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In fluid dynamics, Stokes' law gives the frictional force – also called drag force – exerted on spherical objects moving at very small Reynolds numbers in a viscous fluid. [1] It was derived by George Gabriel Stokes in 1851 by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations .
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 ...
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.
This effect can be quantified through the Stokes's law of sound attenuation. Sound attenuation may also be a result of heat conductivity in the media as has been shown by G. Kirchhoff in 1868. [1] [2] The Stokes-Kirchhoff attenuation formula takes into account both viscosity and thermal conductivity effects.
Stokes derived the drag around a sphere at very low Reynolds numbers, the result of which is called Stokes' law. [30] In the limit of high Reynolds numbers, the Navier–Stokes equations approach the inviscid Euler equations, of which the potential-flow solutions considered by d'Alembert are solutions. However, all experiments at high Reynolds ...
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).
Based on air resistance, for example, the terminal speed of a skydiver in a belly-to-earth (i.e., face down) free fall position is about 55 m/s (180 ft/s). [3] This speed is the asymptotic limiting value of the speed, and the forces acting on the body balance each other more and more closely as the terminal speed is approached.
The Stokes number (Stk), named after George Gabriel Stokes, is a dimensionless number characterising the behavior of particles suspended in a fluid flow. The Stokes number is defined as the ratio of the characteristic time of a particle (or droplet ) to a characteristic time of the flow or of an obstacle, or