Shear stress (often denoted by τ, Greek: tau)

9/22/2025

Shear stress (often denoted by τ, Greek: tau) is the component of stress coplanar with a material cross section.

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General shear stress

The formula to calculate average shear stress τ or force per unit area is:[1]τ=FA,{\displaystyle \tau ={F \over A},}where F is the force applied and A is the cross-sectional area.

The area involved corresponds to the material face parallel to the applied force vector, i.e., with surface normal vector perpendicular to the force.

Other forms

Wall shear stress

Wall shear stress expresses the retarding force (per unit area) from a wall in the layers of a fluid flowing next to the wall. It is defined as:τw:=μ∂u∂y|y=0,{\displaystyle \tau _{w}:=\mu \left.{\frac {\partial u}{\partial y}}\right|_{y=0},}where μ is the dynamic viscosity, u is the flow velocity, and y is the distance from the wall.

It is used, for example, in the description of arterial blood flow, where there is evidence that it affects the atherogenic process.[2]

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