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. This equation can be derived from dimensional analysis. Fg gravitational force, fr force of resistance and fb buoyant force. Force of resistance is evaluated by the stokes law fr 6. Whether the object is rising or falling in a fluid it will experience f d drag force. Then according to stokes law, the viscous drag force.
Stokes law for the resistance of a sphere in a viscous liquid rests, as is. Stokes law definition of stokes law by medical dictionary. Stokes in 1851, is derived by consideration of the forces acting on a particular particle as it sinks through a. The report should be free of spelling and grammatical errors. This experiment confirms the direct proportionality between the force and each of the variables involved. If you drop a ball, it falls due to the gravitational force. 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. 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. 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 theorem and terminal velocity iit jee mains neet. 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. A sphere of known size and density is allowed to descend through the liquid. Lab 2 stokes law stokes law lab 2 1 brief introduction to. A simple experimental demonstration has been made of stokes. Stokes law was established by an english scientist sir george g stokes 18191903. Under this condition, inertial forces are negligible compared to viscous forces. Viscosity coefficient of a liqud by stokes method experiment. Stokes law presentation free download as powerpoint presentation. 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. We also acknowledge previous national science foundation support under grant numbers 1246120, 1525057. As a result, the body experiences a retarding force. Sediment lab investigating stokes law ds density of solid, gcm3 dw density of water, gcm3 g gravity, 980 cmsecond2 d particle diameter in centimeters.
At low velocities, the frictional force on a spherical body moving through a fluid at constant velocity is equal to 6. Newtons law is no longer valid and stokess law shall be used, which has the following form. 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. Pdf an experimental setup to verify stokes law using an electronic. Apr 10, 2020 understanding stokes law with dimensional analysis. Stokes law and the coffee filters university of virginia. 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. To describe the drag force resulting from gas resistance, f d, the following equation can be used. Meanwhile, the resistance of gas molecules drag tend to slow down the movement.
Viscosity measurement using stokes law of drag acting on a spherical particle. 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 is the basis of the fallingsphere viscometer, in which the fluid is stationary in a vertical glass tube. Start recording a video clip for the motion of the free ball falling using the. To make capillary tube free of contamination, it must be rinsed first in a. Scribd is the worlds largest social reading and publishing site. Reynolds number 1both kinds of drag force are present in any real problem, but because they have such different forms. Mar 09, 20 the effective weight of body acts downward, due to which the body accelerates. Learn the stokes law here in detail with formula and proof. Since the velocities of the droplets used in this experiment will be in the range of 0. When small particle size and low velocity are involved, the reynolds number is small and the flow is laminar.
Stokes law and the coffee filters michael fowler, uva 61206 a problem we found that stokes law, which we derived in the form. Department of physical sciencesand engineering prince georges community college largo, maryland. In actual practice the experiment is performed in a liquid column of finite. Stokes law, reynolds number, and measuring liquid viscosity. Be able to calculate the viscosity of an unknown fluid using stokes law and the terminal. 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. Energy of light is dependent on its wavelength, or color. Sedimentation can be either gravitational 1 gforce, or centrifugal many gforce. 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. At a constant temperature, the pressure exerted by an enclosed. Viscosity and stokes law lesson plan template and teaching resources. Viscosity and stokes law share my lesson free lesson.
Consequently stokes law overestimates the friction force, because the droplet actually moves for appreciable times through a frictionless vacuum. The experimental setup is in the physics lab right next to the rock. 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. 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. Is stokes law applicable to body of shapes other than spherical. I have searched through fluid dynamics but there are 838 papers in total, so i ran out of. Stokes law is derived by solving the stokes flow limit for small reynolds numbers of. The law, first set forth by the british scientist sir george g.
I cannot say, for sure, that he published in the royal society publications, but it seems likely. This equation is popularly known as stokes law of falling body through a liquid. To be begin we must draw a free body diagram fbd of the sphere. The free fall velocity is given by stokes law, which describes how fast spherical bodies fall. Weve already seen and studied this kind of drag in the coffee. You might like to compare this with an earlier post with experimental detail. Stokes law and viscosity measurement laboratory investigation no. The effective weight of body acts downward, due to which the body accelerates.
To verify stokes law and hence to determine the coefficient of viscosity of a highly. In order for the electron to absorb the light, however, the light must have enough energy. 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 requires a correction to the viscosity when the velocity of the falling droplet is less than 1 mms. Everything else two densities, radius and terminal velocity is easy enough to measure. In this experiment we will use stokes law and the concept of terminal velocity to determine the viscosity of glycerin. Stokes law predicts the settling velocity of particles in water which is a relationship of distance over time. 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. Basic theory of particle size analysis by sedimentation. Note that this is pretty much the same result we got by ignoring all of the exact details. Dropping the ball slowly michael fowler, uva stokes law. As per this theorem, a line integral is related to a surface integral of vector fields.
He was a member of the royal society, and the paper, if he published them there, are freely available here. 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. 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 states that when light hits an electron that is orbiting an atom, the electron can absorb that light and go into an excited state. 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 millikan oil drop experiment university of sheffield. Stokes law relates the terminal velocity of a sphere to its radius and the viscosity of the fluid it is moving through. 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. Finally, the viscosity calculated using stokes law and depending on the. In 1851, george gabriel stokes derived an expression, now known as stokes law, for the. Figure 2 shows the measured force as a function of. This suggests that stokes law is very sensitive to flow reynolds number, and experimenters must account for. 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. Lab 2 stokes law stokes law lab 2 1 brief introduction. Cd is determined from stokes law which relates drag to reynolds number drag coefficient and reynolds number. Stokes law physics and chemistry for ig and a level.
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. Pdf an experimental setup to verify stokes law using an. A uniform electric field is supplied by a pair of parallel plates with a. An experimental setup to verify stokes law using an. Viscosity of fluids stokes law professor thomson date of submission. Fluid mechanics stokes law and viscosity experiment. The cgs unit of kinematic viscosity was named stokes after his work. Millikan corrected stokes law by using a friction force which magnitude is d 6. Experiments have shown that stokes law is only accurate at predicting the velocity pf particles less than 0. Sinking time of plankton medium consider a small microorganism living in the ocean. Jul 15, 2016 viscosity and stokes law lesson plan template and teaching resources.
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. This suggests that stokes law is very sensitive to flow reynolds number, and experimenters must account for this. Initial acceleration, this shows that the proof stokes law when the body is placed on liquid, then it accelerates initially in downward direction. 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.
Let initial acceleration of body be a, then from newtons second law f ma we have. The derivation of stokes law assumes that the sphere radius is larger than this mean free path. An experimental setup to verify stokes law using an electronic balance 31 spheres. For molecules stokes law is used to define their stokes radius.
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