Hawai'i Space Grant College, Hawai'i Institute of Geophysics and Planetology, University of Hawai'i, 1996 Viscosity Purpose  To determine how fluid a liquid really is by measuring its viscosity. Key Words   mass  density  velocity      Materials   liquid(s) to test  spheres of different densities  balance  graduated cylinders or other long tubes  meter stick  stop watch  calculator  Viscosity "Data Table"  Viscosity "Histogram" Procedure 1. Choose the spheres and liquids to use for this activity. Enter the data for these materials into the Viscosity "Data Table." If necessary, measure the radius of the sphere (hint: it is easier to measure the diameter and divide by two).   2. Determine the density of a sphere by measuring its mass and calculating its volume [remember that volume = (4/3) pr3]. Enter the value at the top of the data table.   3. Enter the density of the liquid you are using (about 920 kg/m3 for oils, 1000 for shampoos) at the top of the data table as "Fluid density."  4. Fill a cylinder with a liquid, up to about 5 cm from the top.   5. Mark with tape a convenient starting point about 2 cm below the surface of the liquid (which will allow the sphere to reach terminal velocity before you begin making measurements). You can use either the top or the bottom of the tape, but use the same points for each measurement you make when you drop the spheres (step 8).   6. Mark an ending point about 5 cm from the bottom.   7. Measure the distance between the starting and ending points, and enter the answer in the data table as "Fall distance."

8.
One team member should hold a sphere just touching the liquid. Another should get ready to measure the time of fall with a stop watch. The timer says "Go," and his or her teammate drops the ball. The timer begins timing when the ball crosses the start line and ends it when it crosses the end line. You can use either the top or the bottom of the tape, but use the same points you used for the distance measurement.

9.
Enter the data into the data table.

10.
When you have made all 20 measurements, calculate the velocity at which the ball fell from this equation: velocity = distance/time. Enter the velocity values into the data table.

11.
Now calculate the viscosity from this equation:

Dr = difference in density between the sphere and the liquid

g = acceleration of gravity

a = radius of sphere

v = velocity

12.
Average your results for each experiment.

13.
How does the viscosity of your liquid compare to the viscosities of water (0.001 Pa s), pahoehoe lava (100 - 1,000 Pa s), and to sticky andesite which makes up stratovolcanoes (10E6 - 10E7 Pa s)?

14.
Compare your results with another team's on the same liquid, but with a different type of sphere. Did you get close to the same answer?

1.
Note the range in the measured viscosities. Having a spread in the data always happens in scientific measurements. The spread gives an idea of the uncertainty in the measurement. That is, how well do we know the viscosity you measured?

2.
We can show the uncertainty in the measurement by making a histogram of the results. To do that, make categories corresponding to ranges in viscosities. To figure out what those ranges should be, start by determining the total range in your measurements (subtract the lowest from the highest) and divide by some number between 5 and 10 try 7 or 8. You can then adjust the ranges to be even intervals (for example, 1-1.9 Pa s; 2-2.9 Pa s; etc.). Next, use the graph to make a "Viscosity Histogram" by making the heights of the bars correspond to the number of measurements in that category. The histogram will give you a good idea of the spread in the measurements.
Extension: Calculating the standard deviation

Statistical analysis can also be used to quantify the variance in the measurements. A simple statistical test called the standard deviation (usually abbreviated s) is available on most scientific hand calculators. You can use standard deviation as a measurement of the certainty of the average of your set of measurements. For instance, plus or minus one standard deviation of the mean you calculated (for example, 6 ±2) signifies that if you repeated the measurements, then there is a 67% chance that the average would be within one standard deviation of your previous average.

Is your average within one standard deviation of another team's average for the same liquid?

Go to Viscosity Data Tables or Histogram (Bar Graph)

Go to Viscosity Teacher pages.