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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: ...
The logarithmic law of the wall is a self similar solution for the mean velocity parallel to the wall, and is valid for flows at high Reynolds numbers — in an overlap region with approximately constant shear stress and far enough from the wall for (direct) viscous effects to be negligible: [3]
A typical timber shear wall consists of braced panels in the wall line, constructed using structural plywood sheathing, specific nailing at the edges, and supporting framing. A shear wall is an element of a structurally engineered system that is designed to resist in- plane lateral forces, typically wind and seismic loads.
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.
Shear velocity is linked to the Darcy friction factor by equating wall shear stress, giving: = where f D is the friction factor. [1] Shear velocity can also be defined in terms of the local velocity and shear stress fields (as opposed to whole-channel values, as given above).
is the wall shear stress, is the suction/injection velocity at the wall, is the displacement thickness and is the momentum thickness. Kármán–Pohlhausen Approximation is derived from this equation.
It is defined as the ratio between the local shear stress and the local flow kinetic energy density: [1] [2] = where f is the local Fanning friction factor (dimensionless); τ is the local shear stress (units of pascals (Pa) = kg/m 2, or pounds per square foot (psf) = lbm/ft 2);
Assuming that the direction of the forces is known, the stress across M can be expressed simply by the single number , calculated simply with the magnitude of those forces, F and the cross sectional area, A. = Unlike normal stress, this simple shear stress is directed parallel to the cross-section considered, rather than perpendicular to it. [13]