This law will form the basis of this laboratory investigation. For small amplitude oscillations, some authors take into account the drag force damping force, which is proportional to the velocity. As per this theorem, a line integral is related to a surface integral of vector fields. Stokes s law, mathematical equation that expresses the settling velocities of small spherical particles in a fluid medium. A friend of mine and i are conducting an experiment to find the relationship between terminal velocity and radius of a sphere i. Stokes in 1851, is derived by consideration of the forces acting on a particular particle as it sinks through a. Stokes law was established by an english scientist sir george g stokes 18191903. Graph 1 velocity versus mass for plastic bbs descending at terminal. Alternatively, calibration may be a part of the experiment. George gabriel stokes was an irishborn mathematician who is most famous for his. Fg gravitational force, fr force of resistance and fb buoyant force. Graph 1 velocity versus mass for plastic bbs descending at terminal velocity in honey. This relationship is known as stokes law, and the velocity is known as the stokes velocity. The physics of polarization high altitude observatory.
The concept of viscosity fluid flow plays a very important part in the processing of materials. The millikan oil drop experiment university of sheffield. On the basis of experimental observations proof george stokes law concluded that the viscous force on a small sphere in a liquid depends upon. Students simply accept the law and its consequences and applications. A simple experimental demonstration has been made of stokes. This means that the particle must be relatively small and slow, so it does not cause turbulence.
Jan 17, 2018 fluid 08 stokes theorem and terminal velocity iit jee mains neet duration. 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. Unfortunately stokes law is only valid when v f is greater than 0. Snells law experiment ran out of memory before an equation was outpul stokes law.
In this experiment, we will use stokes law and the concept of terminal velocity to determine the viscosity of glycerin, caster oil, honey and corn syrup. Sedimentation can be either gravitational 1 gforce, or centrifugal many gforce. It holds for small spherical bodies in a homogenous viscous fluid. The size of the basin is a function of the flow rate of water that must be treated, the size of the sediments in the water, and the water quality required at the outlet. Stokes introduces four quantities, today know as the stokes parameters, that have proven to be quite successful for the description of.
Stokes law and viscosity measurement laboratory investigation no. The experimental setup is in the physics lab right next to the rock. Esci 206 lab exploration sedimentary rocks setting of sediments in this lab, we will investigate how sedimentary particles settle out through a fluid. As in the experiment, we are using a spherical object with smooth surface and a homogenous liquid.
This is only valid if the diameter of the particle is. In 9 different concentrations of sugar solution, the viscosities of the 9 different solutions were measured by acquiring. Since the sphere is falling with constant velocity there is a. However, our measured cvs were higher than this, presumably due to. Can you calculate its drag force, using stokes law. It is filled with the sample liquid under investigation. In the mks system the unit of viscosity is nsm2 whereas in the cgs system the unit of viscosity is the poise 1 poise 1dyneseccm2. Jun 07, 2017 finding viscosity of a liquid by measuring velocity of small balls sinking in the tall tubes, and applying stokes equation. In this book, we will see many examples of processes where the rates of heat transfer, mass transfer and chemical reaction between. Stokes law equations formulas calculator terminal fall. The settling velocity of a particle in liquid is described by stokes law. The instructor will usually supply calibration curves. Stokess law, mathematical equation that expresses the settling velocities of small spherical particles in a fluid medium.
The resulting data from these experiments demonstrated that the method is feasible. The equation is inexact in numerical factors due to the fact that we greatly simpli. Measuring the velocity of fall of the drop in air enables, with the use of stokes law, the calculation of the. One tube is filled with glycerin and the other with water. If correctly selected, it reaches terminal velocity, which can be measured by the time it takes to pass two marks on the tube. The formula for viscosity shows that the terminal velocity v is proportional to the radius squared. The success of the millikan oil drop experiment depends on the ability to measure forces this small. In actual practice the experiment is performed in a liquid column of finite. The same results were obtained for stokes law without equations supplied only after the level of uncertainty was changed from 0. In the brownian motion paper5 einstein used essentially the same argument, applying the vant hoff law to suspensions, assuming stokess law, and describing the brownian motion as a diffusion process.
