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This 3 page Class Notes was uploaded by Jalon Willms on Monday October 19, 2015. The Class Notes belongs to PH 235 at Rose-Hulman Institute of Technology taught by Staff in Fall. Since its upload, it has received 6 views. For similar materials see /class/225118/ph-235-rose-hulman-institute-of-technology in Physics 2 at Rose-Hulman Institute of Technology.
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Date Created: 10/19/15
Viscosity Experiment MJM October 10 2006 Background The classic de nition of viscosity is Fvisc vxy the from the tangential force on 4 gt one part of a uid moving over y gt another gt The sketch shows uid in contact With x a surface and the uid xvelocity increasing with its y distance from the surface The arrow on the dotted line pointing to the left depicts a viscous force exerted on the uid above the dotted line due to the uid below the line This force depends on the area of contact A and the viscosity 11 and the velocity gradient vxay Fvisc TI The 39dynamic viscosity 11 has units of FAvelocitydistance Paos There is also a 39kinematic viscosity39 v given by 11 PV where p is the uid density You should be able to work out the units of v as mzs The cgs unit poise39 for dynamic viscosity is named after Poiseuille who came up with Poiseuille39s law Trivia question Poiseuille was in charge of sewers for what major european city This experiment utilizes Dow Corning 200 silicone oil which is sold in a great variety of viscosities These viscosities are mainly given in centiStokes cSt l 100 of a Stokes which is named after the great 19th century British physicist Sir G G Stokes l poise l Pa s dynamic viscosity 11 l centistokes cSt 10396 mzs or 1 mmzs kinematic viscosity v 11p I am attaching a table of some typical values to give you some idea of whether your viscosity value makes any sense Our experiment involves letting various spheres fall through silicone oil and determining the velocity of each The radius R of each of the four steel spheres is given and the radius of the two te on spheres is to be determined In highly viscous ow as we will be doing the drag force on a sphere is given by Stokes39 law deg 61111 v R where V is the sphere39s velocity If you have done the Millikan oil drop experiment you have already encountered Stokes39 law The drag force on a falling sphere is upward opposite to its velocity The gravitational force mg acts downward and the buoyant force equal to the weight of the displaced uid acts upward It doesn39t take long for these forces to come into balance so the ball travels at a constant velocity The upward forces on a falling sphere are 6111 v R and p uid g 41TR33 while the downward force is psphm g 41TR3 3 Equating the upward and downward forces gives a relation between the velocity v the dynamic viscosity 11 and the ball radius R Your job is to determine terminal velocity v for each of 4 steel balls and for two te on balls All ball diameters are in multiples of 132quot for both steel and te on The steel ball diameters are 2 232quot 3 332quot 4 432quot 5 532quot There are two tall skinny cylinders Each contains either a 3 or a 4 steel ball and one te on ball These are tubes basically free of air bubbles Measure the inside diameter of one or both of these tubes The te on ball diameters in the tall skinny cylinders are supposed to be 316quot and 14quot There is one medium height tube containing one 4 and one 5 steel ball This may have an air bubble in it Measure its inside diameter There are two short tubes which have basically the same diameter as the medium tube Use only the shorter tube containing the two smallest steel balls 2 and 3 To find the velocity of a given ball first center that ball in the tube by tilting the tube When ready turn the tube over expeditiously and set it gently on the table Measure the time for a ball to fall between two scribed circles on the tube and of course carefully measure the distance between these scribed circles Correction for the nite size of tube We want the velocity v as the ball falls at terminal velocity in a large volume of uid but in reality the walls of the tube are nearby Years ago I found a correction formula developed at Iowa State which goes as follows vmrrected vmeasured 1 c c2 where c 94 dD with ball diameter d and tube inner diameter D This is plausible since the walls of the tube probably inibit the downward ow somewhat This summer I came across another version which said Vcorrected Vmeasured 1 24 and called the factor of 24 the Ladenburg constant39 Where this came from I don t know but it appears close to the other correction factor Analysis Steel ball velocities Be sure to measure at least two runs for each ball and be careful to get the right distance through which each ball fell Then calculate and correct each velocity Notice that balls 3 and 4 will be measured in two different diameter tubes Check that the corrected velocity of each ball comes out the same no matter which tube was used The density of steel is right around 7800 kgm3 and that of te on was given originally in the early 70s when we first made up these tubes as 2150 kgm3 and this summer in manufacturer39s literature it was given as 2300 kgm3 The correct density for Dow Corning 200 silicon oil is close to 970 kgm3 Find viscosity T in Pa s For the steel balls find a way to plot a function of velocity and a function of radius so that you get a straight line whose slope will give you the Viscosity 11 I don39t object to you getting a Viscosity from each individual velocity and radius but I do want you to come up with a straightline plot Get viscosity v in cSt When you have a value of v in cSt you can look a the attached table to see if it appears to make sense at all Te on sphere diameters Finally use a ruler or meter stick to estimate roughly the diameter of each of the te on spheres You can also measure some likely ones with a micrometer These are in a little cardboard box smaller than the palm of your hand These little guys like to roll around so be careful not to lose any Use a wool shirt or something on the table so when you drop a ball it will stay on the shirt I found the steel ball Viscosity values fell in a range of only about 5 The te on ball Viscosities were maybe 5 higher than from steel probably because of the density of te on being a little off