In actual practice the experiment is performed in a liquid column of finite. In this experiment we will use stokes law and the concept of terminal velocity to determine the viscosity of glycerin. This suggests that stokes law is very sensitive to flow reynolds number, and experimenters must account for this. 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. Viscosity measurement using stokes law of drag acting on a spherical particle. A note on stokes hypothesis 3557 much shorter for monatomic gases, due to the absence of the rotational and vibrational modes characterizing polyatomic gases. 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. 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. Pdf an experimental setup to verify stokes law using an. 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. Stokes law requires a correction to the viscosity when the velocity of the falling droplet is less than 1 mms. Stokes law was established by an english scientist sir george g stokes 18191903.
To be begin we must draw a free body diagram fbd of the sphere. I have searched through fluid dynamics but there are 838 papers in total, so i ran out of. The derivation of stokes law assumes that the sphere radius is larger than this mean free path. The effective weight of body acts downward, due to which the body accelerates. Lab 2 stokes law stokes law lab 2 1 brief introduction to. A uniform electric field is supplied by a pair of parallel plates with a. Millikan corrected stokes law by using a friction force which magnitude is d 6. This suggests that stokes law is very sensitive to flow reynolds number, and experimenters must account for. 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. Meanwhile, the resistance of gas molecules drag tend to slow down the movement. An experimental setup to verify stokes law using an. If you drop a ball, it falls due to the gravitational force. Experiments have shown that stokes law is only accurate at predicting the velocity pf particles less than 0. Viscosity coefficient of a liqud by stokes method experiment.
Stokes law is the basis of the fallingsphere viscometer, in which the fluid is stationary in a vertical glass tube. Scribd is the worlds largest social reading and publishing site. Stokes law relates the terminal velocity of a sphere to its radius and the viscosity of the fluid it is moving through. The law, first set forth by the british scientist sir george g.
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. Stokes law and the coffee filters university of virginia. In order for the electron to absorb the light, however, the light must have enough energy. The millikan oil drop experiment university of sheffield. Force of resistance is evaluated by the stokes law fr 6. An experimental setup to verify stokes law using an electronic balance 31 spheres. Let initial acceleration of body be a, then from newtons second law f ma we have. The school experiment uses glycerine or golden syrup as the fluid, and the technique is used industrially to check the viscosity of fluids. The experimental setup is in the physics lab right next to the rock.
For molecules stokes law is used to define their stokes radius. Since the velocities of the droplets used in this experiment will be in the range of 0. This equation is popularly known as stokes law of falling body through a liquid. Sedimentation can be either gravitational 1 gforce, or centrifugal many gforce. Consequently stokes law overestimates the friction force, because the droplet actually moves for appreciable times through a frictionless vacuum. Stokes law physics and chemistry for ig and a level. For each sphere radius, the experimental points are on straight lines going through the origin. Stokes law presentation free download as powerpoint presentation. 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. Viscosity and stokes law lesson plan template and teaching resources. Finally, the viscosity calculated using stokes law and depending on the. Sinking time of plankton medium consider a small microorganism living in the ocean.
Basic theory of particle size analysis by sedimentation. 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. Department of physical sciencesand engineering prince georges community college largo, maryland. Mar 09, 20 the effective weight of body acts downward, due to which the body accelerates. Whether the object is rising or falling in a fluid it will experience f d drag force.
Lab 2 stokes law stokes law lab 2 1 brief introduction. At a constant temperature, the pressure exerted by an enclosed. 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. 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 report should be free of spelling and grammatical errors. We also acknowledge previous national science foundation support under grant numbers 1246120, 1525057. Viscosity of fluids stokes law professor thomson date of submission. Then according to stokes law, the viscous drag force. 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.
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. In 1851, george gabriel stokes derived an expression, now known as stokes law, for the. Newtons law is no longer valid and stokess law shall be used, which has the following form. To describe the drag force resulting from gas resistance, f d, the following equation can be used. He was a member of the royal society, and the paper, if he published them there, are freely available here. Dropping the ball slowly michael fowler, uva stokes law. Fg gravitational force, fr force of resistance and fb buoyant force. 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. Because its validity is limited to conditions in which the motion of the particle does not produce turbulence in the fluid. Stokes law predicts the settling velocity of particles in water which is a relationship of distance over time. Initial acceleration, this shows that the proof stokes law when the body is placed on liquid, then it accelerates initially in downward direction.
Learn the stokes law here in detail with formula and proof. Weve already seen and studied this kind of drag in the coffee. Stokes theorem and terminal velocity iit jee mains neet. As per this theorem, a line integral is related to a surface integral of vector fields. 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. 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. Figure 2 shows the measured force as a function of. 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. Stokes law is derived by solving the stokes flow limit for small reynolds numbers of. As a result, the body experiences a retarding force. Fluid mechanics stokes law and viscosity experiment.
Sediment lab investigating stokes law ds density of solid, gcm3 dw density of water, gcm3 g gravity, 980 cmsecond2 d particle diameter in centimeters. 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. Stokes law for the resistance of a sphere in a viscous liquid rests, as is. To verify stokes law and hence to determine the coefficient of viscosity of a highly. A simple experimental demonstration has been made of stokes.
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. Is stokes law applicable to body of shapes other than spherical. 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. 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. At low velocities, the frictional force on a spherical body moving through a fluid at constant velocity is equal to 6. The cgs unit of kinematic viscosity was named stokes after his work. A sphere of known size and density is allowed to descend through the liquid. Note that this is pretty much the same result we got by ignoring all of the exact details. The free fall velocity is given by stokes law, which describes how fast spherical bodies fall.
When small particle size and low velocity are involved, the reynolds number is small and the flow is laminar. Apr 10, 2020 understanding stokes law with dimensional analysis. 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. Stokes in 1851, is derived by consideration of the forces acting on a particular particle as it sinks through a. 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. Stokes law and viscosity measurement laboratory investigation no.
Stokes law definition of stokes law by medical dictionary. Reynolds number 1both kinds of drag force are present in any real problem, but because they have such different forms. 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. Energy of light is dependent on its wavelength, or color. 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. Stokess law, mathematical equation that expresses the settling velocities of small spherical particles in a fluid medium. Stokes law and the coffee filters michael fowler, uva 61206 a problem we found that stokes law, which we derived in the form. Everything else two densities, radius and terminal velocity is easy enough to measure.
Be able to calculate the viscosity of an unknown fluid using stokes law and the terminal. Cd is determined from stokes law which relates drag to reynolds number drag coefficient and reynolds number. Stokes law, reynolds number, and measuring liquid viscosity. You might like to compare this with an earlier post with experimental detail. Pdf an experimental setup to verify stokes law using an electronic. 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. I cannot say, for sure, that he published in the royal society publications, but it seems likely. This equation can be derived from dimensional analysis. Viscosity and stokes law share my lesson free lesson. To make capillary tube free of contamination, it must be rinsed first in a. Under this condition, inertial forces are negligible compared to viscous forces. 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.
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