Newtonian fluid

A fluid whose shear stress is proportional to the rate of shear deformation, with viscosity independent of shear rate at fixed temperature and pressure.

Newtonian constitutive equation: A linear relation between a Newtonian fluid’s stress tensor and its rate-of-deformation tensor. It states mathematically how this fluid’s viscosity converts deformation rates into stress.
Shear stress: The tangential force per unit area acting across a surface within a material. It is the stress component that scales with shear rate in the defining law.
Non-Newtonian fluid: A fluid whose stress response is not a linear, shear-rate-independent-viscosity relation under specified conditions. It is the broad counterpart for materials whose apparent viscosity changes with deformation rate or history.
Laminar flow in a pipe: An orderly pipe-flow regime in which fluid moves in smooth layers with limited cross-stream mixing. For a Newtonian fluid in a circular pipe, this regime yields the Hagen–Poiseuille relation.
Water: The chemical compound H₂O, a liquid across a broad range of ordinary temperatures and pressures. Liquid water is approximately Newtonian under many everyday flow conditions.
Dynamic viscosity: A measure of a fluid’s resistance to shear flow, relating shear stress to velocity gradient in simple flow. Its constant value sets the proportionality between shear rate and shear stress.
Shear rate: The spatial rate of change of tangential velocity across a flowing layer. It is the deformation rate to which a Newtonian fluid’s shear stress is proportional.
Shear-thinning fluid: A non-Newtonian fluid whose apparent viscosity decreases as shear rate increases. Its falling apparent viscosity directly violates Newtonian shear-rate independence.
Hagen–Poiseuille equation: A formula relating pressure drop to volumetric flow rate for steady laminar flow of a Newtonian fluid in a circular pipe. It turns Newtonian viscosity into a direct prediction of pipe-flow resistance.
Air: The mixture of gases forming Earth's atmosphere, composed mainly of nitrogen and oxygen. Air is commonly modeled as a Newtonian fluid in ordinary aerodynamic calculations.

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