Shear rate

Shear rate is the rate at which a shear is applied.

imple Shear

Shear rate is defined using the following equation:

$dot\; gamma\; =\; frac\; \{\; u\}\; \{h\}$

Where:

*$gamma$ = The shear rate, measured in reciprocal seconds
*$u$ = The velocity, measured in metres per second
*$h$ = The distance between the two parallel faces that are experiencing the shear.

Or,$dot\; gamma\_\{ij\}=frac\; \{partial\; v\_i\}\; \{partial\; x\_j\}\; +\; frac\{partial\; v\_j\}\; \{partial\; x\_i\}$

For the simple shear case, it is just a gradient of velocity in a flowing material. The SI unit of measurement for shear rate is sec^-1, expressed as "reciprocal seconds" or "inverse seconds."Cite web
title = Brookfield Engineering - Glossary section on Viscosity Terms
accessdate = 2007-06-10
url = http://www.brookfieldengineering.com/education/viscosity_glossary.asp]

For a Newtonian fluid wall Shear stress ($au\_\{w\}$) can be related to shear rate by$au\_\{w\}\; =\; \{dot\; gamma\_\{x\}\; mu\}$, where $mu$ is the Viscosity of the fluid. For Non-Newtonian fluids, there are different constitutive laws depending on the fluid, which relates the stress tensor to the shear rate tensor.

References