Pipe Flow Rate, Velocity & Diameter Calculator — Reynolds Number and Flow Regime Validator
Calculate volumetric flow rate, flow velocity, or pipe diameter using pipe diameter, velocity, flow rate, density, and viscosity.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Calculation mode
Fluid properties
Viscosity
Pipe / flow parameters
Results
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Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
Volumetric flow rate, flow velocity, and pipe diameter formula:
For flow rate mode:
A = π · D² / 4
Q = v · A
For velocity mode:
A = π · D² / 4
v = Q / A
For diameter mode:
A = Q / v
D = √(4 · A / π)
Viscosity used in Reynolds number calculation:
If dynamic viscosity is provided:
μeff = μ
If kinematic viscosity is provided:
μeff = ρ · ν
Secondary calculations:
Re = ρ · v · D / μeff
ṁ = ρ · Q
q = 0.5 · ρ · v²
hv = v² / (2 · 9.81)
γ̇ = 8 · v / D
where:
- Q — volumetric flow rate (m³/s)
- v — flow velocity (m/s)
- D — pipe diameter (m)
- A — pipe cross-sectional area (m²)
- ρ — fluid density (kg/m³)
- μ — dynamic viscosity (Pa·s)
- ν — kinematic viscosity (m²/s)
- μeff — effective dynamic viscosity used in the Reynolds number formula (Pa·s)
- Re — Reynolds number (—)
- ṁ — mass flow rate (kg/s)
- q — dynamic pressure (Pa)
- hv — velocity head (m)
- γ̇ — shear rate (1/s)
When to use this calculator
When to use this calculator:
- Calculate volumetric flow rate when pipe diameter and flow velocity are known.
- Calculate flow velocity when pipe diameter and volumetric flow rate are known.
- Calculate pipe diameter when volumetric flow rate and target flow velocity are known.
- Check the Reynolds number and classify the result as laminar, transitional, or turbulent flow.
- Compare calculated flow velocity against the density-based recommended velocity range.
- Calculate mass flow rate, dynamic pressure, velocity head, and shear rate from the same pipe-flow input set.
How to interpret the result
Volumetric flow rate is defined as the volume of fluid passing through the pipe per unit time. Flow velocity is defined as volumetric flow rate divided by pipe cross-sectional area. Pipe diameter is defined as the circular pipe size required to match the selected flow rate and velocity condition.
The result depends on pipe diameter, flow velocity, volumetric flow rate, fluid density, and viscosity. Increasing pipe diameter increases volumetric flow rate in flow-rate mode and decreases flow velocity in velocity mode. Increasing flow velocity increases volumetric flow rate in flow-rate mode and decreases the required pipe diameter in diameter mode.
- Safe — Reynolds number is below 2300.
- Warning — Reynolds number is from 2300 to below 4000, or Reynolds number is greater than 10000000.
- Info — Reynolds number is 4000 or higher, or Reynolds number is below 1.
- Limit — calculated flow velocity is outside the recommended velocity range.
- Unsafe — flow velocity is greater than 10 m/s and fluid density is greater than 500 kg/m³.
- Invalid — required positive inputs are missing, non-positive, or viscosity is not provided as exactly one valid viscosity input.
The flow regime is classified as laminar when Reynolds number is below 2300, transitional when Reynolds number is from 2300 to below 4000, and turbulent when Reynolds number is 4000 or higher.
The recommended velocity range is 0.5–3.0 m/s when fluid density is greater than 800 kg/m³ and lower than 1200 kg/m³. For other density values, the recommended velocity range is 0.1–1.5 m/s.
Calculation example
Example:
A user wants to calculate the volumetric flow rate in a pipe when the internal diameter and flow velocity are already known.
- Calculation mode: Flow rate (Q)
- ρ — Fluid density: 1000 kg/m³
- μ — Dynamic viscosity: 0.001 Pa·s
- D — Pipe diameter: 0.1 m
- v — Flow velocity: 2 m/s
The pipe cross-sectional area is 0.00785 m², so the volumetric flow rate is Q = 0.0157 m³/s.
Assumptions and limitations
- The pipe cross-section is circular because area is calculated as π · D² / 4.
- Density must be greater than zero.
- Only one viscosity input is allowed: dynamic viscosity or kinematic viscosity.
- If kinematic viscosity is used, effective dynamic viscosity is calculated from density multiplied by kinematic viscosity.
- Flow rate, flow velocity, and pipe diameter must be greater than zero for the selected calculation mode.
- The recommended velocity range is selected only from the fluid density value.