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The formula to calculate average shear stress τ or force per unit area is: [1] =, 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.
The mean wall shear stress ... Pipe pressure drop calculator for two phase flows. Archived 2019-07-13 at the Wayback Machine; Open source pipe pressure drop calculator.
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);
In the hydrodynamic entrance region, the wall shear stress, , is highest at the pipe inlet, where the boundary layer thickness is the smallest. Shear stress decreases along the flow direction. [ 6 ] That is why the pressure drop is highest in the entrance region of a pipe, which increases the average friction factor for the whole pipe.
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 notable aspect of the flow is that shear stress is constant throughout the domain. In particular, the first derivative of the velocity, /, is constant. According to Newton's Law of Viscosity (Newtonian fluid), the shear stress is the product of this expression and the (constant) fluid viscosity.
For the thin-walled assumption to be valid, the vessel must have a wall thickness of no more than about one-tenth (often cited as Diameter / t > 20) of its radius. [4] This allows for treating the wall as a surface, and subsequently using the Young–Laplace equation for estimating the hoop stress created by an internal pressure on a thin-walled cylindrical pressure vessel:
Rankine's theory (maximum-normal stress theory), developed in 1857 by William John Macquorn Rankine, [1] is a stress field solution that predicts active and passive earth pressure. It assumes that the soil is cohesionless, the wall is frictionless, the soil-wall interface is vertical, the failure surface on which the soil moves is planar , and ...