How to calculate Reynolds number in a pipe
Reynolds number compares inertial effects with viscous effects in a flow. It has no unit and helps describe the flow regime; it is not itself a pressure loss.
What the formula is saying
For a full circular pipe, use Re = ρvD/μ. Multiply density, average velocity and internal diameter, then divide by dynamic viscosity μ. If given kinematic viscosity ν instead, the equivalent form is vD/ν.
Read the symbols in plain language
- ρ
- Densitykg/m³
- v
- Velocitym/s
- D
- Diameterm
- μ
- Dynamic viscosityPa·s
Sort out the units first
D in m and μ in Pa·s. 50 mm = 0.05 m. The example specifies μ = 0.001 Pa·s; actual fluid properties depend on the problem conditions.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
- ρ · Density
- 1000 kg/m³
- v · Velocity
- 1 m/s
- D · Diameter
- 0.05 m
- μ · Dynamic viscosity
- 0.001 Pa·s
Combine density, speed and diameter
Use internal diameter, not radius.
(1000) × (1) × (0.05) = 50 Pa·sCompare with dynamic viscosity
Dividing cancels the remaining units, so Re is dimensionless.
(50) ÷ (0.001) = 50000
Does this worked answer make sense?
The worked example gives 50,000. The number scales directly with velocity at fixed properties and diameter. Halving the speed must halve Reynolds number.
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Use these new values. Work it out first, then check your answer.
- ρ · Density
- 1000 kg/m³
- v · Velocity
- 0.02 m/s
- D · Diameter
- 0.05 m
- μ · Dynamic viscosity
- 0.001 Pa·s
Find: Reynolds number in a pipe
A hint, not the answer
For a full circular pipe, use Re = ρvD/μ. Multiply density, average velocity and internal diameter, then divide by dynamic viscosity μ. If given kinematic viscosity ν instead, the equivalent form is vD/ν.
D in m and μ in Pa·s. 50 mm = 0.05 m. The example specifies μ = 0.001 Pa·s; actual fluid properties depend on the problem conditions.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Combine density, speed and diameter
Use internal diameter, not radius.
(1000) × (0.02) × (0.05) = 1 Pa·sCompare with dynamic viscosity
Dividing cancels the remaining units, so Re is dimensionless.
(1) ÷ (0.001) = 1000
Avoid the common trap
Using kinematic viscosity in the μ field counts density twice. Do not divide the diameter by two: the formula already uses D.
When this method applies — and when it does not
Average flow in a full circular pipe. Transition thresholds are approximate and depend on disturbances; consult the applicable flow model before selecting friction laws.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Lesson updated: · Worked examples checked against the implemented formula; not an independent engineering certification.