Let initial acceleration of body be a, then from newtons second law f ma we have. Download as ppt, pdf, txt or read online from scribd. 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. An experimental setup to verify stokes law using an. Stokes law and the coffee filters university of virginia. Be able to calculate the viscosity of an unknown fluid using stokes law and the. Basic theory of particle size analysis by sedimentation sedimentation of particles in a fluid has long been used to characterise particle size distribution. Newtons law is no longer valid and stokess law shall be used, which has the following form. You might like to compare this with an earlier post with experimental detail. Jul 15, 2016 viscosity and stokes law lesson plan template and teaching resources. Figure 2 shows the measured force as a function of.
Under low speed attached unseparated flow conditions, the drag acting on. Finally, the viscosity calculated using stokes law and depending on the. As per this theorem, a line integral is related to a surface integral of vector fields. Stokes law 1 is used to determine an unknown distribution of spherical particle sizes by measuring. 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. The cgs unit of kinematic viscosity was named stokes after his work. 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 sound attenuation that describes propagation of sound in newtonian liquid. For a wider range of reynolds number, namely re pdf from che 377 at purdue university. Determination of dynamic viscosity in a stokes viscometer is based on a study of free fall of an iron ball in examined fluid. To describe the drag force resulting from gas resistance, f d, the following equation can be used. Alternatively, extensional viscosity, a linear combination of shear and bulk viscosity, describes the reaction to elongation, widely used for characterizing polymers. 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, reynolds number, and measuring liquid viscosity.
Pdf an experimental setup to verify stokes law using an electronic. Application of the results to endeffect correlations in the. Newtons law is no longer valid and stokes s law shall be used, which has the following form. Based on theoretical laws involving the stokes law, the oseen law, and the goldstein law, general formulas for drag coefficient and settling velocity can be developed and fitted using 480 groups of experimental data re stokes law and the coffee filters michael fowler, uva 61206 a problem we found that stokes law, which we derived in the form. Basic theory of particle size analysis by sedimentation. In this experiment we will use stokes law and the concept of terminal velocity to determine the viscosity of glycerin. The school experiment uses glycerine or golden syrup as the fluid, and the technique is used. Viscosity stokes law terminal velocity streamline and turbulent flow critical velocity.
Concluding questions 1 in part i, step 8, what is the value of the reynolds number, and using this value is stokes law valid. Stokes law and the coffee filters michael fowler, uva 61206 a problem we found that stokes law, which we derived in the form. This suggests that stokes law is very sensitive to flow reynolds number, and experimenters must account for this. Energy of light is dependent on its wavelength, or color. This experiment confirms the direct proportionality between the force and each of the variables involved. Stokes law is derived by solving the stokes flow limit for small reynolds numbers of. General formulas for drag coefficient and settling. Note that this is pretty much the same result we got by ignoring all of the exact details.
You measured that the drag force was proportional to v2 and to the radius squared namely, the area. Pdf an experimental setup to verify stokes law using an. Jun 07, 2017 finding viscosity of a liquid by measuring velocity of small balls sinking in the tall tubes, and applying stokes equation. Reynolds number 1both kinds of drag force are present in any real problem, but because they have such different forms. 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. Whether the object is rising or falling in a fluid it will experience f d drag force. Relationship between viscosity and sugar concentration in. The newtonian fluid encyclopedia of life support systems. Department of physical sciencesand engineering prince georges community college largo, maryland. In order to determine the drag coefficient in the stokes s regime, we can compare the above equation to the newtons resistance equation. Stokes law relates the terminal velocity of a sphere to its radius and the viscosity of the fluid it is moving through.
This curriculum bene ts from a ccli grant from the national science foundation division of undergraduate education due9952773. The slow motion of a sphere through a viscous fluid towards a plane. In this paper, a series of new formulas for drag coefficient of spherical particles based on theoretical laws, such as the stokes law, the oseen law, and the goldstein law, were developed and fitted using 480. In 1851, george gabriel stokes derived an expression, now known as stokes law, for the. Law of conservation of linear momentum and its applications. General formulas for drag coefficient and settling velocity. Everything else two densities, radius and terminal velocity is easy enough to measure. Lab 2 stokes law stokes law lab 2 1 brief introduction. In order to determine the drag coefficient in the stokess regime, we can compare the above equation to. Stokes in 1851, is derived by consideration of the forces acting on a particular particle as it sinks through a. Sinking time of plankton medium consider a small microorganism living in the ocean. Mar 09, 20 the effective weight of body acts downward, due to which the body accelerates. Laminar flow is defined as a condition where fluid particles move along in smooth paths in lamina fluid layers gliding over one another. Viscosity of fluids stokes law professor thomson date of submission.