In this experiment, the relationship between viscosity and sugar concentration in aqueous sugar solution was determined by calculating viscosity with stokes law and newtons first law of motion. The importance of the phenomena related to this law sub. As a result, the body experiences a retarding force. Stokes law fluid mechanics calculator solving for terminal velocity given acceleration of gravity, particle diameter, medium density, particle density and viscosity stokes law equations formulas calculator terminal fall settling velocity fluid mechanics. Viscosity measurement using stokes law of drag acting on a spherical particle. The behavior of small charged droplets of oil, weighing only 10. To verify stokes law and hence to determine the coefficient of viscosity of a highly. Learn the stokes law here in detail with formula and proof.
Small particles also have a high probability to enter deep into the lungs when inhaled. F 6rv f viscous drag n coefficient of viscosity of the. Determination of the coefficient of viscosity by using stokess method. Full text full text is available as a scanned copy of the original print version. Stokes in 1851, is derived by consideration of the forces acting on a particular particle as it sinks through a liquid column under the influence of gravity. Pdf an experimental setup to verify stokes law using an electronic. Viscosity coefficient of a liqud by stokes method experiment. For laminar flow mmg 6 rv t where m is the mass of the sphere, m is the mass of the. An experimental setup to verify stokes law using an. 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. Re law are that it only applies when the viscosity of the fluid a particle is sinking in is the predominant limitation on acceleration. Stokes seeks a division of the property known as 450 pinetree drive in lawrenceville, georgia, which is the home of the parties.
In 9 different concentrations of sugar solution, the viscosities of the 9 different solutions were measured by acquiring the average velocity of the marble to reach certain height within the solution. The school experiment uses glycerine or golden syrup as the fluid, and the technique is used. Handbooks commonly quote viscosity in centipoise 1 cp 0. In terms of the avogadro constant and faraday constant f faraday constant, n a avagadro constant. Stokes law only holds for reynolds numbers that are less than 10. Fluids, viscosity, and stokes law instructional physics lab. This document is highly rated by jee students and has been viewed 5248 times. 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.
Report on the sedimentation experiments final version. The falling time is recorded and then utilized to determine the viscosity at room temperature. Viscosity coefficient of a liqud by stokes method experiment coefficient of viscosity using stokes method youtube mech props experiment viscosity stokes method youtube. Examples orientableplanes, spheres, cylinders, most familiar surfaces nonorientablem obius band. Begin by making a movie of the teflon sphere falling in corn syrup. Then according to stokes law, the viscous drag force. The experiment is one of the most fundamental of the experiments in the. I designed this activity to serve several purposes. What links here related changes upload file special pages permanent link page. The q, values of all swimming behaviors were between 0. Mar 09, 20 proof stokes law equating powers of both sides, we get.
An experimental setup to verify stokes law using an electronic balance. In the brownian motion paper5 einstein used essentially the same argument, applying the vant hoff law to suspensions, assuming stokes s law, and describing the brownian motion as a diffusion process. Stokes law for the resistance of a sphere in a viscous liquid rests, as is well known, on the fundamental assumptions. 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. Determination of dynamic viscosity in a stokes viscometer is based on a study of free fall of an iron ball in examined fluid. Basic theory of particle size analysis by sedimentation. One purpose is to help students understand how sediments settle out through fluids sorting, graded bedding. Below are detailed instructions for capturing and analyzing a video.
Pdf an experimental setup has been designed to allow direct measurement of the force acting upon a sphere immersed in a moving fluid. What factors will affect how fast a sedimentary particle will settle out of a fluid. George stokes entitled on the composition and resolution of streams of polarized light from different sources, that the desricption in mathematical terms of polarized radiation becomes fully consistent. 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. The flow past follows the stokes law as the experiment. In this experiment we will use stokes law and the concept of terminal velocity to determine the viscosity of glycerin. The dimensions of viscosity are force per unit area divided by velocity gradient as in eq. The flow past follows the stokes law as the experiment fits all assumption in the stokes law. So, it looks like we have a means to calculating everything. Slowness of motion, so that the inertia terms in the hydrodynamical.
