Shear rate

Shear rate is the rate at which a progressive shearing deformation is applied to some material.
Simple shear.
The shear rate for a fluid flowing between two parallel plates, one moving at a constant speed and the other one stationary (Couette flow), is defined by
where: 
Or:
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 s−1, expressed as "reciprocal seconds" or "inverse seconds".
The shear rate at the inner wall of a Newtonian fluid flowing within a pipe is
where:
The linear fluid velocity "v" is related to the volumetric flow rate "Q" by
where "A" is the cross-sectional area of the pipe, which for an inside pipe radius of "r" is given by
thus producing
Substituting the above into the earlier equation for the shear rate of a Newtonian fluid flowing within a pipe, and noting (in the denominator) that "d" = 2"r":
which simplifies to the following equivalent form for wall shear rate in terms of volumetric flow rate "Q" and inner pipe radius "r":
For a Newtonian fluid wall, shear stress (w) can be related to shear rate by w = "xμ", where "μ" is the dynamic 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.