Newtonian Behavior

Abstract

The most basic difference between solids and fluids is that solids can sustain shear stresses but fluids cannot. If shear stresses are imposed on a body of fluid at rest, the fluid changes its configuration by flow until the shear stresses are zero at every point and it is again in a state of rest. In this condition the stress tensor at every point is

$$ \left[ {\begin{array}{*{20}{c}} {\sigma 11} & 0 & 0 \\ 0 & {\sigma 22} & 0 \\ 0 & 0 & {\sigma 33} \\ \end{array} } \right] $$

with σ₁₁ = σ₂₂ = σ₃₃ = p, where p is the pressure.