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# Generalized Newtonian fluid

A generalized Newtonian fluid is an idealized fluid for which the shear stress, τ, is a function of shear rate at the particular time, but not dependent upon the history of deformation.

$\tau = F\left( \frac {\partial u} {\partial y} \right)$

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where: ∂u/∂y is the shear rate or the velocity gradient perpendicular to the plane of shear (SI unit s−1).

The quantity

$\mu_{\operatorname{eff}} = { {F \left( \frac {\partial u} {\partial y} \right)}\bigg/{\frac {\partial u} {\partial y}}}$

represents an apparent or effective viscosity as a function of the shear rate (SI unit Pa⋅s).

The most commonly used types of generalized Newtonian fluids are: