Measuring Viscosity with a Stormer Viscometer byDan SchwarzSchool of EngineeringGrand Valley State UniversityEGR 365 – Fluid MechanicsSection 01Instructor: Dr. S. FleischmannMay 29, 2007OutlineI. Purpose Statementa. The viscosity of glycerin, µ, was experimentally determined using a StormerViscometer.II. Backgrounda. Viscosity is a constant value that relates the shear stress applied at a fluidboundary to the transfer of velocity through the fluid.b. In this experiment, shear stress will be applied to glycerin by a submergedcylinder spinning within a cylindrical container. Glycerin at the boundary of thespinning cylinder will move at the same speed as the outer cylinder wall.Adjacent layers of fluid will move at gradually slower velocities in accordancewith the viscosity of the Glycerin.c. The experimental device shown in Figure 1 provides a means of measuring theviscosity of glycerin when the cylinder rotates at a constant speed due to thefalling weight, W. Figure 1: Stormer Viscometer (Dimensions in meters) d. The torque applied to the inner cylinder by the weight is given by Equation 1.WrTs(1)WHs=0.0026mhb=0.006mL=0.1426mR=0.05735mrs=0.02985me. The viscosity of the glycerin resists the applied torque along the side surface ofthe rotating cylinder. This torque is given by Equation 2. See Appendix A fordetails.ssidehLRT23(2)f. The viscosity of the glycerin also resists the applied torque along the bottomsurface of the rotating cylinder. This torque is given by Equation 3. See appendixB for details.bbottomhRT24(3)g. The ratio of the resistive torque at the side and the resistive torque at the bottom isapproximately 23. Consequently, it was determined that the resistive torque at thebottom of the cylinder is negligible. See Appendix C for details.h. At constant velocity the applied torque balances the resistive torque from the sideof the cylinder. This torque balance can be solved for µ to obtain Equation 4. SeeAppendix D for details.LRWhrss23(4)i. For experimental purposes it is necessary to determine the distance the weightmust fall before it reaches terminal velocity. The angular acceleration of thesystem is given by Equation 5. See Appendix E and Appendix F for details.   sioioshrrmLRrrmWrdtd223225.025.0 (5)j. For simplicity Equation 5 can be written in the form given by Equation 6. SeeAppendix G for details.CCdtd(6)k. Equation 6 can be integrated to obtain the angular velocity of the cylinder as afunction of time. The results are given by Equation 7. CteCCCCdtd(7)l. The path length required for the falling weight to reach terminal velocity is givenby Equation 8. See Appendix H for details.  2min10lnCCrLsalter(8)m. Experimental Methodi. Equation 8 was used to determine the path length required for each of thetest weights to reach terminal velocity.ii. The Stormer viscometer was filled with glycerin and placed on the edge ofa high surface.iii. A meter stick was fastened beneath the viscometer to measure the heightof the weight as it falls to the floor.iv. The smallest weight was connected to the fish line.v. The spool of fish line was wound up until the bottom of the weight was atthe top of the meter stick.vi. The weight was released and the clock was started as soon as the weighttraveled the required path length for terminal velocity.vii. The weight was allowed to drop 0.5 meters before the timer was stopped.viii. Steps iv through vii were repeated until all of the weights were tested.ix. The linear velocity of the falling weight was calculated by dividing the falldistance by the time duration. x. The angular velocity of the cylinder was calculated from the linearvelocity of the falling weight.xi. The viscosity of the glycerin was obtained using Equation 4.III. Results / Discussiona. The maximum free fall distance required for the weight to reach terminal velocitywas less than a millimeter as shown in Table 1. Consequently, the terminal pathwas considered negligible when collecting data from the experimental procedure.Table 1: Terminal path lengths required for each test weight.Mass (kg) Terminal Path (m)0.100 0.000070.070 0.000110.050 0.000210.040 0.00028b. Table 2 shows the data taken during the experimental procedure. The data showsthat the terminal velocity decreases as the mass of the test weights decrease.Table 2: Experimental data.Mass (kg) Time (s) Fall Distance (m)0.100 11.90 0.5000.070 17.80 0.5000.050 28.87 0.5000.040 36.99 0.500c. Table 3 compares the published viscosity value of glycerin with the experimentalvalues. The discrepancy decreases significantly as the mass of the test weightsdecrease. Thus, light weights produce more accurate viscosity measurements.Table 3: Comparison of experimental and published viscosity values.Mass (kg)Published Viscosity,µ (Ns/m)ExperimentalViscosity, µ (Ns/m)% Discrepancy % Error0.100 1.500 0.320 369% 2%0.070 1.500 0.335 348% 2%0.050 1.500 0.388 287% 2%0.040 1.500 0.398 277% 2%d. The % error propagation for this procedure was calculated by Equation 9. Table 3shows that the error propagation was approximately 2%. This indicates that themeasuring devices were appropriate for obtaining accurate calculations of theviscosity of glycerin.2min22222min94alterLLRshtsrLuLuRuhuturuualterss(9)IV. Conclusionsa. The extremely high discrepancy between the experimental and published valuesindicates that there may have been a calculation error. b. Another possible cause of the high discrepancy is that the glycerin has absorbedwater. This would decrease the viscosity of the glycerin since water has a verylow viscosity.c. The low percentage of error propagation suggests that the measuring devices weresufficiently accurate to produce good result. Thus, experimental error was mostlikely not a contributing factor to the high discrepancies.d. Due to the high discrepancy, this method of calculating viscosity using a StormerViscometer has not been proven valid. V. Appendicesa. Appendix A – Resisting Torque From the Side of Viscometeri. Start with general torque equation.vsideRFT ii. Substitute the product of shear stress and area