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The Stokeslet is the Green's function of the Stokes-Flow-Equations. The conservative term is equal to the dipole gradient field. The formula of vorticity is analogous to the Biot–Savart law in electromagnetism. Alternatively, in a more compact way, one can formulate the velocity field as follows:
The SI unit of kinematic viscosity is square meter per second (m 2 /s), whereas the CGS unit for kinematic viscosity is the stokes ... For this formula to be valid, ...
The incompressible Navier–Stokes equations with uniform density and viscosity and conservative external field is the fundamental equation of hydraulics. The domain for these equations is commonly a 3 or less dimensional Euclidean space , for which an orthogonal coordinate reference frame is usually set to explicit the system of scalar partial ...
In order to apply this to the Navier–Stokes equations, three assumptions were made by Stokes: The stress tensor is a linear function of the strain rate tensor or equivalently the velocity gradient. The fluid is isotropic. For a fluid at rest, ∇ ⋅ τ must be zero (so that hydrostatic pressure results).
This coefficient of proportionality is called volume viscosity. Common symbols for volume viscosity are and . Volume viscosity appears in the classic Navier-Stokes equation if it is written for compressible fluid, as described in most books on general hydrodynamics [6] [1] and acoustics. [9] [10]
Stokes–Einstein–Sutherland equation, for diffusion of spherical particles through a liquid with low Reynolds number: = Here q is the electrical charge of a particle; μ q is the electrical mobility of the charged particle; η is the dynamic viscosity;
Where the viscosity is naturally high, such as polymer solutions and polymer melts, flow is normally laminar. The Reynolds number is very small and Stokes' law can be used to measure the viscosity of the fluid. Spheres are allowed to fall through the fluid and they reach the terminal velocity quickly, from which the viscosity can be determined ...
Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion, [1] is a type of fluid flow where advective inertial forces are small compared with viscous forces. [2] The Reynolds number is low, i.e. R e ≪ 1 {\displaystyle \mathrm {Re} \ll 1} .