PHYS&242 Physics Lab For Scientists and Engineers. VISCOSITY

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1 PHYS&22 Physics Lab For Scientists and Engineers. 8Feb2013 VISCOSITY In this lab you will investigate viscous flow in two different phenomena; flow through a tube and flow around a sphere causing drag and terminal velocity. Materials: Sponge and warm water Jar of corn syrup and tubes attached 2 plastic beakers Squeeze bottle of corn syrup Stopwatch Calipers Graduated cylinder Balance to weigh beakers 1. Viscous flow through a tube. Poisseuille investigated viscous flow through a tube and came up with the relation P 8 L Where η is the viscosity in units of Pa s. Tables often list viscosity in centipoise (cp). To convert the value, 1 cp = 1mPa s. From the equation, you can see that, besides the viscosity which is to be calculated, the variables to be measured and controlled are the radius and length of the tube, the pressure difference across the length of the tube and the volume flow rate. You will use three different tubes in this experiment and the lengths will be provided on the containers to which they are attached. You will measure the inner diameter of each one using calipers and clean pieces of the two different diameters available on the shelves in the lab. Measure the diameters of the small and large diameter tubes and record them on the report sheet. A tub with a jar with tubes attached at the bottom should be at your lab station. The jar will be filled with corn syrup and all the screw caps or press-fit caps should be on, please return it the same way. You will need to use two different jars to get data for all three tubes. There should also be a squeeze bottle of corn syrup and 2 beakers in the tub. Label the beakers and determine the mass of them while empty.

2 Place the jar on top of a block so that the syrup coming out of the tube will be caught in a beaker to be weighed. Place a beaker under the end of one of the tubes as shown in figure 1. Using a marker for transparencies, mark the jar where the top of the syrup is and measure the height of the mark above the center of the tube with the beaker under it. Record this on the data sheets. There is one table for each of the three tubes. Perform 2 runs with each tube, do a third run only if there is a large disagreement between the first two runs. To determine the volume flow rate, unscrew the kid from the jar and set the stopwatch to zero. When you are ready, one person should unscrew the end cap and tell their partner to start the r. Time how long it takes to nearly fill the beaker. While the syrup is flowing, keep the liquid level in the jar constant using the squeeze bottle of syrup. Screw the cap back on the tube when the run is to be stopped. Weigh the beaker with the syrup in it and record both the and the mass in the appropriate table. Pour the syrup from the beaker back into the squeeze bottle and wipe up any spills with a wet sponge. Perform a second run and record the data. Again return the syrup to the squeeze bottle and wipe up any spills with the sponge. You do not need to get every last bit of the syrup out of the beaker, just weigh them again before using them for the next tube so you know how much to subtract from the mass of the full beaker at the end of the next run. Repeat this for all three tubes. When you are done, drain the syrup from the beakers back into the squeeze bottles and clean out the beakers before you leave lab.

3 2. Viscous drag and terminal velocity. In this part of the lab, you will drop a marble through the syrup and, after it has reached terminal velocity, it s fall between two marks a known distance apart. You will retrieve the marble from the bottom using the tool provided and repeat the fall three s. The drag force on the marble is given by Stokes Law: Fd 6 r v To ensure that this is applicable, calculate the Reynolds number, which should turn out to be 2 or less for the Stokes Law to apply. This is the creeping flow or slow flow limit where the flow is laminar. In the case where the Reynolds Number is in the hundreds or higher, the pushing force limit should be used: F r v d 2 2 Obtain a marble from the container on the shelf and measure its diameter using the calipers. Record this on your data sheets. Take the marble, a plastic ruler and a stopwatch to the bench with the tall cylinders full of syrup and make sure the retrieval tool is in the cylinder you are going to use. Measure the distance between the marks and record it on your data sheet. Drop the marble fro less than a center above the surface of the syrup. Start the stopwatch when the marble passes the top line and stop it when the marble reaches the bottom line. Be sure to use the same part of the marble both s (bottom, center or top). Retrieve the marble, push the retrieval tool back to the bottom and repeat the drop. Perform three runs and determine the average viscosity from the terminal velocity. When you are done, retrieve the marble, clean it off and return it to the container on the shelf. Clean up any spills using a wet sponge..

4 Name Partners VISCOSITY Report Sheet 1. Viscous flow through a tube. Small tube diameter:. Large tube diameter:. Beakers: Mass when empty A g B g Density of syrup: Mass of empty graduated cylinder g. of syrup in graduated cylinder ml. Mass of graduated cylinder with syrup g. Density of syrup in g/ml: ρ = g/ml. Depth of syrup from top surface to center of tube = h Length of tube = L Tube 1: h= cm L = ΔP = ρgh = Pa r = run 1 run 2 run 3 mass of beaker + syrup mass of empty beaker mass of syrup

5 Tube 2: h= cm L = ΔP = ρgh = Pa r = run 1 run 2 run 3 mass of beaker + syrup mass of empty beaker mass of syrup Tube 3: h= cm L = ΔP = ρgh = Pa r = run 1 run 2 run 3 mass of beaker + syrup mass of empty beaker mass of syrup

6 Calculations: mass t 8L P V t Tube1: 8L un1 run2 run3 viscosity η average viscosity = Pa s Tube2: 8L un1 run2 run3 viscosity η average viscosity = Pa s Tube3: 8L un1 run2 run3 viscosity η

7 average viscosity = Pa s 2. Viscous drag and terminal velocity. Diameter of marble = Mass of marble = g of marble = 3 r 3 cm 3 Weight of marble: mg = N Drag force = N Buoyant force on marble = 3 3 r N Distance between marks = m Times : s, s, s velocities: m/s, m/s, m/s Drag force: F 6 d v η= Pa s, Pa s, Pa s Average viscosity = Pa s Compare the viscosities using student s t test. You should compare the results from the three different tubes with each other and with the result from the terminal velocity experiment.