially. For flow over a body it is more subtle: a turbulent boundary layer can delay separation and actually reduce total drag, which is exactly why golf balls have dimples.
What is kinematic viscosity?
Dynamic viscosity divided by density, which combines the two into one property. The Reynolds number can be written using it as simply speed times length divided by kinematic viscosity.
For pressure and speed along a streamline, see the Bernoulli equation calculator. For open channel flow, see the open channel flow calculator.