Finally, the viscosity calculated using stokes law and depending on the. Stokes law relates the terminal velocity of a sphere to its radius and the viscosity of the fluid it is moving through. Lab 2 stokes law stokes law lab 2 1 brief introduction to. Energy of light is dependent on its wavelength, or color. Stokess law finds application in several areas, particularly with regard to the settling of sediment in fresh water and in measurements of the viscosity of fluids. The data collected from the falling ball experiment did not verify stokes law, though it did show that the revised version of stokes law correcting for reynolds number was fairly accurate. Initial acceleration, this shows that the proof stokes law when the body is placed on liquid, then it accelerates initially in downward direction. Stokes law requires a correction to the viscosity when the velocity of the falling droplet is less than 1 mms. Sinking time of plankton medium consider a small microorganism living in the ocean. An experimental setup to verify stokes law using an electronic balance 31 spheres. Is stokes law applicable to body of shapes other than spherical. Viscosity measurement using stokes law of drag acting on a spherical particle. The school experiment uses glycerine or golden syrup as the fluid, and the technique is used industrially to check the viscosity of fluids.
Note that this is pretty much the same result we got by ignoring all of the exact details. Is there some way we could see the drag force must be proportional to the radius, and to the speed, without wading through all of sir georges mathematics. The free fall velocity is given by stokes law, which describes how fast spherical bodies fall. To describe the drag force resulting from gas resistance, f d, the following equation can be used. In order for the electron to absorb the light, however, the light must have enough energy. Force of resistance is evaluated by the stokes law fr 6. Mar 27, 2014 the data collected from the falling ball experiment did not verify stokes law, though it did show that the revised version of stokes law correcting for reynolds number was fairly accurate. In this experiment, stokes law is assumed to be valid, ie b 6 r, where is the viscosity of air and r the radius of the drop. Stokes law presentation free download as powerpoint presentation.
In this experiment we will use stokes law and the concept of terminal velocity to determine the viscosity of glycerin. This equation can be derived from dimensional analysis. Stokes law states that when light hits an electron that is orbiting an atom, the electron can absorb that light and go into an excited state. Mar 09, 20 the effective weight of body acts downward, due to which the body accelerates. Stokes law1 is used to determine an unknown distribution of spherical particle sizes by measuring the time required for the particles to settle a known distance in a fluid of known viscosity and density. Consequently stokes law overestimates the friction force, because the droplet actually moves for appreciable times through a frictionless vacuum. Dropping the ball slowly michael fowler, uva stokes law. When any object rises or falls through a fluid it will experience a viscous drag, whether it is a parachutist or spacecraft falling through air, a stone falling through water or a bubble rising through fizzy lemonade. If you drop a ball, it falls due to the gravitational force. An experimental setup to verify stokes law using an. Reynolds number 1both kinds of drag force are present in any real problem, but because they have such different forms.
I have searched through fluid dynamics but there are 838 papers in total, so i ran out of. Under this condition, inertial forces are negligible compared to viscous forces. Treatment processes screening aeration prechlorination sedimentation flocculation coagulation sedimentation sedimentation is the downwards movement of an object relative to its surrounding medium, due to the force of gravity. As per this theorem, a line integral is related to a surface integral of vector fields. This equation is popularly known as stokes law of falling body through a liquid. Whether the object is rising or falling in a fluid it will experience f d drag force. Learn the stokes law here in detail with formula and proof. Stokes law is the basis of the fallingsphere viscometer, in which the fluid is stationary in a vertical glass tube. Then according to stokes law, the viscous drag force.
Fluid mechanics stokes law and viscosity experiment. A sphere of known size and density is allowed to descend through the liquid. Stokes law for the resistance of a sphere in a viscous liquid rests, as is. Sedimentation can be either gravitational 1 gforce, or centrifugal many gforce. The experimental setup is in the physics lab right next to the rock. The report should be free of spelling and grammatical errors. Meanwhile, the resistance of gas molecules drag tend to slow down the movement. In actual practice the experiment is performed in a liquid column of finite. When any object rises or falls through a fluid it will experience a viscous drag, whether it is a parachutist or spacecraft falling through air.
Stokes law, the bernoulli equation, turbulence, boundary layers, flow separation introduction 1 so far we have been able to cover a lot of ground with a minimum of material on fluid flow. Be able to calculate the viscosity of an unknown fluid using stokes law and the terminal. Start recording a video clip for the motion of the free ball falling using the. The law, first set forth by the british scientist sir george g. Pdf an experimental setup to verify stokes law using an. This experiment confirms the direct proportionality between the force and each of the variables involved. Jul 15, 2016 viscosity and stokes law lesson plan template and teaching resources. To be begin we must draw a free body diagram fbd of the sphere. Stokes law was established by an english scientist sir george g stokes 18191903. As a result, the body experiences a retarding force. Stokes law is derived by solving the stokes flow limit for small reynolds numbers of. This suggests that stokes law is very sensitive to flow reynolds number, and experimenters must account for.