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. For each sphere radius, the experimental points are on straight lines going through the origin. They arise from the application of newtons second law in combination with a. While stokes law is straight forward, it is subject to some limitations. Stokes law of viscosity friction physics class 11 hsc cbse iit jee neet duration.
For molecules stokes law is used to define their stokes radius. The law, first set forth by the british scientist sir george g. Then according to stokes law, the viscous drag force. Cd is determined from stokes law which relates drag to reynolds number drag coefficient and reynolds number. Learn the stokes law here in detail with formula and proof. The settlement of particles is of great importance in many areas. 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. Fg gravitational force, fr force of resistance and fb buoyant force. 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. One tube is filled with glycerin and the other with water. Its a while since ive done any motion calcs so im after some guidance. As a result, the body experiences a retarding force. 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.
Meanwhile, the resistance of gas molecules drag tend to slow down the movement. 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. Viscosity and stokes law lesson plan template and teaching resources. Fluids, viscosity, and stokes law instructional physics lab. Fluid dynamics and the navierstokes equations the navierstokes equations, developed by claudelouis navier and george gabriel stokes in 1822, are equations which can be used to determine the velocity vector eld that applies to a uid, given some initial conditions. If you drop a ball, it falls due to the gravitational force. Finding viscosity of a liquid by measuring velocity of small balls sinking in the tall tubes, and applying stokes equation. Jan 17, 2018 stokes law of viscosity friction physics class 11 hsc cbse iit jee neet duration.
Under this condition, inertial forces are negligible compared to viscous forces. Stokes law is the basis of the fallingsphere viscometer, in which the fluid is stationary in a vertical glass tube. For a wider range of reynolds number, namely re law and terminal velocity. The viscous force acting on a spherical body falling in a liquid with velocity v is f 6 r v. Fluid mechanics pdf notes fm pdf notes smartzworld. Handbooks commonly quote viscosity in centipoise 1 cp 0. Stokes law was established by an english scientist sir george g stokes 18191903. Lab 2 stokes law stokes law lab 2 1 brief introduction to. The accurate determination of drag coefficient and settling velocity in wide reynolds number re range remains a problem. 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. An experimental setup to verify stokes law using an electronic balance 31 spheres. 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.
Stokes law predicts the settling velocity of particles in water which is a relationship of distance over time. Scribd is the worlds largest social reading and publishing site. For example, at room temperature, water has a dynamic shear viscosity. Oct 21, 2009 its a while since ive done any motion calcs so im after some guidance. A sphere of known size and density is allowed to descend through the liquid. 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. In order for the electron to absorb the light, however, the light must have enough energy. Once revised the newton law of viscosity as originally stated in the principia mathematica, the concept of viscosity is introduced by means of the classical simple shear experiment and, afterwards, the threedimensional form of newtons law is analyzed. 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.
Stokes law physics and chemistry for ig and a level. It would be interesting to verify the above formula by experiments on liquids with similar values of fi and. Sedimentation can be either gravitational 1 gforce, or centrifugal many gforce. Stokess law, mathematical equation that expresses the settling velocities of small spherical particles in a fluid medium. Stokes law and viscosity measurement laboratory investigation no.
Unit i introduction to dimensions and units physical properties of fluids specific gravity, viscosity, surface tension, vapor pressure and their influences on fluid motion pressure at a point, pascals law, hydrostatic law atmospheric, gauge and. Experiments have shown that stokes law is only accurate at predicting the velocity pf particles less than 0. Weve already seen and studied this kind of drag in the coffee. I am vertically dropping a range of materials size 820 mm into a horizontal air stream in a pipe pipe diammeter d, 0. The dimensions of viscosity are force per unit area divided by velocity gradient as in eq. 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. Stokes law presentation free download as powerpoint presentation. The report should be written in such a way that anyone could replicate the performed experiment and obtain similar. 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. It holds for small spherical bodies in a homogenous viscous fluid. According to stokes law, droplets in an fdsemulsion will tend to either lift or to settle. A simple experimental demonstration has been made of stokes. Click on upload file and upload the archive file you created.
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