Continuum mechanics  


A Newtonian fluid (named after Isaac Newton) is a fluid whose stress versus strain rate curve is linear and passes through the origin. The constant of proportionality is known as the viscosity.
A simple equation to describe Newtonian fluid behaviour is
where
In common terms, this means the fluid continues to flow, regardless of the forces acting on it. For example, water is Newtonian, because it continues to exemplify fluid properties no matter how fast it is stirred or mixed. Contrast this with a nonNewtonian fluid, in which stirring can leave a "hole" behind (that gradually fills up over time  this behavior is seen in materials such as pudding, starch in water (oobleck), or, to a less rigorous extent, sand), or cause the fluid to become thinner, the drop in viscosity causing it to flow more (this is seen in nondrip paints, which brush on easily but become more viscous when on walls).
For a Newtonian fluid, the viscosity, by definition, depends only on temperature and pressure (and also the chemical composition of the fluid if the fluid is not a pure substance), not on the forces acting upon it.
If the fluid is incompressible and viscosity is constant across the fluid, the equation governing the shear stress, in the Cartesian coordinate system, is
with comoving stress tensor (also written as )
where, by the convention of tensor notation,
If a fluid does not obey this relation, it is termed a nonNewtonian fluid, of which there are several types, including polymer solutions, molten polymers, many solid suspensions and most highly viscous fluids.

