VISCOSITY LABEGR 365 – FLUID MECHANICSPURPOSE:THEORY:FIRST FIND viscous­_side:It is known that:NOW FIND viscous­_bottom:It is known that:APPARATUS:ITEMPROCEDURE:RESULTS:Table 2 – Time Trial ResultsANALYSIS:CONCLUSION:ERROR CALCULATION:Grand Valley State UniversityThe Padnos School of EngineeringVISCOSITY LABEGR 365 – FLUID MECHANICSBrad Vander Veen May 13, 2003Lab PartnersJulie WatjerThomas FreundlPURPOSE: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 momentumthrough 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 thefluid 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: Iresistapplied (1)-where  is the torque, I is the mass moment of inertia, and  is the angular accelerationNow consider the experimental setup in Figure 1 below:Applying Equation (1) to the setup:dtdwIrWbottomviscoussideviscouss__)( (2)Since the angular velocity is constant:bottomviscoussideviscoussrW__)( (3)FIRST FIND viscous_side:It is known that:RFsideviscoussideviscous__ (4)By definition:AclearancevelocityFsideviscous_ (5)-where  is the viscosity of the fluid, and A is the lateral surface area of the rotating cylinderSubstituting:LRhRFssideviscous2_ (6)Simplifying:LhRFssideviscous22_ (7)Substituting (7) into (4):RLhRssideviscous22_ (8)Simplifying:LhRssideviscous23_ (9)NOW FIND viscous_bottom:It is known that:bottomviscousbottomviscousdFR__ (10)By definition:dAclearancevelocitydFbottomviscous_ (11)-where A is a differential area (ring) on the bottom of the cylinder, and  is the viscosity of the fluidSubstituting (11) into (10): dAclearancevelocityRbottomviscous_ (12)Simplifying: dRRhRRbbottomviscous2_ (13)Simplifying: dRRhbbottomviscous3_2 (14)Integrating:424_Rhbbottomviscous (15)Simplifying:bbottomviscoushR224_ (16)The governing equations are now set up for the Viscometer:For Steady State:bsshRLhRrW222)(43 (17)For Full, Unsteady State:dtdwIhRLhRrWbss222)(43 (18)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 StopwatchCalipers Various MassesPROCEDURE: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 2meters 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 mmhs =2.52 mmhb = 12.0 mmR = 57.65 mmL = 74.2 mmm = .95 kgNOTE: Each measurement above has the last significant digit after the decimal place estimatedIn Table 2 below, the results of the time trials can be seen.TRIAL MASS(kg) TIME(seconds)1 0.05 66.32 0.10 32.63 0.20 16.14 0.30 12.7Table 2 – Time Trial ResultsThe 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 0.0226 0.75162 0.0460 1.52863 0.0932 3.09534 0.1181 3.9239Table 3 – Velocity ValuesANALYSIS:Using results from Table 2, the experimental viscosity can be found. Consider the following equation:LhRssideviscous23_ (9)By substituting srW  in for , and solving for :LRhWrss2)(3 (19)The result of inserting velocity values into this equation is seen below in Table 4.TRIAL VISCOSITY (Ns/m)1 0.55362 0.54443 0.53774 0.6362Table 4 – Viscosity ValuesCONCLUSION: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 stoppingwas amplified. Therefore, the experimental viscosity is as follows:332155. Ns/m2Since 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