Pipe Flow Rate & Velocity Calculator — Diameter, Reynolds Number & Flow Regime
Calculate volumetric flow rate, average pipe velocity, or inside diameter, with optional mass flow rate, Reynolds number, and pipe-flow regime diagnostics.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Calculation mode
Pipe / flow parameters
Optional fluid diagnostics
Results
Calculation tools Save, export and manage your results
Save your calculation, export available results, or store a finalized engineering artifact in your account.
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
Pipe flow rate, velocity and diameter formulas
The calculator uses the internal cross-sectional area of a circular pipe:
A = πD2 / 4
where:
- A — pipe cross-sectional area [m2]
- D — pipe inside diameter [m]
Flow rate mode
When inside diameter and average flow velocity are known:
Q = vA = vπD2 / 4
Velocity mode
When volumetric flow rate and inside diameter are known:
v = Q / A = 4Q / (πD2)
Diameter mode
When volumetric flow rate and target average velocity are known:
D = √(4Q / (πv))
where:
- Q — volumetric flow rate [m3/s]
- v — average flow velocity [m/s]
- D — pipe inside diameter [m]
Optional mass flow rate
If fluid density is provided, the calculator also determines mass flow rate:
ṁ = ρQ
- ṁ — mass flow rate [kg/s]
- ρ — fluid density [kg/m3]
- Q — volumetric flow rate [m3/s]
Optional Reynolds number
With dynamic viscosity:
Re = ρvD / μ
Dynamic-viscosity mode requires both fluid density and dynamic viscosity.
With kinematic viscosity:
Re = vD / ν
- Re — Reynolds number [—]
- ρ — fluid density [kg/m3]
- v — average flow velocity [m/s]
- D — pipe inside diameter [m]
- μ — dynamic viscosity [Pa·s]
- ν — kinematic viscosity [m2/s]
Flow regime classification used by the calculator
- Re = 0: no flow
- 0 < Re < 2300: laminar flow
- 2300 ≤ Re < 4000: transitional flow
- Re ≥ 4000: turbulent flow
When to use this calculator
When to use this calculator
Use this calculator when two of the three basic pipe-flow quantities — volumetric flow rate, average velocity, and inside diameter — are known and the third must be calculated for a circular pipe.
- Calculate flow rate: enter pipe inside diameter and average flow velocity.
- Calculate velocity: enter volumetric flow rate and pipe inside diameter.
- Calculate diameter: enter volumetric flow rate and the target average velocity.
- Calculate mass flow rate: optionally provide fluid density.
- Evaluate Reynolds number: optionally provide either dynamic viscosity with density or kinematic viscosity.
- Identify the pipe-flow regime: classify the calculated Reynolds number as no flow, laminar, transitional, or turbulent.
The diameter input represents the actual inside diameter available to the fluid. A nominal pipe size or outside diameter should not be substituted unless it is equal to the actual bore.
What this calculator does not calculate
This calculator does not determine pressure drop, friction factor, pipe roughness effects, fitting losses, pump head, cavitation margin, water hammer, or a code-based allowable pipe velocity. Those quantities require additional hydraulic calculations.
The diameter result is a mathematical inside diameter derived from flow rate and target velocity. It does not automatically select a commercial nominal pipe size, wall thickness, or pipe schedule.
How to interpret the result
How to interpret the results
Volumetric flow rate Q is the volume of fluid passing through the pipe per unit time. At a fixed inside diameter, flow rate increases directly with average velocity.
Average flow velocity v is the cross-sectional mean velocity through the pipe. For a fixed volumetric flow rate, increasing the inside diameter increases flow area and decreases average velocity. Because circular-pipe area is proportional to D2, velocity changes strongly with diameter.
Pipe inside diameter D is the circular bore required to carry the entered volumetric flow rate at the entered target average velocity. The calculated value is not automatically a commercial nominal pipe size or schedule.
Cross-sectional area A is calculated from the inside diameter using A = πD2/4.
