Inputs
Liquid-water properties reference ↗ · Pure water, 0–99°C at 100 kPa absolute.
Results
Equations
Kinematic viscosity: Re = VD / ν
This calculator classifies internal pipe flow as laminar for Re ≤ 2300, transition for 2300 < Re < 4000, and turbulent for Re ≥ 4000. The transition region is inherently less predictable.
What Reynolds number tells you
Reynolds number compares inertial effects with viscous effects in a flowing fluid. For internal pipe flow it is dimensionless and is commonly written as Re = ρVD/μ or Re = VD/ν. It is one of the main inputs used to determine whether flow is laminar, transitional, or turbulent and which friction-factor relation is appropriate.
This calculator uses the common circular-pipe classification of laminar at Re ≤ 2300, transition between 2300 and 4000, and turbulent at Re ≥ 4000. These limits are practical engineering boundaries, not perfectly sharp physical switches. Disturbances, entrance conditions, pipe roughness, vibration, and upstream fittings can affect transition.
When to use it
- Selecting a pipe friction-factor method.
- Checking whether a heat-transfer, pressure-drop, or mixing correlation is being used in the correct flow regime.
- Comparing flow behavior when diameter, flow rate, temperature, or viscosity changes.
- Converting a known velocity and fluid property set into a dimensionless flow parameter.
Assumptions and limits
- The diameter entered is the relevant internal characteristic length. For this pipe-flow tool, that normally means inside diameter.
- Fluid properties should be evaluated at conditions representative of the flowing fluid.
- For noncircular ducts, hydraulic diameter may be used in many engineering correlations, but this calculator does not determine hydraulic diameter for you.
- For strongly non-Newtonian fluids, a generalized Reynolds number may be more appropriate than the conventional form used here.
Common mistakes
- Mixing dynamic and kinematic viscosity. If you enter dynamic viscosity, density is required. If you enter kinematic viscosity, density is already embedded through ν = μ/ρ.
- Using the wrong viscosity at temperature. Liquid viscosity can change by multiples over a normal process-temperature range.
- Using nominal pipe size instead of inside diameter.
- Treating transition as reliably turbulent or laminar. Pressure drop and flow behavior in the transition region are less predictable.
- For gas flow, using velocity and properties at inconsistent pressure or temperature conditions.
As a quick check, water-like fluid at 6 ft/s in a 2-inch ID pipe gives Re of roughly 9.3 × 10⁴, which is turbulent.
What to do with the result
For straight-pipe loss, take the Reynolds number to the Darcy Friction Factor Calculator. For a complete one-section line calculation, the Pipe Friction Loss Calculator calculates Reynolds number automatically from flow, diameter, density, and dynamic viscosity.
Reference background: the U.S. Department of Energy fluid-flow handbook discusses Reynolds number, flow regime, and frictional head loss. DOE fluid-flow handbook.
Darcy or Fanning?
Darcy vs. Fanning reference ↗ · Compare the definitions, convert friction factors, and check which equation to use.
Equation values and input guide
Choose the viscosity form for your property data. Supply density only with dynamic viscosity; use properties at the operating temperature. The pipe-flow regime labels apply to internal flow in a circular pipe.
- Re
- Reynolds number, dimensionless, expressing the ratio of inertial to viscous effects.
- ρ
- Fluid density, converted to kg/m³.
- V
- Average flow velocity, converted to m/s.
- D
- Characteristic length, converted to m; use actual inside diameter for a full circular pipe.
- μ
- Dynamic viscosity, converted to Pa·s; 1 cP = 0.001 Pa·s.
- ν
- Kinematic viscosity μ/ρ, converted to m²/s; 1 cSt = 10⁻⁶ m²/s. Do not enter cP as cSt.
Use the unit selectors beside the inputs. Units shown in the equations must be consistent when checking the math by hand.