Hawai'i Space Grant College, Hawai'i Institute of Geophysics and
Planetology, University of Hawai'i, 1996
To determine how fluid a liquid really is by measuring its viscosity.
liquid(s) to test
spheres of different densities
graduated cylinders or other long tubes
Viscosity "Data Table"
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).
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.
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."
Fill a cylinder with a liquid, up to about 5 cm from the
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).
Mark an ending point about 5 cm from the bottom.
Measure the distance between the starting and ending points,
and enter the answer in the data table as "Fall distance."
Analyzing your data
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.
Enter the data into the data table.
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.
Now calculate the viscosity from this equation:
Dr = difference in density between the sphere and
g = acceleration of gravity
a = radius of sphere
v = velocity
Average your results for each experiment.
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)?
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?
Extension: Calculating the standard deviation
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?
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.
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
Go to Viscosity Teacher
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