Mass flow rate ṁ is available when density is entered and is calculated from ṁ = ρQ. A higher density produces a proportionally higher mass flow rate for the same volumetric flow rate.
Reynolds number Re compares inertial and viscous effects for the entered pipe-flow condition. Increasing velocity or diameter increases Reynolds number, while increasing viscosity decreases it when the other variables remain unchanged.
- Re = 0: no flow.
- 0 < Re < 2300: the calculator reports laminar flow.
- 2300 ≤ Re < 4000: the calculator reports transitional flow and flags the result as a warning condition.
- Re ≥ 4000: the calculator reports turbulent flow.
The flow-regime result is a diagnostic classification, not a complete pipe-design verdict. It does not confirm acceptable pressure loss, noise, erosion, cavitation resistance, transient behavior, or compliance with a piping design standard.
Calculation example
Example — calculate flow rate and Reynolds number
A circular pipe has an inside diameter of 50 mm and carries a fluid at an average velocity of 2.0 m/s. The fluid density is 998 kg/m3 and its dynamic viscosity is 1.002 mPa·s. Determine the volumetric flow rate, mass flow rate, Reynolds number, and flow regime.
1. Convert the inputs to SI units
D = 50 mm = 0.050 m
v = 2.0 m/s
ρ = 998 kg/m3
μ = 1.002 mPa·s = 0.001002 Pa·s
2. Calculate pipe cross-sectional area
A = πD2 / 4
A = π(0.050)2 / 4
A = 0.0019635 m2
3. Calculate volumetric flow rate
Q = vA
Q = 2.0 × 0.0019635
Q = 0.003927 m3/s
This is approximately 3.927 L/s or 235.6 L/min.
4. Calculate mass flow rate
ṁ = ρQ
ṁ = 998 × 0.003927
ṁ = 3.919 kg/s
5. Calculate Reynolds number
Re = ρvD / μ
Re = (998 × 2.0 × 0.050) / 0.001002
Re ≈ 99,601
6. Interpret the result
A Reynolds number of approximately 99,601 is above 4000, so the calculator classifies this case as turbulent flow.
This classification describes the Reynolds-number regime only. It does not determine pressure loss, friction factor, pipe capacity, or whether the selected velocity is acceptable for a specific piping system.
Assumptions and limitations
Assumptions and limitations
- The pipe is represented by a circular internal cross-section, using the actual inside diameter.
- The velocity used by the calculator is the cross-sectional average velocity, not the local velocity at the pipe centerline or wall.
- Flow rate, velocity, and diameter are related only through the geometric relation Q = vA. The calculator does not solve the momentum or energy equations for the piping system.
- The diameter calculation requires both volumetric flow rate and target velocity to be greater than zero.
- Flow-rate and velocity modes allow a zero-flow condition, provided the pipe diameter remains greater than zero.
- Mass flow rate assumes the entered density is applicable to the same operating condition as the entered or calculated volumetric flow rate.
- Dynamic-viscosity Reynolds calculations require a positive density and positive dynamic viscosity.
- Kinematic-viscosity Reynolds calculations require a positive kinematic viscosity; density is not required unless mass flow rate is also needed.
- The Reynolds-number regime boundaries are the fixed thresholds implemented by the calculator. Actual transition behavior can be influenced by inlet disturbances, geometry, surface condition, and other system effects.
- The calculator does not account for pipe roughness, friction factor, pipe length, fittings, valves, elevation changes, or local losses.
- It does not calculate pressure drop, required pump head, cavitation margin, water hammer, or other transient hydraulic effects.
- It does not model compressible-flow effects such as pressure-dependent density changes or choking.
- It is not an open-channel or partially full pipe-flow solver and does not substitute hydraulic diameter for non-circular passages.
- The calculated diameter is not rounded to a standard commercial pipe size and does not select wall thickness or pipe schedule.
- Final pipe sizing should also consider the applicable design criteria, operating limits, pressure-loss requirements, fluid properties, materials, and governing engineering standards.