Stokes law, used to determine the settling velocity of a water droplet settling through the continuous oil phase, includes the oil viscosity. The sphere accelerates until it reaches a steady terminal speed. Answer to stokes law can be used to determine the viscosity of a fluid by dropping. Similar use of the equation can be made in the settlement of fine particles in water or other fluids. According to stokes law, droplets in an fdsemulsion will tend to either lift or to settle. As the oil viscosity increases, the settling velocity of a given droplet decreases.
This lesson will explain stokes law and provide applications of it to other. Stokes law is the basis of the fallingsphere viscometer, in which the fluid is stationary in a vertical glass tube. Stokes in 1851, is derived by consideration of the forces acting on a particular particle as it sinks through a liquid column under the influence of gravity. But what many books fail to point out, or mention only cursorily, is that stokes law is of limited validity. A sphere of known size and density is allowed to descend through the liquid. It was done in the 1840s by sir george gabriel stokes. Navierstokes equations in cylindrical coordinates, bhg. I turn to one of my favorite books on fluid dynamics. For a falling ball, f is equal to the gravitational force on the sphere, less any upthrust.
This is a typical situation in flows where the fluid velocities are very slow, the viscosities are very large, or the lengthscales of the flow are very small. Derivation of the stokes drag formula in a remarkable 1851 scientific paper, g. The navier stokes equations are an expression of newtons second law for fluids, stating that mass times the acceleration of. Understanding stokes law with dimensional analysis. Stokes law of fluorescence quick reference a law stating that the wavelength of the emitted fluorescent light. Hookes law, law of elasticity that relates the size of the deformation of an object to the deforming force or load. Stokes law can be used to determine the viscosity of a. Stokes law equations formulas calculator terminal fall settling. Stokes law equations formulas calculator medium viscosity.
Stokes s law, mathematical equation that expresses the settling velocities of small spherical particles in a fluid medium. Stokes lawrence is a law firm assisting businesses, families and individuals with business transactions and disputes, to estate and succession planning. Navierstokes equation for dummies kaushiks engineering. Stokes which relates the velocity of fall v of a spherical body under gravity g through a fluid medium to the radius r of the body, to the viscosity.
The law was discovered by sir george gabriel stokes. Stokess law describes drag force on a sphere in creeping. Fundamentals of thermalfluid sciences with student resource dvd 4th. Stokes flow named after george gabriel stokes, also named creeping flow or creeping motion, is a type of fluid flow where advective inertial forces are small compared with viscous forces. The law, first set forth by the british scientist sir george g. Fluid dynamics and the navier stokes equations the navier stokes equations, developed by claudelouis navier and george gabriel stokes in 1822, are equations which can be used to determine the velocity vector eld that applies to a uid, given some initial conditions. Stokes law appears in chapter 4 of the 4th edition of intermediate physics for. Stokes first derived the basic formula for the drag of a sphere of radius ra moving with speed uo through a viscous fluid of density. Stokes law, 9786518202, please note that the content of this book primarily consists of articles available from wikipedia or other free. Stokes law equations formulas calculator particle diameter.
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