Include manufacturer of the instrument, model and serial numbers. Stokes law exercise for rocks and minerals in this exercise students determine the velocity of different kinds and sizes of particles through different kinds of fluids. Stokes law defines the drag force that exists between a sphere moving through a fluid with constant velocity. Prepare a set of 5060 excel files numbered according to the number of a trial and save the files in your computer. Stokes law, reynolds number, and measuring liquid viscosity.
The law, first set forth by the british scientist sir george g. Most processes are based on the use of fluids either as raw materials, reagents, or heat transfer media. Dropping the ball slowly michael fowler, uva stokes law. Stokes first derived the basic formula for the drag of a sphere of radius ra moving with speed uo through a viscous fluid of density. Esci 206 lab exploration sedimentary rocks setting of. The original formulation of stokes law simply described the force needed to drive a sphere through a quiescent, continuous, viscous fluid is f6. Modification to stokes law ebenezer cunningham 18811977 george gabriel stokes 18191903 av ag 6 for small particle radius a stokes law need to be corrected. Measuring the velocity of fall of the drop in air enables, with the use of stokes law, the calculation of. Pdf an experimental setup to verify stokes law using an.
Stokes law is written as, fd6pmvd where fd is the drag force of the fluid on a sphere, m is the fluid viscosity, v is the. Get a printable copy pdf file of the complete article 457k, or click on a page image below to browse page by page. Viscosity is the resistance of a fluid to flow, and with increasing viscosity, the. In 1851, george gabriel stokes derived an expression, now known as stokes law, for the. Graphs must be drawn neatly following a specific format. 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. The final experiment had possible errors due to the experimental setup. This experiment confirms the direct proportionality between the force and each of the variables involved spherefluid relative velocity, sphere radius and fluid. Anes thetized daphnia followed stokes law, showing an increase in sinking rate of 70% over the temperature range. In the initial experiment performed with the guar gum, a formula derived from stokes law was used to determine the apparent viscosity of the guar gum. Two of the experiments provided results consistent with the known value for the viscosity. Stokes lawrence i 1420 fifth avenue, suite 3000 seattle, washington 981012393 206. Settling basins for trickle irrigation in florida 2 require longer settling times and, hence, longer water transit times through the basin. In this experiment we will use stoke s law and the concept of terminal velocity to determine the viscosity of glycerin.
Using stokes s law, the ratios of the viscosities for white wefgm, yellow wefgm and water were 1. One of the experiments did not provide sufficient data for analysis. Note that this is pretty much the same result we got by ignoring all of the exact details. Stokes law is a proposition that relates the drag force experienced by a falling sphere to the spheres constant velocity in a liquid of known viscosity. Stokes law shows that the frictional drag f is directly proportional to the weight of the sphere. This is described by en 481 and based on the aerodynamic diameter of the particles. No results were obtained for snells law or stokes law with equations supplied. Sedimentation stokes law, if size stokes law and viscosity measurement laboratory investigation no. Sedimentation the overflow rate is calculated in the following way. Derivation of the stokes drag formula in a remarkable 1851 scientific paper, g. Calculating drag force with stokes law elementary imagine a sphere with fluid flowing around it. Applied to our experiments, we would have predicted cvs of 0. Stokes law is the basis of the fallingsphere viscometer, in which the fluid is stationary in a vertical glass tube. A steel ball is allowed to fall down this tube over a calibrated distance.
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 liquid is infinite, as the velocity turned out too great by 50 per cent. From these assumptions he derived an expression for the mean square displacement x2. The behavior of small charged droplets of oil, having masses of only l012 gram or less, is observed in a gravitational and an electric field. Click on upload file and upload the archive file you created. A sphere of known size and density is allowed to descend through the liquid. Sediment lab investigating stokes law ds density of solid, gcm3 dw density of water, gcm3 g gravity, 980 cmsecond2 d particle diameter in centimeters. Relationship between viscosity and sugar concentration in. Settling velocity deposition stokes law the drag on a spherical particle in a fluid is described by stokes law for the following conditions.
159 1626 1248 811 484 1558 657 453 1389 1370 1458 243 1317 15 593 929 1422 1090 834 817 979 300 683 846 38 1324 257 1115 1079 671 552 1021 787 1410 1507 293 1634 616 145 507 915 645 641 1285 195 714