Grand Valley State University The Padnos School of Engineering VISCOSITY LAB EGR 365 FLUID MECHANICS Brad Vander Veen May 13 2003 Lab Partners Julie Watjer Thomas Freundl PURPOSE The purpose of this lab is to experimentally determine the absolute viscosity of a fluid using a Stormer Viscometer and to determine whether the fluid being tested is newtonian or non newtonian THEORY The viscosity of a fluid is a transport property associated with the transport of momentum through that fluid via intermolecular collisions and intermolecular forces Fluid immediately adjacent to a solid surface will move at the surface velocity This is known as the no slip boundary condition and is a direct result of momentum transfer between the fluid molecules and the solid surface Moving away from the solid surface the fluid velocities can change indicating fluid shear stresses Fluid shear stresses acting over the surface of a solid body result in fluid forces on that body Consider Newton s Second Law for rotating bodies applied resist I where is the torque I is the mass moment of inertia and is the angular acceleration Now consider the experimental setup in Figure 1 below 1 Applying Equation 1 to the setup dw W rs viscous side viscous bottom I dt 2 Since the angular velocity is constant W rs viscous side viscous bottom 3 viscous side Fviscous side R 4 velocity Fviscous side A clearance 5 FIRST FIND viscous side It is known that By definition where is the viscosity of the fluid and A is the lateral surface area of the rotating cylinder Substituting R Fviscous side 2 R L hs 6 R 2 Fviscous side 2 L hs 7 Simplifying Substituting 7 into 4 R 2 viscous side 2 L R hs 8 R 3 viscous side 2 L hs 9 viscous bottom R dFviscous bottom 10 velocity dFviscous bottom dA clearance 11 Simplifying NOW FIND viscous bottom It is known that By definition where A is a differential area ring on the bottom of the cylinder and is the viscosity of the fluid Substituting 11 into 10 velocity viscous bottom R dA clearance Simplifying 12 R viscous bottom R 2 R dR hb 13 Simplifying viscous bottom 2 R 3 dR hb 14 2 R 4 hb 4 15 2 R 4 2hb 16 Integrating viscous bottom Simplifying viscous bottom The governing equations are now set up for the Viscometer For Steady State R 3 2 R 4 W rs 2 L hs 2hb 17 R 3 2 R 4 dw W rs 2 L I hs 2hb dt 18 For Full Unsteady State NOTE In this lab the viscous torque from the bottom will be neglected because it is small compared to the torque created by the viscous torque on the side APPARATUS ITEM Stormer Viscometer Meter stick Stopwatch Calipers Various Masses PROCEDURE 1 Measure all pertinent dimensions of the Stormer Viscometer 2 Set the Viscometer on the edge of a table or something similar at a height of at least 2 meters off the ground 3 Mark a distance of 1 5 meters off the ground 4 Hang various masses on the string of the Viscometer allowing the mass to reach terminal velocity before the 1 5 meter mark Time how long it takes for the mass to go from a height of 1 5 meters to 0 meters ground RESULTS Below is a list of the measured properties of the Stormer Viscometer rs 30 10 mm hs 2 52 mm hb 12 0 mm R 57 65 mm L 74 2 mm m 95 kg NOTE Each measurement above has the last significant digit after the decimal place estimated In Table 2 below the results of the time trials can be seen TRIAL MASS kg TIME seconds 1 2 3 4 0 05 0 10 0 20 0 30 66 3 32 6 16 1 12 7 Table 2 Time Trial Results The distance traveled by the mass was 1 5 meters In Table 3 below the calculated velocity of the mass can be seen as well as the angular velocity of the spool TRIAL VELOCITY m s ANGLULAR VELOCITY rad s 1 2 3 4 0 0226 0 0460 0 0932 0 1181 0 7516 1 5286 3 0953 3 9239 Table 3 Velocity Values ANALYSIS Using results from Table 2 the experimental viscosity can be found Consider the following equation R 3 viscous side 2 L hs 9 By substituting W rs in for and solving for rs W h s R 3 2 L The result of inserting velocity values into this equation is seen below in Table 4 TRIAL VISCOSITY Ns m 1 2 3 4 0 5536 0 5444 0 5377 0 6362 Table 4 Viscosity Values 19 CONCLUSION The experimental viscosity of the glycerin used in this lab experiment was found by averaging the results from trails one two and three The fourth trial was excluded because of the difficulty in measuring the velocity of the falling mass It was hard to measure the velocity because of the errors in starting and stopping the stopwatch on time Since in the fourth trail the mass was falling the fastest the error in starting and stopping was amplified Therefore the experimental viscosity is as follows 1 2 3 3 55 Ns m2 Since the experimental viscosity of the fluid did not change as we doubled and even quadrupled the falling mass it can be assumed that glycerin is Newtonian Fluid ERROR CALCULATION The propagated error in this lab is as follows error 4 error 4 U rs rs 2 U t 2 U hs 2 U U U 9 R 2 L 2 L 2 t hs R L L 01 2 1 01 2 01 2 1 1 2 2 9 2 60 20 32 2 52 57 65 1500 0 74 2 propagated error 03 Therefore the viscosity of the glycerin with error calculation is 55 03 Ns m The recognized value of the viscosity of glycerin at room temperature is 0 8 Ns m The experimental value found in this lab was 55 Ns m Therefore the discrepancy between the two is 0 25 Ns m This turns out to be a error of 31 25