shear viscosity

For a Newtonian fluid, the shear viscosity is often termed simply viscosity since in most situations it is the only one considered. It relates the shear components of stress and those of rate of strain at a point in the fluid by:

$σ x y = σ y x = η ( ∂ v x ∂ y + ∂ v y ∂ x ) = 2 η γ . y x$

where $γ . y x$ , the shear component of rate of strain is defined as follows:

$γ . y x = 1 2 ( ∂ v x ∂ y + ∂ v y ∂ x )$

Corresponding relations hold for $σ x z$ and $σ y z$ ; $σ x y$ is the component of stress acting in the $y$ -direction on a plate normal to the $x$ -axis; $v x$ , $v y$ , $v z$ are the components of velocity.