Re=ρVD/μ compares inertial to viscous forces.
Re=ρVL/μ=VL/ν compares inertial and viscous forces. For pipes use diameter D and critical Re≈2300. Over a flat plate transition occurs near 5×10⁵. Re guides regime, friction and similarity.
Water at 1 m/s in a 50 mm pipe has Re≈50 000 (turbulent).
The Reynolds number determines flow regime and scaling, so it is the single most useful dimensionless number in fluid mechanics.
Re=ρVD/μ compares inertial to viscous forces.
The Reynolds number determines flow regime and scaling, so it is the single most useful dimensionless number in fluid mechanics.
About 2300 for smooth circular pipes, although the exact value depends on disturbances and roughness.
The diameter is the characteristic length of the pipe, so the number reflects the balance of inertia to viscous forces in that geometry.
Typical applications include deciding whether a pipe flow is laminar or turbulent before choosing a friction model, scaling a wind tunnel test to a full-size aircraft and estimating the regime of blood flow in an artery.
Study "Laminar and turbulent flow" first (topic 56 of 105 in Thermodynamics & Fluids). It covers the groundwork this topic builds on.
Dimensionless. Low Re: creeping flow. High Re: turbulent.
Water at 1 m/s in a 50 mm pipe has Re≈50 000 (turbulent).
The next topic is "Pipe flow", which builds directly on this one.
It is classed as Intermediate in Thermodynamics & Fluids (topic 57 of 105). It is an intermediate topic. Work through the beginner topics in Thermodynamics & Fluids first.
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