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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.
In these instances, it can be useful to express internal shear stress as shear flow, which is found as the shear stress multiplied by the thickness of the section. An equivalent definition for shear flow is the shear force V per unit length of the perimeter around a thin-walled section. Shear flow has the dimensions of force per unit of length. [1]
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.
Thus the zero-trace part ε s of ε is the familiar viscous shear stress that is associated to progressive shearing deformation. It is the viscous stress that occurs in fluid moving through a tube with uniform cross-section (a Poiseuille flow) or between two parallel moving plates (a Couette flow), and resists those motions.
In a Newtonian fluid, the relation between the shear stress and the shear rate is linear, passing through the origin, the constant of proportionality being the coefficient of viscosity. In a non-Newtonian fluid, the relation between the shear stress and the shear rate is different. The fluid can even exhibit time-dependent viscosity. Therefore ...
Shear velocity, also called friction velocity, is a form by which a shear stress may be re-written in units of velocity.It is useful as a method in fluid mechanics to compare true velocities, such as the velocity of a flow in a stream, to a velocity that relates shear between layers of flow.
A Newtonian fluid is a power-law fluid with a behaviour index of 1, where the shear stress is directly proportional to the shear rate: = These fluids have a constant viscosity, μ, across all shear rates and include many of the most common fluids, such as water, most aqueous solutions, oils, corn syrup, glycerine, air and other gases.
The apparent viscosity of a dilatant fluid is higher when measured at a higher shear rate (η 4 is higher than η 3), while the apparent viscosity of a Bingham plastic is lower (η 2 is lower than η 1). In fluid mechanics, apparent viscosity (sometimes denoted η) [1] is the shear stress applied to a fluid divided by the shear rate: