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For an incompressible and isotropic Newtonian fluid in laminar flow only in the direction x (i.e. where viscosity is isotropic in the fluid), the shear stress is related to the strain rate by the simple constitutive equation = where is the shear stress ("skin drag") in the fluid,
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.
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]
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 flat plate exerts an equal amount of force on the fluid. (Newton's third law) Experiments on the fluid flow parallel to a flat plate reveal that the force, known as shear stress can be expressed mathematically as = / Note this is valid only for one dimensional fluid flow in rectangular coordinates.
Strength depends upon material properties. The strength of a material depends on its capacity to withstand axial stress, shear stress, bending, and torsion.The strength of a material is measured in force per unit area (newtons per square millimetre or N/mm², or the equivalent megapascals or MPa in the SI system and often pounds per square inch psi in the United States Customary Units system).
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, and can even be time-dependent.
A generalized Newtonian fluid is an idealized fluid for which the shear stress is a function of shear rate at the particular time, but not dependent upon the history of deformation. Although this type of fluid is non-Newtonian (i.e. non-linear) in nature, its constitutive equation is a generalised form of the Newtonian fluid .