## shear viscosity

https://doi.org/10.1351/goldbook.S05642
For a @[email protected], the shear @[email protected] is often termed simply @[email protected] since in most situations it is the only one considered. It relates the shear components of stress and those of rate of @[email protected] at a point in the fluid by: $\sigma _{xy}=\sigma _{yx}=\eta \ (\frac{\partial \nu_{x}}{\partial y}+\frac{\partial \nu_{y}}{\partial x})=2\ \eta \ \overset{\text{.}}{\gamma }_{yx}$ where $$\overset{\text{.}}{\gamma }_{yx}$$, the shear component of rate of @[email protected] is defined as follows: $\overset{\text{.}}{\gamma }_{yx}=\frac{1}{2}\ (\frac{\partial \nu_{x}}{\partial y}+\frac{\partial \nu_{y}}{\partial x})$ Corresponding relations hold for $$\sigma _{xz}$$ and $$\sigma _{yz}$$; $$\sigma _{xy}$$ is the component of stress acting in the $$y$$-direction on a plate normal to the $$x$$-axis; $$\nu_{x}$$, $$\nu_{y}$$, $$\nu_{z}$$ are the components of velocity.