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High School Physics: Help and Review22 chapters | 265 lessons

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Instructor:
*Laura Foist*

Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science.

In this lesson, you will learn about viscosity - what it is, how it is measured, and the equation needed to figure out the viscosity of a fluid. You'll also discover the reasons why viscosity is important.

Imagine trying to drink apple juice, but it slides down your throat like apple sauce. Or having to drink a container of yogurt like milk because it is so runny, instead of scooping it with a spoon. You would probably think there is something wrong with each of these products. In fact, you probably wouldn't want to eat either of them. The thickness of a substance is called viscosity.

**Viscosity** is a fluid's resistance to flow. It can also be described as how thick a product is. Think of a funnel. Water runs through a funnel really quickly because it has very little resistance to flow, or very little viscosity. In other words, it isn't very thick. On the other hand, if you run pudding through a funnel it may take a little longer. This is because it has more resistance to flow, more viscosity, and is thicker.

Viscosity can be measured with a piece of equipment called a viscometer that measures the force necessary to move through a liquid. Or, it can be measured with household instruments, such as measuring how far a liquid can move on a slight incline after a certain amount of time.

The idea behind measuring viscosity is to determine how resistant that material is to flowing. If a fluid can flow down a slight incline very quickly, it has very little resistance to flow. If it takes a lot of force to move through a liquid, it has a lot of resistance to flow. A fluid will be more resistant to flow the more internal friction it has.

One way to think about viscosity is that it is the amount of force required to get that substance moving. It is the force per unit area, so viscosity is equal to force divided by area. With an ideal fluid (called a Newtonian fluid), it is also directly proportional to what is called the shear rate. **Shear rate** is the speed that the liquid is moving divided by the distance that is moves. In order to end this equation with the proper units, the proportionality constant is included. This constant is called the viscosity coefficient (n).

The viscosity coefficient is multiplied by shear rate in order to equal viscosity. So for every 1 unit increase in viscosity, the shear rate must increase by a certain amount (depending on the liquid). For example: for every 1 Pascal second (Pa s) increase in viscosity of water, the shear rate must increase by 0.00089 s. So we multiply the shear rate by 'n', which is equal to 0.00089 Pa.

In this equation the sheer rate is shown as dv/dr. This simply refers to the velocity divided by the distance. The 'd' before the v and the r refers to a derivative of each being taken. Since we typically measure viscosity by watching how quickly something spreads over a certain area this is the formula that is often used.

This formula also shows that this all equals F/A. Recall that viscosity is equal to force divided by area; the F refers to force and the A refers to area. Therefore, F/A is another way to refer to viscosity.

Not all fluids react perfectly. Sometimes fluids will thicken when energy is applied. For example, try mixing corn starch and water together. If you pour this slurry into your hand, it will run right off of your hand like a liquid. But as soon as you start to stir the slurry, it hardens. Stirring is an example of energy being added. Energy can also be added in the form of heat or stretching. These fluids are collectively known as pseudoplastic fluids.

You can see on this graph typical (Newtonian) fluids compared to shear-thinning and shear-thickening fluids. Newtonian fluids increase viscosity at the same rate as the shear thickening fluids. But the pseudoplastic fluids increase at a different rate. The more stirring force that is added to the corn starch slurry, the more viscosity it will have. The equation for pseudoplastic fluids takes this into account by adding an exponent called the *flow behavior index.* This is a constant for each liquid, shown as *m.*

Most food companies (and other companies) frequently check the viscosity of their products. Typically, there is an acceptable range, and anything outside of that range is investigated and not sold. The apple juice and yogurt from the beginning of the lesson probably would not have fallen within the acceptable range. In order for the viscosity of these items to be checked, the yogurt would have to be run through a viscometer to measure the force necessary to move, and the apple juice could be put on a slight incline to see how far it will move in ten seconds. The apple juice, being a Newtonian fluid, can then use the Newtonian equation to determine the viscosity and see if it is in the acceptable range. The yogurt, being a pseudoplastic fluid (because when you stir it the viscosity can decrease), will need to use the pseudoplastic equation to determine the viscosity.

**Viscosity** is the resistance to flow, or how thick a fluid is. The viscosity of a fluid can be measured with simple equipment, such as seeing how far a fluid can flow down an incline. Or we can use equipment such a viscometer, which measures the amount of force needed to move through a material. The information obtained can be used in the viscosity equation which multiplies **shear rate** by a proportionality factor 'n'. If the fluid is a Newtonian fluid, then it is a direct proportion between the shear rate and viscosity. If the fluid is a pseudoplastic, then the flow behavior index constant needs to be added as an exponent. This information can be used for quality assurance in companies such as yogurt processors.

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High School Physics: Help and Review22 chapters | 265 lessons

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