##  [Viscosity](/viscosity-0) 

 Definition

Measure of a fluid's resistance to shear or flow; commonly given as dynamic viscosity (η) with units pascal-seconds (Pa·s) or kinematic viscosity (ν) as m²·s⁻¹ when divided by density.

 

 

 

 

 

 





## Principle

Principle

Dynamic viscosity characterizes internal momentum transport: shear stress τ is proportional to velocity gradient (τ = η du/dy) in Newtonian fluids; non-Newtonian fluids deviate with rate-dependent effective viscosity.

 

 

 

 

 





## Demonstration

Demonstration

Water at 20 °C has dynamic viscosity ~1.002 mPa·s; measuring the torque on a rotating spindle immersed in oil yields its viscosity, and the flow rate through a capillary relates to viscosity via the Hagen–Poiseuille relation for laminar flow.

 

 

 

 

## Misapplication

Misapplication

Reporting a single viscosity value for a non-Newtonian fluid without stating shear rate, or comparing viscosities measured at different temperatures or shear conditions as if directly comparable.

 

 

 

 

 





## Consequence

Consequence

Appropriate use of viscosity values enables prediction of flow profiles, pressure drops, mixing behavior, and heat/mass transfer rates in engineering and process design when state conditions and rheology are specified.

 

 

 

 

## Reversal

Reversal

Ideal inviscid flow assumes zero viscosity and no internal shear dissipation; while a useful approximation in some high-Reynolds-number analyses, it omits viscous boundary layers and energy dissipation critical to real flows.

 

 

 

 

 





## Boundary

Boundary

Applies to continuum fluid descriptions at scales where bulk rheology holds; excludes molecular-scale slip effects, rarefied gas regimes where mean free path is comparable to system dimensions, and unspecified shear-/temperature-dependence for complex fluids.

 

 

 

 

 





## Semantic Tension

Semantic Tension

Tension between a single-number viscosity for Newtonian approximation and the full rheological description for complex fluids (shear-thinning, viscoelasticity) creates ambiguity unless measurement conditions are reported.

 

 

 

 

 





## Synthesis

Synthesis

Viscosity quantifies a fluid's internal resistance to deformation under shear; as dynamic viscosity it links shear stress to velocity gradient in Newtonian fluids and, when properly characterized (temperature, shear rate), predicts flow and transport behavior.