Viscosity (Dynamic & Kinematic) — Definition & Formula Links

A fluid’s internal resistance to flow, in two forms: dynamic μ (Pa·s) and kinematic ν = μ/ρ — the property pair behind Reynolds number and friction.


Updated August 20, 2026

Viscosity comes in a pair that engineering keeps deliberately separate: dynamic viscosity μ, and kinematic viscosity ν = μ/ρ — the form Reynolds number actually wants, since Re = ρ·v·D/μ is the same thing as v·D/ν. Good property tables compute the kinematic column from the μ and ρ columns beside it rather than transcribing it, which is why a consistent table agrees with published ν values to the last digit.

For water, temperature is almost the whole story: between freezing and boiling its viscosity drops more than sixfold, so hot water flows through a pipe with a fraction of the friction of cold. The habit that follows is to evaluate at the actual operating temperature — a chilled-water loop at 7 °C is 40% more viscous than a condenser loop at 40 °C, which moves the Reynolds number and the pressure drop by the same factor. The trusted numbers trace to the Cengel property tables (Sengers & Watson correlation), cross-checked against the NIST WebBook.

Gases run the other way: unlike liquids, gas viscosity grows with temperature — heat air from 0 to 300 °C and μ rises about 70% while density halves, so the kinematic viscosity more than triples. Since ν is what sets Reynolds number, reading it at the film temperature instead of assuming a cold-air value routinely shifts an external-flow problem between laminar and turbulent regimes.

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Sources & Further Reading

  • Cengel & Cimbala, Fluid Mechanics, Table A-3 / Cengel & Ghajar, Heat and Mass Transfer, Tables A-9 and A-15 — saturated water and dry-air properties (viscosity basis: Sengers & Watson 1986)
  • NIST Chemistry WebBook (IAPWS-95) — density, viscosity, and saturation-pressure cross-check for the water properties chart