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stokes law
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STOKES LAW DERIVATION • a law stating that in fluorescence the wavelength of the emitted radiation is longer than that of the radiation causing it. This is not true in all cases. • 2. • an expression describing the resisting force on a particle moving through a viscous fluid and showing that a maximum velocity is reached in such cases, e.g. for an object falling under gravity through a fluid. Stoke's Law in interference • The force of viscosity on a small sphere moving through a viscous fluid is given by:[2] • {\\displaystyle F_{d}=6\\pi \\,\\eta \\,R\\,v\\,} {\\displaystyle F_{d}=6\\pi \\,\\eta \\,R\\,v\\,} • where: • Fd is the frictional force – known as Stokes' drag – acting on the interface between the fluid and the particle • η is the dynamic viscosity (Some authors use the symbol μ) • R is the radius of the spherical object • v is the flow velocity relative to the object. • In SI units, Fd is given in Newtons, η in Pa·s, R in meters, and v in m/s. • 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. • Note that for molecules Stokes' law is used to define their Stokes radius. • The CGS unit of kinematic viscosity was named stokes after his work. • Applications : • 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. Several school experiments often involve varying the temperature and/or concentration of the substances used in order to demonstrate the effects this has on the viscosity. Industrial methods include many different oils, and polymer liquids such as solutions. • The importance of Stokes' law is illustrated by the fact that it played a critical role in the research leading to at least three Nobel Prizes.[3] • Stokes' law is important for understanding the swimming of microorganisms and sperm; also, the sedimentation of small particles and organisms in water, under the force of gravity.[4] • In air, the same theory can be used to explain why small water droplets (or ice crystals) can remain suspended in air (as clouds) until they grow to a critical size and start falling as rain (or snow and hail).[5] Similar use of the equation can be made in the settlement of fine particles in water or other fluids. • Terminal velocity of sphere falling in a fluid[edit] • Creeping flow past a falling sphere in a fluid (e.g., a droplet of fog falling through the air): streamlines, drag force Fd and force by gravity Fg. • At terminal (or settling) velocity, the excess force Fg due to the difference between the weight and buoyancy of the sphere (both caused by gravity)i • • with ρp and ρf the mass densities of the sphere and fluid, respectively, and g the gravitational acceleration. Requiring the force balance Fd = Fg and solving for the velocity v gives the terminal velocity vs. Note that since buoyant force increases as R3 and Stokes' drag increases as R, the terminal velocity increases as R2 and thus varies greatly with particle size as shown below. If the particle is falling in the viscous fluid under its own weight, then a terminal velocity, or settling velocity, is reached when this frictional force combined with the buoyant force exactly balances the gravitational force. This velocity v (m/s) is given by:[6] • {\\displaystyle v={\\frac {2}{9}}{\\frac {\\left(\ ho _{p}-\ ho _{f}\ ight)}{\\mu }}g\\,R^{2}} {\\displaystyle v={\\frac {2}{9}}{\\frac {\\left(\ ho _{p}-\ ho _{f}\ ight)}{\\mu }}g\\,R^{2}} • (vertically downwards if ρp ρf, upwards if ρp ρf ), where: • g is the gravitational acceleration (m/s2) • R is the radius of the spherical particle. • ρp is the mass density of the particles (kg/m3) • ρf is the mass density of the fluid (kg/m3) • μ is the dynamic viscosity (kg/m*s). • know more about strokes law at : • https://en.wikipedia.org/wiki/Stokes%... • related tags : • application of Stokes law,derivation of Stokes law, Stokes law explanation, Stokes law animation, Stokes law • • • HELUM -NEON LASER CONSTRUCTION AND WO... • • Ruby laser working and construction
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