Stokes lawrence is a law firm assisting businesses, families and individuals with business transactions and disputes, to estate and succession planning. 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. I turn to one of my favorite books on fluid dynamics. 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. 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. Navierstokes equations in cylindrical coordinates, bhg. Stokes law, 9786518202, please note that the content of this book primarily consists of articles available from wikipedia or other free.
Answer to stokes law can be used to determine the viscosity of a fluid by dropping. This lesson will explain stokes law and provide applications of it to other. The law was discovered by sir george gabriel stokes. 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. Similar use of the equation can be made in the settlement of fine particles in water or other fluids. Stokes law appears in chapter 4 of the 4th edition of intermediate physics for. It was done in the 1840s by sir george gabriel stokes. The drag force is also directly proportional to the speed, not, for example to v2. Stokess law describes drag force on a sphere in creeping. Stokes law is the basis of the fallingsphere viscometer, in which the fluid is stationary in a vertical glass tube. Navierstokes equation for dummies kaushiks engineering. Hookes law, law of elasticity that relates the size of the deformation of an object to the deforming force or load.
Understanding stokes law with dimensional analysis. Stokes law, used to determine the settling velocity of a water droplet settling through the continuous oil phase, includes the oil viscosity. Stokes law equations formulas calculator terminal fall settling. Fundamentals of thermalfluid sciences with student resource dvd 4th. The navier stokes equations are an expression of newtons second law for fluids, stating that mass times the acceleration of. For a falling ball, f is equal to the gravitational force on the sphere, less any upthrust. As the oil viscosity increases, the settling velocity of a given droplet decreases. Stokes law equations formulas calculator particle diameter. Stokes law relates the terminal velocity of a sphere to its radius and the viscosity of the fluid it is moving through. Derivation of the stokes drag formula in a remarkable 1851 scientific paper, g. 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. 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. They arise from the application of newtons second law in combination with a.