FluidCalc

Reynolds Number Calculator

The dimensionless number that predicts whether fluid flow stays smooth (laminar) or becomes chaotic (turbulent).

Fluid density (kg/m³)

Flow velocity (m/s)

Pipe diameter (m)

Dynamic viscosity (Pa·s)

Reynolds number

100,000

Re = ρvD/μ

What you entered

Fluid density (kg/m³): 1000Flow velocity (m/s): 2Pipe diameter (m): 0.05Dynamic viscosity (Pa·s): 0.001

1
Re = ρvD/μ
1000 × 2 × 0.05 / 0.001= 100000
2
Flow regime (<2300 laminar, 2300–4000 transitional, >4000 turbulent)
Re = 100000= Turbulent

Result

Reynolds number: 100,000

Re = 100,000 — the flow is turbulent.

Reynolds number and flow regime

Reynolds number is density times velocity times diameter divided by viscosity. It is dimensionless and predicts whether flow is smooth or turbulent.

Density (kg/m3)	Velocity (m/s)	Diameter (m)	Viscosity (Pa s)	Reynolds number	Regime
1000	0.01	0.05	0.001	500.00	Laminar
1000	0.05	0.02	0.001	1000.00	Laminar
1000	1	0.05	0.001	50000.00	Turbulent
1000	2	0.1	0.001	200000.00	Turbulent
1.225	10	0.5	1.81e-5	338397.79	Turbulent

The conventional boundaries for pipe flow are laminar below about 2,000 and fully turbulent above about 4,000, with a transitional band between. Rows one and three are the same water in the same pipe at different speeds, crossing from orderly layers to chaotic mixing purely by speeding up a hundredfold. Being dimensionless is what makes the number so useful: a scale model tested at the same Reynolds number behaves like the full-size object, which is the basis of wind tunnel testing. The last row is air rather than water, and its very low viscosity is why airflow turns turbulent so readily.

What the Reynolds number tells you

Re below ~2,300 indicates laminar flow (smooth, predictable layers); above ~4,000 is turbulent (chaotic mixing); between is the transition zone. This single number captures the ratio of inertial forces to viscous forces and is one of the most important parameters in fluid mechanics.

Why engineers care about flow regime

Laminar and turbulent flows have completely different friction, heat transfer, and mixing characteristics. A pipe designed for laminar flow will have dramatically different pressure drops than one operating in turbulent flow — getting the Reynolds number right is the first step in any fluid system design.

Frequently asked questions

Water flows at 2 m/s through a 5 cm pipe. Is the flow laminar or turbulent?

Re = ρvD/μ = 1000 × 2 × 0.05 / 0.001 = 100,000. Since Re >> 4,000, the flow is fully turbulent. For laminar flow (Re < 2,300) in this pipe, velocity would need to be below v = 2300 × 0.001/(1000 × 0.05) = 0.046 m/s — barely a trickle.

Why is Re = 2,300 the critical number for pipes?

Osborne Reynolds discovered experimentally (1883) that pipe flow transitions from smooth to chaotic around Re ≈ 2,300. Below this, viscous forces dominate and keep the flow orderly. Above it, inertial forces overwhelm viscosity and create turbulent eddies. The transition zone (2,300-4,000) is unpredictable.

How do engineers use the Reynolds number in real designs?

It determines pipe friction factors, heat transfer coefficients, and mixing efficiency. Turbulent flow has ~5-20× higher friction than laminar but also ~5-10× better heat transfer. Chemical reactors want turbulence (better mixing); microfluidic devices want laminar flow (precise control).