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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]
Stokes's law is an expression for the frictional force exerted on spherical objects with very small Reynolds numbers, named for George Gabriel Stokes (1819–1903). 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.
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 ...
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.
After an example, he concludes (with used to represent volume viscosity): Hence, if the relaxation time of these processes is long, a considerable dissipation of energy occurs when the fluid is compressed or expanded, and, since this dissipation must be determined by the second viscosity, we reach the conclusion that ζ {\displaystyle \zeta ...
The hydrometer method of determining soil texture is a quantitative measurement providing estimates of the percent sand, clay, and silt in the soil based on Stokes' law, which expresses the relationship between the settling velocity and particle size. [11] According to this law the particles settle down because of the weight and gravity action.
Boyle's law, which stipulates the reciprocal relation between the pressure and the volume of a gas, was first noted by Richard Towneley and Henry Power. In France, the law is known as Mariotte's law, after Edme Mariotte, who published his results later than Boyle, but crucially added that the relation holds only when temperature is kept constant.
The drag force acting on the drop can then be worked out using Stokes' law: F u = 6 π r η v 1 , {\displaystyle F_{u}=6\pi r\eta v_{1},\,} where v 1 is the terminal velocity (i.e. velocity in the absence of an electric field) of the falling drop, η is the viscosity of the air, and r is the radius of the drop.