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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.
Terminal velocity is the maximum speed attainable by an object as it falls through a fluid (air is the most common example). ... is called Stokes' law.
Terminal velocity is achieved when the drag force is equal in magnitude but opposite in direction to the force propelling the object. Shown is a sphere in Stokes flow, at very low Reynolds number . Stokes flow (named after George Gabriel Stokes ), also named creeping flow or creeping motion , [ 1 ] is a type of fluid flow where advective ...
This method is mainly used for particles smaller than 1 μm. The smaller or lighter particles rise to the top (overflow) because their terminal sedimentation velocities are lower than the velocity of the rising fluid. The terminal velocity of any particle in any medium can be calculated using Stokes' law if the particle's Reynolds number is ...
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.
Where the viscosity is naturally high, such as polymer solutions and polymer melts, flow is normally laminar. The Reynolds number is very small and Stokes' law can be used to measure the viscosity of the fluid. Spheres are allowed to fall through the fluid and they reach the terminal velocity quickly, from which the viscosity can be determined ...
The azimuthal velocity component u φ does not depend on the stream function. Due to the axisymmetry, all three velocity components ( u ρ , u φ , u z ) only depend on ρ and z and not on the azimuth φ. The volume flux, through the surface bounded by a constant value ψ of the Stokes stream function, is equal to 2π ψ.
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's law can be used to calculate the viscosity of the fluid.