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The pound and pound-force are equivalent; the two systems differ only in how force and mass are defined. In the BG system the pound is a basic unit from which the unit of mass (the slug ) is defined by Newton's Second Law , whereas in the EE system the units of force and mass (the pound-force and pound-mass respectively) are defined ...
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
The following formula describes the viscous stress tensor for the special case of Stokes flow. It is needed in the calculation of the force acting on the particle. In Cartesian coordinates the vector-gradient is identical to the Jacobian matrix. The matrix I represents the identity-matrix.
magnetohydrodynamics (ratio of electromagnetic to inertial forces) Taylor number: Ta = fluid dynamics (rotating fluid flows; inertial forces due to rotation of a fluid versus viscous forces) Ursell number: U =
The Reynolds and Womersley Numbers are also used to calculate the thicknesses of the boundary layers that can form from the fluid flow’s viscous effects. The Reynolds number is used to calculate the convective inertial boundary layer thickness that can form, and the Womersley number is used to calculate the transient inertial boundary thickness that can form.
Dynamic viscosity is a material property which describes the resistance of a fluid to shearing flows. It corresponds roughly to the intuitive notion of a fluid's 'thickness'.
Scaling of equation can be done, in a flow where inertia term is smaller than the viscous term i.e. when Re → 0 then inertia terms can be neglected, leaving the equation of a creeping motion. R e ∂ u ∗ ∂ t ∗ = − ∇ ∗ p ∗ + ∇ ∗ 2 u ∗ . {\displaystyle Re{\frac {\partial \mathbf {u^{*}} }{\partial t^{*}}}=-\nabla ^{*}p ...
It has dimensions (mass / (length × time)), and the corresponding SI unit is the pascal-second (Pa·s). Like other material properties (e.g. density, shear viscosity, and thermal conductivity) the value of volume viscosity is specific to each fluid and depends additionally on the fluid state, particularly its temperature and pressure.