# Race Your Marbles to Discover a Liquid's Viscosity

 Difficulty Time Required Average (6-10 days) Prerequisites None Material Availability The graduated cylinder must be ordered from a science supply store. Cost Low ($20 -$50) Safety You should only test non-toxic, non-flammable, and non-volatile liquids. Adult supervision is recommended.

## Abstract

How do you like your mashed potatoes? Thin and whipped smooth? Or thick and mashed into chunks? Your mouth checks out not just the taste of your food, but its viscosity, or how it flows on your tongue, every time you take a bite! In this science fair project, you'll learn what viscosity is, and how to measure it in common liquids around your home.

## Objective

To determine the viscosity of common liquids by measuring the transit time of marbles through the liquids.

## Credits

Kristin Strong, Science Buddies

Edited by Peter Boretsky, Lockheed Martin and Ben Finio, PhD, Science Buddies

This project follows much of the experimental procedure outlined in the following source:

### MLA Style

Science Buddies Staff. "Race Your Marbles to Discover a Liquid's Viscosity" Science Buddies. Science Buddies, 26 Aug. 2015. Web. 9 Oct. 2015 <http://www.sciencebuddies.org/science-fair-projects/project_ideas/Chem_p055.shtml>

### APA Style

Science Buddies Staff. (2015, August 26). Race Your Marbles to Discover a Liquid's Viscosity. Retrieved October 9, 2015 from http://www.sciencebuddies.org/science-fair-projects/project_ideas/Chem_p055.shtml

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Last edit date: 2015-08-26

## Introduction

On a cold winter morning, have you ever tried to squeeze some honey out of the honey bear onto your toast? It is pretty tough, huh? Honey is one of those liquids that is very sensitive to temperature. As the temperature goes down, the viscosity, or resistance to flow, goes way up and you can squeeze and squeeze all you want, but very little honey comes out. If you set the honey bear in a pan of warm water for a few minutes and try again, what happens? One little squeeze and honey comes gushing out all over your toast. The viscosity, or resistance to flow, goes way down as the temperature goes up.

As a measure of a liquid's resistance to flow, viscosity can be thought of as friction inside the liquid. If, for example, you try to ride your bike with the hand brakes on (a form of friction), it is difficult to roll the bike forward. The resistance to motion is high. Likewise, in highly viscous liquids (those with high internal friction), the resistance to flow is high.

Viscosity is a very important quality of liquids that scientists, engineers, and even doctors are frequently trying to measure and change. It is difficult, for example, to transport highly viscous crude oil through offshore pipelines, so scientists and engineers use a variety of methods to try and lower the oil's resistance to flow through the pipelines. Likewise, in medicine, doctors try to keep blood viscosity in the correct range. If blood is "too thick," or viscous, a patient can develop blood clots. If blood is "too thin," or lacks viscosity, however, then the patient is at risk for bruising or bleeding events. Blood viscosity, like most things in medicine, has a happy medium.

Volcanologists (people who study volcanoes) have a big interest in viscosity, too. The viscosity of molten rock or magma determines how easily a volcano will erupt, and what shape the lava flows and resulting mountains will take on. A very thin and fluid magma erupts more easily and forms gentle mountain slopes, while a very thick magma erupts explosively and forms a fat lava flow and steep mountain slopes. So, if you see a mountain formed from a volcano, you can estimate the viscosity of the magma that formed it just by looking at the angle of its slope!

Common liquids around your house (thankfully) don't form mountain slopes though, so to measure their viscosities, you have to use some other method. One of the oldest methods is the dropped-sphere method—a glass marble or sphere of some other material is dropped into a column of a liquid. If the liquid is very viscous (imagine cold honey), it will take a long time for the marble to drop to the bottom of the column. Dropping the marble into a less viscous liquid (like water) will take much less time.

Viscosity of a liquid can be calculated from the time elapsed, provided that you know the height of the column and the densities of the sphere and the liquid. Density is a measure of how "compact" something is. It is the ratio of mass to volume, and is a measure of how much matter is packed into a space. Think of a 1-inch cube of bread. Then think of a 1-inch cube of potato. The potato is denser than the bread (there is more "stuff" in the same space). You can calculate density yourself for an object by using a scale to find out the object's mass and then dividing that by the object's volume. You can also look up the densities of many common substances, like glass, stainless steel, water, seawater, oils, etc. in materials tables.

Knowing the time it took to travel through the column of liquid, the height of the column, the density of the sphere, and the density of the liquid, you can then calculate the viscosity of the liquid with the viscosity equation:

Equation 1:

 μ (the lowercase Greek letter mu, pronounced "mew") is the liquid's viscosity, in newton-seconds per meter squared (Ns/m2). Δρ is the difference in density between the sphere and the liquid, in kilograms per meter cubed (kg/m3). Δ (the capital Greek letter Delta) means "change" or "difference," and ρ (the lowercase Greek letter rho, pronounced "row") means density. g is the acceleration due to gravity, 9.81 meters per second squared (m/s2). a is the radius of the sphere in meters (m). v is the average velocity, defined as the distance the sphere falls divided by the time it takes to fall, in meters per second (m/s).

Note: Equation 1 depends on certain assumptions, mainly that the ball has reached its terminal velocity and that something called the Reynolds number is very small. You do not need to understand the technical details of these assumptions to do this experiment. The practical result is that Equation 1 is valid for "thick" liquids like molasses and honey, but it will give inaccurate results for "thin" liquids like water and milk. For more details about Equation 1, see the Bibliography.

So, now it's time to race some marbles and see if common liquids in your home are thick or thin!

## Terms and Concepts

• Viscosity
• Friction
• Density
• Terminal velocity
• Reynolds number
• Inverse relationship
• Direct relationship

### Questions

• What is liquid viscosity?
• How does viscosity change (in general) with temperature?
• Why is it important to understand viscosity?

## Bibliography

This source discusses what viscosity is, its importance to understanding volcanology, and how to measure viscosity in the laboratory:

This source provides more background information about Equation 1 and the conditions required for it to be accurate:

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## Materials and Equipment

• Tall, slender drinking glasses or glass jars with straight sides, equally sized (4)
• Bowls or containers for storing liquids in between tests. This will allow you to re-use liquids instead of pouring them down the drain and wasting materials.
• Marker, water soluble (1)
• Ruler, preferably metric
• Glass marbles, equally sized (5)
• Safe liquids to test (4), approximately 1/2 gallon of each. Remember that you need to test "thick" liquids. Equation 1 will not be valid for "thin" liquids like water, juice, or milk. Here are some suggested liquids:
• Corn syrup
• Honey
• Glycerin
• Molasses Note: It can be challenging to see the marble in the molasses. We recommend using light molasses. You may also need to experiment with different colored marbles to find which ones are most easy to see.
• Stopwatch
• Strainer
• Liquid dish soap
• Dish towel
• Graduated cylinder, at least 1,000-mL size (1); available from Carolina Biological, item #: 721606
• Lab notebook
• Helper

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## Experimental Procedure

### Preparing Your Glasses for the Marble Race

1. Measure down about 2 cm from the top of each glass with the ruler, and mark the 2-cm location with the water-soluble marker.
2. Fill each glass with a different test liquid, all the way up to the 2-cm mark.

1. Have a helper hold two marbles level with the tops of two glasses. You hold two marbles level with the tops of two glasses also.
2. Say, "Ready, Set, Go!" and then you and your helper should drop your marbles at the same time and see which marble hits the bottom first and which one hits the bottom last. Record your observations in your lab notebook. If you have trouble figuring out a clear winner between two liquids, race the marbles with just those liquids a second and third time after first completing the next set of steps: Marble Retrieval and Cleanup.

Figure 1. An example race for two marbles. The left glass has maple syrup and the right glass has vegetable oil.

### Marble Retrieval and Cleanup

1. Place the strainer over a bowl or container that you can use to temporarily store a liquid (this will allow you to re-use it for the next part of the experiment).
2. Pour the contents of a glass (the liquid and the marble) slowly into the strainer.
3. Retrieve the marble from the strainer, and wash and dry the marble, glass, and strainer.
4. Repeat these steps for each of your other liquids, until you have retrieved all of the marbles.

### Preparing the Graduated Cylinder to Measure the Viscosity of Each Liquid

1. Fill the graduated cylinder up with one of the liquids to a level 5 cm below the top of the cylinder, as shown in Figure 2. To avoid waste, you can re-use some liquid that you poured into a bowl in the previous section.
2. Measure down at least 2 cm below the surface of the liquid (as shown in Figure 2) and mark a starting line on the graduated cylinder with the marker. The starting line needs to be lower than the surface of the liquid to allow time for your marble to reach its terminal velocity before you start taking measurements.
3. Measure up from the bottom of the graduated cylinder, approximately 5 cm, and mark an ending line on the graduated cylinder with the marker. You don't want the ending line to be at the bottom of the cylinder because the marble will slow down as it approaches the bottom, due to interactions with this boundary.
4. Measure the distance between the starting point and the ending point. Record this distance in your lab notebook. This is the distance that you will use to calculate the speed of the marble as it travels through the liquid. Remember, the average speed is equal to the distance traveled, divided by the time it took to travel that distance. Now you're ready to test and get some travel times.

Figure 2. This drawing shows how to prepare the graduated cylinder for testing.

1. Create a data table like Table 1 in your lab notebook.
2. You or the helper should hold a marble at the surface of one of the liquids.
3. The other person should zero out the stopwatch.
4. The person holding the stopwatch should say "Go!" and have the other person drop the marble. As the marble passes the starting point, which was marked in the previous section, the person holding the stopwatch should start the stopwatch. As the marble passes the ending point, which was marked in the previous section, the person holding the stopwatch should stop it.
5. Record the time elapsed in your data table.
6. Repeat steps 1–4 of this section, with the same liquid and graduated cylinder, four more times with four other marbles. Be sure to record the times for all five trials in your data table.
Liquid name Trial 1 time (sec) Trial 2 time (sec) Trial 3 time (sec) Trial 4 time (sec) Trial 5 time (sec) Average of times (sec)
Example: Corn syrup

Table 1. An example data table for recording how long it takes the marble to fall.

### Marble Retrieval and Cleanup

1. Place the strainer over a bowl or container that you can use to temporarily store a liquid (this will allow you to re-use it if necessary).
2. Pour the contents of the graduated cylinder (the liquid and the marbles) slowly into the strainer.
3. Retrieve the marbles from the strainer and wash and dry the marbles and the graduated cylinder.
4. Repeat the experiment up to this step, starting from Preparing the Graduated Cylinder to Measure the Viscosity of Each Liquid, for each of the remaining test liquids.
5. If you kept all of your marbles and containers clean throughout the experiment and avoided cross-contamination of liquids, you may be able to store them for regular use. If your liquids got dirty or contaminated somehow during the experiment, you will need to dispose of them properly. Be careful doing this because pouring large amounts of some liquids, like oil, down the drain can clog a sink. Ask an adult for help cleaning up and disposing of the liquids if necessary.

1. Calculate the average for the five time trials for each liquid and enter it in your data table.
2. Calculate the average velocity for each liquid by dividing the distance, measured in step 4 of Preparing the Graduated Cylinder to Measure the Viscosity of Each Liquid, by the average time it took to travel that distance. Record your calculation in a second data table, like Table 3.
3. Remember Δρ from the viscosity equation, Equation 1 in the Introduction? Calculate Δρ, the difference in densities between the marble and each liquid, by using the values in Table 2. Record each Δρ calculation in your data table.
1. Note: If you tested a liquid that is not in Table 2, you can look up its density online by searching for "density of (material)."
2. You can also calculate the density of a liquid yourself by making some measurements. Density equals mass divided by volume, or ρ=m/V, so you need to measure the mass and volume of a fixed amount of the liquid. You can use your graduated cylinder to measure volume, and use a kitchen scale to measure mass (be sure to subtract the mass of the empty graduated cylinder to get the mass of the liquid alone). Be sure to convert to the right units (kg/m3).
Material Density (kg/m3)
Water 1000
Corn syrup 1380
Molasses 1400
Honey (room temperature) 1500
Vegetable or cooking oils 920
Glycerin 1260
Ocean water 1030
Milk 1030
Glass marble 2800
Stainless steel 7800
Table 2. Densities of some common materials.
1. If you know the diameter of your marbles, divide the diameter by 2 to get the radius of the marbles. If you don't know the diameter of your marbles, measure the diameter with a ruler, and then divide by 2 to get the radius. Record the radius of your marbles in your lab notebook.
2. Calculate the viscosity of each liquid using Equation 1 from the Introduction. Record the calculations in your data table.
Liquid name Calculated average velocity (m/s) Δρ (kg/m3) Viscosity (kg/meter sec)
Example: Corn syrup

Table 3. Table for calculating liquid viscosities.
1. Compare your viscosity test results with the marble race results. Do they match up and make sense? Did the liquids with the lowest viscosities win the race? Plot the viscosity of each liquid on the y-axis and the calculated average velocity on the x-axis. Is the relationship between viscosity and velocity inverse or direct?

## Variations

• Choose one liquid and repeat the experiment using different sizes and densities of spheres. For example, try different diameters of glass marbles, stainless steel balls, or BB's. (Note: For your viscosity calculations, the density of a stainless steel ball bearing is 7,800 kg/m3. If the diameter of any of your spheres is more than half the radius of the graduated cylinder, you should purchase a larger-diameter graduated cylinder to avoid having the spheres interact with the sides of the cylinder.) Are the velocities of the different spheres different? What about the measured viscosities from those velocities? Are they the same? Obtain some statistics, such as the standard deviation, on your measured viscosities.
• Choose a very temperature-sensitive liquid, such as honey, and evaluate how viscosity changes as a function of temperature.

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