Stokes' law

In fluid dynamics, Stokes' law is an empirical law for the frictional force – also called drag force – exerted on spherical objects with very small Reynolds numbers in a viscous fluid. It was derived by George Gabriel Stokes in 1851 by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations. The force of viscosity on a small sphere moving through a viscous fluid is given by: where (in SI units): Fd is the frictional force – known as Stokes' drag – acting on the interface between the fluid and the particle (newtons, kg m s−2); μ (some authors use the symbol η) is the dynamic viscosity (Pascal-seconds, kg m−1 s−1); R is the radius of the spherical object (meters); v is the flow velocity relative to the object (meters per second). Stokes' law makes the following assumptions for the behavior of a particle in a fluid: Laminar flow Spherical particles Homogeneous (uniform in composition) material Smooth surfaces Particles do not interfere with each other. For molecules Stokes' law is used to define their Stokes radius and diameter. The CGS unit of kinematic viscosity was named "stokes" after his work. Stokes' law is the basis of the falling-sphere viscometer, in which the fluid is stationary in a vertical glass tube. A sphere of known size and density is allowed to descend through the liquid. If correctly selected, it reaches terminal velocity, which can be measured by the time it takes to pass two marks on the tube. Electronic sensing can be used for opaque fluids. Knowing the terminal velocity, the size and density of the sphere, and the density of the liquid, Stokes' law can be used to calculate the viscosity of the fluid. A series of steel ball bearings of different diameters are normally used in the classic experiment to improve the accuracy of the calculation. The school experiment uses glycerine or golden syrup as the fluid, and the technique is used industrially to check the viscosity of fluids used in processes.