Viscosity is an internal property of a fluid that offers resistance to flow. For example, pushing a spoon with a small force moves it easily through a bowl of water, but the same force moves mashed potatoes very slowly. In fact, one of the major differences between styles of mashed potatoes is the viscosity of the starchy mass: some people like their potatoes running and teeming with milk and butter (they are fans of low-viscosity potatoes), while others like their potatoes drier and stickier, so they almost crack rather than flow (these people are devoted to high-viscosity potatoes).
Viscosity is important in volcanology. The more fluid a magma, the more likely it is to erupt. On the other hand, when more viscous (higher viscosity) lavas do erupt, they usually do so explosively. Viscosity also affects the shapes of lava flows and the mountains they erupt from. The more viscous the magma, the fatter the lava flow. Also, the more viscous the magmas a volcano erupts, the steeper the volcano. Thus, shield volcanoes like we have in Hawai'i have gentle slopes (less than 10 degrees), while stratovolcanoes like the Cascades in the northwestern mainland are much steeper (roughly 25 degrees). As expected, hawaiian volcanoes erupt more fluid lavas (called basalt) than do the Cascade volcanoes, which erupt a lava called andesite.
There are many ways to measure viscosity, including attaching a torque wrench to a paddle and twisting it in a fluid, using a spring to push a rod into a fluid, and seeing how fast a fluid pours through a hole. This exercise uses one of the oldest and easiest ways: we will simply see how fast a sphere falls through a fluid. The faster the sphere falls, the lower the viscosity. This makes sense: if the fluid has a high viscosity it strongly resists flow, so the sphere falls slowly. If the fluid has a low viscosity, it offers less resistance to flow, so the ball falls faster.
The measurement involves determining the velocity of the falling sphere. This is accomplished by dropping each sphere through a measured distance of fluid and measuring how long it takes to traverse the distance. Thus, you know distance and time, so you also know velocity, which is distance/time.
The formula for determining the viscosity is impressive, decorated with Greek letters and a squared term, but simply amounts to multiplying some numbers and then dividing by some others:
delta p = difference in density between the sphere and the liquid
g = acceleration of gravity
a = radius of sphere
v = velocity = d/t = (distance sphere falls)/(time of it takes to fall)
This equation makes sense in that spheres that fall slowly have low velocities. This makes the denominator small, so the answer (viscosity) is large. Viscosity is measured in units of Pa s (Pascal seconds), which is a unit of pressure times a unit of time. This is not especially intuitive. How does it relate to flowing liquids? One way of looking at it is to realize that pressure is force per square area. This makes a little more sense: force applied to the fluid, acting for some length of time. [Note: the exercise uses kilograms, meters, and seconds, rather than grams, centimeters, and seconds. Viscosity can be measured in g-cm-s, with the resulting unit called the poise; 10 poise = 1 Pa s. You may prefer those units to kg-m-s because densities are the more familiar grams per cubic centimeters.]
The measurement should be repeated many times to arrive at a good average value, and, most important, to observe the scatter in the results. This allows an assessment of the uncertainty in the measurement. Using spheres of different radii and densities and measuring the viscosities of at least two liquids gives a good idea of this unusual physical property and the power of an equation to predict behavior. For example, if group A uses a marble (density of about 2800 kg/m3) and group B uses a steel ball bearing (7800 kg/m3), and both measure the viscosity of the same liquid, they will find that the velocities differ, but the viscosities will be the same, within the error of measurement.
Why do all this?
Viscosity is an important property of lavas and other liquids.
Shows that different materials have different viscosities.
Shows that this property can be measured; i.e., we can put a number on it. This allows its use in equations to predict behavior and for comparison of one material to another.
The experiment gives a feeling for the physical meaning of the viscosities of lavas, so when we say that an a'a flow has a viscosity of 1000 Pa s, we can mentally imagine a sphere dropping through it and how long it might take.
The replicate measurements and their variation show that scientific determinations are not exact. All measurements have experimental uncertainty.
The exercise is set up so you can either give the densities to students, or have them measure it first. For convenience, here are some density values:
oil (most kinds): 920 kg/m3
shampoo: 1000 kg/m3
water: 1000 kg/m3
glass marble: 2800 kg/m3
steel ball bearing: 7800 kg/m3