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The importance of Stokes' law is illustrated by the fact that it played a critical role in the research leading to at least three Nobel Prizes. [5] Stokes' law is important for understanding the swimming of microorganisms and sperm; also, the sedimentation of small particles and organisms in water, under the force of gravity. [5]
In acoustics, Stokes's law of sound attenuation is a formula for the attenuation of sound in a Newtonian fluid, such as water or air, due to the fluid's viscosity.It states that the amplitude of a plane wave decreases exponentially with distance traveled, at a rate α given by = where η is the dynamic viscosity coefficient of the fluid, ω is the sound's angular frequency, ρ is the fluid ...
An illustration of Stokes' theorem, with surface Σ, its boundary ∂Σ and the normal vector n.The direction of positive circulation of the bounding contour ∂Σ, and the direction n of positive flux through the surface Σ, are related by a right-hand-rule (i.e., the right hand the fingers circulate along ∂Σ and the thumb is directed along n).
The viscous resistance for a spherical particle is given by Stokes' law: = where η is the viscosity of the medium, r 0 is the radius of the particle and v is the velocity of the particle. Stokes' law applies to small spheres in an infinite amount of fluid at the small Reynolds Number limit.
The expression for the drag force given by equation is called Stokes' law. When the value of C d {\displaystyle C_{d}} is substituted in the equation ( 5 ), we obtain the expression for terminal speed of a spherical object moving under creeping flow conditions: [ 11 ]
Stokes' formula can refer to: Stokes' law for friction force in a viscous fluid. Stokes' law (sound attenuation) law describing attenuation of sound in Newtonian liquids.
The derivation of Stokes' law, which is used to calculate the drag force on small particles, assumes a no-slip condition which is no longer correct at high Knudsen numbers. The Cunningham slip correction factor allows predicting the drag force on a particle moving a fluid with Knudsen number between the continuum regime and free molecular flow.
In vector calculus and differential geometry the generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, [1] is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus.