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- 1. VISCOSITYYEDİTEPE UNIVERSITY DEPARTMENT OF MECHANICAL ENGINEERING
- 2. YEDITEPE UNIVERSITY ENGINEERING FACULTY MECHANICAL ENGINEERING LABORATORY1. OBJECTIVE To calibrate the system with a known viscosity. To measure fluid viscosity and observing the difference between Newtonian and non- Newtonian fluids.2. EQUIPMENT Capillary tube Multimeter Pressure Sensor Compressor Thermometer Beaker Pressure Tank Stop-watch Water container (the cup that capillary tube is connected) Electronic balance Power Supply 1
- 3. 3. PROCEDURE Water Tank Cappilary Tube Figure 1: Schematic diagram of the test setup3.1 Calibration of the capillary tube 1. Fill the beaker with tap water and measure its temperature by using a thermometer. 2. Poor the tap water into the water tank and close the lid of the capillary tube. 3. The beaker is weight. 4. Prepare the stop-watch and place the beaker under the capillary tube. 5. Measure the initial height of the fluid (H1) and record it. 6. Simultaneously open the lid of the capillary tube and start the stop-watch. 2
- 4. 7. When water level drops to a specific height (do not allow the water completely flow through the tank stop the experiment before it completely finishes) stop the stop-watch and measure the final height of the fluid. Record the height and time measured by the stop-watch. 8. Weigh the beaker (this time with the water in it!) and determine the mass of the water by subtracting the empty weight of the beaker measured in the step 3. Than record it. 9. Repeat steps 2 times. 10. Use measurements to calculate capillary tube diameter according to Eq. 4.4 via the computer software and compare result with the known value.3.2 Measuring the viscosity of the water and peach juice 1. Fill the beaker with tap water and measure its temperature by using a thermometer. 2. Poor the tap water into the water tank and close the lid of the capillary tube. 3. The beaker is weight. 4. Check that valve 1 is open and valve 2 is closed shown in Fig 1. 5. Fill the pressure vessel with pressurized air from the compressor until the pressure in the compressor air tank reaches to 0.2 bars (run the compressor until this moment than stop it). 6. After stopping the compressor you will see that the pressure is balanced between compressor and pressure vessel and the final value will be 0.4 bars. 7. Prepare the stop-watch and place the beaker under the capillary tube. 8. Measure the initial height of the fluid (H1) and record it. 9. Open the valve 2 and valve 3 shown in Fig. 1. 10. Measure the ampere (A1) from the multimeter and record it. 11. Simultaneously open the lid of the capillary tube and start the stop-watch. 12. When water level drops to a specific height (do not allow the water completely flow through the tank stop the experiment before it completely finishes) stop the stop-watch and measure the final height of the fluid (H2) and the final ampere (A2). Record the height and time measured by the stop-watch. 3
- 5. 13. Weigh the beaker (this time with the water in it!) and determine the mass of the water by subtracting the empty weight of the beaker measured in the step 3. Than record it. 14. Repeat steps 2 times. 15. Use measurements to calculate viscosity of the fluid by using Equation 4.2 and compare the results by known value. 16. Repeat all steps for peach juice 4. THEORY A fluid has an ability to flow by changing positions of its molecules with respect toanother. As expected this ability to flow is different for different fluids. As an example from reallife: if you poor a cup of water and honey on a surface it is seen that water flows easier than thehoney. This is because viscous effects on honey are much bigger than viscous effects on water. There two related measures of fluid viscosity. These are known as the dynamic (absolute)viscosity and the kinematic viscosity. Dynamic viscosity, μ, is the measure of the internalresistance. It is the tangential force per unit area that required for the movement of the fluid layerwith respect to the neighboring one at unit displacement for a unit velocity. Kinematic viscosity,υ, is the ratio of the dynamic viscosity to density of the fluid. No force is applied in this quantity.It is expressed as υ = μ/ρ. Velocity gradient and stresses effecting on the fluid flowing in the pipeis given in Fig. 2Figure 2: Velocity is zero on the wall of the pipe as no slip condition states. Also it is seen that velocity increases as y reaches to the middle of the pipe and gets its highest value. 4
- 6. 2.1. Newtonian and Non-Newtonian fluids When shear stress applied, viscosity of some fluid change. These types of fluids arecalled as Non-Newtonian fluids. Non-Newtonian fluids can be categorized as shear-thinning andshear thickening. Fluids that have no change in their viscosity by an applied shear stress arecalled as Newtonian fluids. As an example mixing the fluid by a spoon or applying pressure onthe fluid creates shear stress on the fluid.Shear thinning: Shear thinning liquids have macromolecules or particles. And these molecules arerandomly stayed together under no flow. But at large shear stress levels they start to orientthemselves to the flow and their molecules rotate become parallel to the flow. Shear thinningliquids’ viscosity decreases as the shear force increases.Shear thickening: Shear thickening liquids usually have solid particle suspensions. At low shear the fluidlayers act like a thin film layer to the relative motion and viscosity is low too. Contrary to shearthinning liquids when the shear stress is increased the particle to particle contact and frictionappears. Thus the viscosity of shear thickening liquids increases as the shear force increases. Figure 3: Viscosity vs. Shear Rate 5
- 7. 2.2 Reynolds Number In fluid mechanics Reynolds number, which is a dimensionless number, shows thebehavior of the flow. It is literarily the ratio of internal forces to viscous forces. Also it refers tothe flow situations, relative motion of the fluid, in various conditions. Reynolds number is givenas the following; (4.1)Where;Re Reynolds numberρ Fluid densityL Characteristic lengthu Velocity of the fluidμ Viscosity of the fluidThe flow type of the fluid should be known to make further calculations for the fluid viscosity.For a flow through a pipe, the flow isLaminar when Re < 2300Transient when 2300 < Re < 4000Turbulent when Re > 40002.3 Equations for Calculations The viscosity of the fluid is calculated by using equation which is given below. Thisequation is used only for the laminar flow condition. 6
- 8. ̇ ( ) ( ) {( ) } (4.2) ̇ ̇Where;ρ Fluid densityL Length of the capillary tube (thickness of the connection member is included) ̇ Mass flow rateg Gravitational accelerationPt Applied pressurePa Atmospheric pressureD Diameter of the capillary tubeHt Average of the initial height and the final height of the fluid ( )α2 Kinetic energy correction factor for fully developed laminar flowKent Entrance lossOutput of the pressure sensor is milliampere which is 4-20mA.Range of the pressure sensor is 0-10psi (0-0.69bar). The applied pressure is obtained from equation which is given below; ( ) (4.3)Pt Applied pressureAave Average milliampere which is read from multimeter ( ) 7
- 9. The diameter of the capillary tube is calculated by doing algebraic arrangements to aboveequation as follows. ̇ ̇ ( ) ( ( ) ( ( )) ) (4.4)Take Kent, α2 and μ (water) as following for the calculations.Kent=0.24α2 =2μ water = 0.0010449 ( )Shear stress on the pipe wall can be found by using equation 4.5. ̇ (4.5)The following “Figure 4” is the graph of the ( ) - ( )for ketchup. The coefficient ofx in the graph (can be denoted as n) is found as 0.3089. The reason of taking the logarithm of the“ ” and “ ” is very important.Ifn<1 the fluid is Non-Newtoniann>1 the fluid is NewtonianWhere;V Fluid velocityD Diameter of the capillary tube 8
- 10. Figure 4: The slope of the line on the ( ) and ( ) plot shows if the fluid is shear thinning or shear thickening. 5. ANALYSIS AND DISCUSSION 1. Give a sample calculation of the diameter, the viscosity, and the wall shear stress. 2. Show the variations of the ( ) (in x axis) - ( ) (in y axis) for each fluid in the different graphs and comment the graph. 3. Discuss how the viscosity changes with τ wall. 9

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