Wandreibungsstress

Wandreibungsstress, often referred to in English as wall shear stress (WSS), is the tangential force per unit area that a moving fluid exerts on a boundary. For Newtonian fluids, the magnitude of the wall shear stress at the wall is tau_w = mu (du/dy) evaluated at the wall, where mu is the dynamic viscosity and du/dy is the velocity gradient perpendicular to the wall. The concept generalizes to non-Newtonian fluids through the appropriate constitutive relation. Wall shear stress depends on viscosity, flow rate, the geometry of the conduit, and surface roughness, and can vary along the boundary in non-uniform flows.

In engineering, WSS is a key parameter in pipe and channel design; for laminar fully developed flow in a circular pipe, tau_w = 4 μ Q / (π R^3), linking WSS to flow rate Q and pipe radius R. In turbulent or complex flows, WSS is often considered as a time-averaged quantity or evaluated locally. Surface roughness and secondary flows can create spatial variation in tau_w.

In physiology and biology, WSS in arteries and microvessels influences endothelial cell behavior and vascular remodeling. Typical arterial WSS values range on the order of 1–2 pascals; reduced or oscillatory WSS is associated with atherogenesis, while excessively high WSS can indicate stenosis-induced changes in flow. WSS is commonly estimated through computational fluid dynamics (CFD) or measured indirectly via particle image velocimetry (PIV) or Doppler techniques.

Wandreibungsstress is used in various fields and is related to the broader concept of shear stress.