Stokes law and the coffee filters university of virginia. Viscosity stokes law viscosity is a property of uids liquids and gases which determines how much resistance is experienced by an object trying to move through the uid. Introduction the objectives of the experiment include determining the time for sphere shaped particles to reach terminal velocity given a distance in a column of fluid. The millikan oil drop experiment university of sheffield. Department of physical sciencesand engineering prince georges community college largo, maryland. A simple experimental demonstration has been made of stokes.
Scribd is the worlds largest social reading and publishing site. To make capillary tube free of contamination, it must be rinsed first in a. Pdf an experimental setup to verify stokes law using an electronic. The effective weight of body acts downward, due to which the body accelerates. Jul 25, 2012 when any object rises or falls through a fluid it will experience a viscous drag, whether it is a parachutist or spacecraft falling through air, a stone falling through water or a bubble rising through fizzy lemonade. At low velocities, the frictional force on a spherical body moving through a fluid at constant velocity is equal to 6. Free fall in a viscous liquid determination of dynamic viscosity in a stokes viscometer is based on a study of free fall of an iron ball in examined fluid. On the other side, his experiments, on bubbles of gas moving through liquid, gave the unexpected result that the slip at clean surfaces between gas and. Cd is determined from stokes law which relates drag to reynolds number drag coefficient and reynolds number. A note on stokes hypothesis 3557 much shorter for monatomic gases, due to the absence of the rotational and vibrational modes characterizing polyatomic gases. Stokes law and viscosity measurement laboratory investigation no. Stokess law, mathematical equation that expresses the settling velocities of small spherical particles in a fluid medium. You might like to compare this with an earlier post with experimental detail. Let initial acceleration of body be a, then from newtons second law f ma we have.
At a constant temperature, the pressure exerted by an enclosed. Stokes in 1851, is derived by consideration of the forces acting on a particular particle as it sinks through a. Stokes theorem and terminal velocity iit jee mains neet. Stokes law is important in millikans experiment for the measurement of the charge on an electron, and it also explains why large raindrops hurt much more than small ones when they fall on you its not just that they are heavier, they are actually falling faster. This suggests that stokes law is very sensitive to flow reynolds number, and experimenters must account for this. He was a member of the royal society, and the paper, if he published them there, are freely available here. We also acknowledge previous national science foundation support under grant numbers 1246120, 1525057.
Since the velocities of the droplets used in this experiment will be in the range of 0. Stokes law definition of stokes law by medical dictionary. Stokes law, reynolds number, and measuring liquid viscosity. Weve seen how viscosity acts as a frictional brake on the rate at which water flows through a pipe, let us now examine its frictional effect on an object falling through a viscous medium. The particles undergo free fall the entire time, but while they are in the air stream they are subjected to an additional force f 6piaunu, where a is the diameter of the particle, u the velocity of the air stream, and nu the kinematic viscosity of air units. Stokes law and the coffee filters michael fowler, uva 61206 a problem we found that stokes law, which we derived in the form. Sediment lab investigating stokes law ds density of solid, gcm3 dw density of water, gcm3 g gravity, 980 cmsecond2 d particle diameter in centimeters. For molecules stokes law is used to define their stokes radius. Oct 21, 2009 the particles undergo free fall the entire time, but while they are in the air stream they are subjected to an additional force f 6piaunu, where a is the diameter of the particle, u the velocity of the air stream, and nu the kinematic viscosity of air units of stokes st. A uniform electric field is supplied by a pair of parallel plates with a. Stokes law predicts the settling velocity of particles in water which is a relationship of distance over time. Figure 2 shows the measured force as a function of. Stokes theorem also known as generalized stokes theorem is a declaration about the integration of differential forms on manifolds, which both generalizes and simplifies several theorems from vector calculus.
Everything else two densities, radius and terminal velocity is easy enough to measure. Viscosity of fluids stokes law professor thomson date of submission. Because its validity is limited to conditions in which the motion of the particle does not produce turbulence in the fluid. To verify stokes law and hence to determine the coefficient of viscosity of a highly. The derivation of stokes law assumes that the sphere radius is larger than this mean free path. I cannot say, for sure, that he published in the royal society publications, but it seems likely. Viscosity coefficient of a liqud by stokes method experiment. Experiments have shown that stokes law is only accurate at predicting the velocity pf particles less than 0. In 1851, george gabriel stokes derived an expression, now known as stokes law, for the. Stokes law physics and chemistry for ig and a level. The cgs unit of kinematic viscosity was named stokes after his work. Weve already seen and studied this kind of drag in the coffee.
When a spherical body moves down through an infinite column of highly viscous liquid, it drags the layer of the liquid in contact with it. Other objectives were calculating the viscosity of a liquid and applying stokes law, learning how to take accurate measurements and analyze data, and investigating the relationship between theory and practice. In 1851, george gabriel stokes derived an expression, now known as stokes law, for the frictional force also called drag force exerted on spherical objects with very small reynolds numbers in a viscous fluid. Millikan corrected stokes law by using a friction force which magnitude is d 6.
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