1. Purpose2. Experiment Design3. Experiment Process3.1 Setup3.2 Data acquisition3.3 Data reduction3.4 Uncertainty assessment3.5 Data analysis4. References57:020 Mechanics of Fluids & Transfer ProcessesLaboratory Experiment #1Measurement of Kinematic ViscosityMarian Muste, Fred Stern1. PurposeTo measure the kinematic viscosity of a fluid, the uncertainty of the measurement, to compare the measuredkinematic viscosity with manufacturer’s value, and to demonstrate the effects of viscosity by comparison of the falltimes for spheres of different densities and diameters. 2. Experiment Design A fluid deforms continuously under the action of a shear stress(http://css.engineering.uiowa.edu/fluidslab/referenc/concepts.html - select Viscosity). The rate of strain in a fluid isproportional to the shear stress. The proportionality constant is the dynamic viscosity (m). Viscosity is athermodynamic property that varies with pressure, temperature, and fluid nature. For instance, for a given state ofpressure and temperature, there is a variation of three orders of magnitude between water and glycerin, the fluid whichwill be used in this experiment. The kinematic viscosity n m r= where r is the density of the fluid, is mostfrequently used in the equations of fluid mechanics.Common methods used to determine viscosity are the rotating-concentric-cylinder method (Englerviscosimeter) and the capillary-flow method (Saybolt viscosimeter). Alternatively, we will measure the kinematicviscosity through its effect on a falling object. The maximum velocity attained by an object in free fall (terminalvelocity) is strongly affected by the viscosity of the fluid through which it is falling. When terminal velocity isattained, the body experiences no acceleration, so the forces acting on the body are in equilibrium (Figure 1). Figure 1. Experimental arrangementThe forces acting on the body are the gravitational force,g 6D = mg = Fsphereg3 (1)The force due to buoyancy,g 6D = Ffluidb3 (2)and the resistance of the fluid to the motion of the body, similar to friction. For Re = VD/ν << 1 (Re is a dimensionlessnumber that characterizes the flow), the drag force on a sphere is described by the Stokes expressionD V 3 = Ffluidd (3)where D is the sphere diameter, fluidr is the density of the fluid, spherer is the density of the falling sphere, n is theviscosity of the fluid, dF, bF, and gF, denote the drag, buoyancy, and weight forces, respectively, V is the velocity ofthe sphere through the fluid (in this case, the terminal velocity), and g is the acceleration due to gravity (White 1994).Once terminal velocity is achieved, a summation of the vertical forces must balance. Equating the forcesgives:-1-FFFVS p h e r ef a l l i n g a tt e r m i n a lv e l o c i t ybdg 18t 1) - /( g D = fluidsphere2 (4)where t is the time for the sphere to fall the vertical distance l.Using equation (4) for two different balls, namely, teflon and steel spheres, the following relationship for thedensity of the fluid is obtained, where subscripts s and t refer to the steel and teflon balls, respectively.t D - tD t D - t D = s2sttss2stt2tfluid2 (5)3. Experiment Process3.1 SetupThe equipment (measurement systems) in the experiment includes: A transparent cylinder (beaker) containing glycerin. A scale is attached to its side to read thedistance the sphere has fallen. Teflon and steel spherical balls of different sizes Stopwatch Micrometer Thermometer 3.2 Data acquisitionIn this experiment, we will allow a sphere to fall through a long transparent cylinder filled with the glycerinFigure 1. After the sphere has fallen a long enough distance so that it achieves terminal velocity, we will measure thelength of time required for the sphere to fall through the distancel.The experiment procedure follows the sequence described below:1. Measure the temperature of the room.2. Two horizontal lines are marked on the vertical cylinder. Measure the distance between the two lines, .3. Measure the diameter of each sphere (teflon and steel) using the micrometer.4. Release the sphere at the surface of the fluid in the cylinder. Then, release the gate handle.5. Release the spheres, one by one6. Measure the time for the sphere to travel the length 7. Repeat steps 3- 6 for all spheres. At least 10 measurements will be taken for each type of spheres.Since the fall time of the sphere is very short, it is important to measure the time as accurately as possible.Start the stopwatch as soon as the bottom of the ball hits the first mark on the cylinder and stop it as soon as thebottom of the ball hits the second mark. Two people should cooperate in this measurement with one looking at thefirst mark and handling the stopwatch, and the other looking at the second mark. A spreadsheet will be provided torecord the measurements.3.3 Data reductionFigure 2 illustrates the block diagram of the measurement systems and data reduction equations for theresults. A spreadsheet will be provided to conduct the data reduction. Data reduction includes the following steps 1. Calculate the fluid density for each measurement using equation (5).2. Calculate the kinematic viscosity for each measurement using equation (4) for either sphere type. 3.4 Uncertainty assessmentUncertainties for the experimentally determined glycerin density and kinematic viscosity will be evaluated. The methodology for estimating uncertainties follows the AIAA S-071-1995 Standard (AIAA, 1995) assummarized in Stern et al. (1999) for multiple tests (M = 10). The block diagram for propagation of errors in themeasured density and viscosity is provided in Figure 2. The data reduction equations for density and viscosity ofglycerin are equation (5) and (4), respectively. First, the elemental errors for each of the independent variable, Xi, indata reduction equations should be identified using the best available information (for bias errors) and repeatedmeasurements (for precision errors). Table 1 contains the summary of the elemental errors assumed for the presentexperiment.-2-E X P E R I M E N T A L E R