In fluid dynamics, a Carreau fluid is a type of generalized Newtonian fluid (named after Pierre Carreau) where viscosity, ${\displaystyle \mu _{\operatorname {eff} }}$, depends upon the shear rate, ${\displaystyle {\dot {\gamma }}}$, by the following equation:

Where: ${\displaystyle \mu _{0}}$, ${\displaystyle \mu _{\operatorname {\inf } }}$, ${\displaystyle \lambda }$ and ${\displaystyle n}$ are material coefficients: ${\displaystyle \mu _{0}}$ is the viscosity at zero shear rate (Pa.s), ${\displaystyle \mu _{\operatorname {\inf } }}$ is the viscosity at infinite shear rate (Pa.s), ${\displaystyle \lambda }$ is the characteristic time (s) and ${\displaystyle n}$ power index.

The dynamics of fluid motions is an important area of physics, with many important and commercially significant applications.

Computers are often used to calculate the motions of fluids, especially when the applications are of a safety critical nature.