# NEWTONIAN FLUIDS

A Newtonian fluid is one where there is a linear relationship between

*stress*and*strain-rate*. The ratio of stress to strain-rate is the**Viscosity**of the fluid. A fluid where there is no linear relationship between stress and strain-rate is called a**Non-Newtonian fluid**.
For a Newtonian fluid the stress (strictly, the

*deviatoric stress*) τ is given by:
(1)

where e denotes the strain-rate given in terms of the velocity u by:

(2)

and η denotes the viscosity of the fluid, which is independent of e, though it may depend on temperature T and perhaps on pressure p.

Because e is a

*symmetrical tensor*, it follows from (1) that t too is a symmetrical tensor:
(3)

Angular momentum conservation then implies that Newtonian fluids are

*nonpolar*and hence, that the angular momentum is just the moment of the linear momentum.