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# Shear rate

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

imple Shear

Shear rate is defined using the following equation:

$dot gamma = frac \left\{ u\right\} \left\{h\right\}$

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,$dot gamma_\left\{ij\right\}=frac \left\{partial v_i\right\} \left\{partial x_j\right\} + frac\left\{partial v_j\right\} \left\{partial x_i\right\}$

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 ($au_\left\{w\right\}$) can be related to shear rate by$au_\left\{w\right\} = \left\{dot gamma_\left\{x\right\} mu\right\}$, 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

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