Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
Concept
Shear rate
Summary
In physics, shear rate is the rate at which a progressive shearing deformation is applied to some material.
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:
is the shear rate, measured in reciprocal seconds;
v is the velocity of the moving plate, measured in meters per second;
h is the distance between the two parallel plates, measured in meters.
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". However, when modelling fluids in 3D, it is common to consider a scalar value for the shear rate by calculating the second invariant of the strain-rate tensor
The shear rate at the inner wall of a Newtonian fluid flowing within a pipe is
where:
is the shear rate, measured in reciprocal seconds;
v is the linear fluid velocity;
d is the inside diameter of the pipe.
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 = 2r:
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 (τ_w) can be related to shear rate by 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.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.