Shear_rate

Shear rate

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

Simple Shear

Shear rate is defined using the following equation:

$\dot \gamma = \frac {\nu} {h}$

Where:

$γ$ = The shear rate, measured in reciprocal seconds
$ν$ = 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."^[1]

For a Newtonian fluid wall Shear stress ( $τ w$ ) can be related to shear rate by $\tau_{w} = {\dot \gamma_{x} \mu}$ , where $μ$ 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

^ "Brookfield Engineering - Glossary section on Viscosity Terms". Retrieved on 2007-06-10.

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