In this explainer, we will learn how to describe the effect of viscosity on fluid flow for vehicular, engineering, and medical applications.
Viscosity is a property of fluids that affects how those fluids move and how other objects move through fluids. Specifically, viscosity is the magnitude of internal friction in a liquid.
What this means is that a fluid with a higher viscosity will have more friction between its particles, meaning it is harder to do things like stir it. When comparing different fluids, you likely already have an understanding of which are more or less viscous. Consider two vials of liquid, one of honey and one of water.
Honey is a much more viscous fluid, and water is less viscous. This means that the honey, having more internal friction, will take longer to pour out of its vial than the water, which will easily slide out.
Viscosity also affects objects attempting to move through the fluid as well. Suppose we begin to stir the water and honey using some rods. The honey will induce a much greater drag force () on the rod than the water will. The drag force is the friction force applied to objects moving through a fluid.
This means the rod in the more viscous honey will be more resistant to motion. If you were to stir the two fluids with the same force, you would be able to stir the rod in the water much faster.
If you try stirring the honey faster, you will find that will increase as well, meaning more resistance to the motion. How much increases is related to the speed () at which you stir the fluid.
At low speeds, is proportional to , but at high speeds, is proportional to .
The exact speed at which the proportion begins to go from to is dependent on both the fluid and the object moving through it, so it is not possible to look up in a table somewhere.
Let’s look at some examples.
Example 1: Drag Force through Fluid Proportions
Which of the following most correctly describes how the drag force exerted by a fluid on an object moving through the fluid varies with the speed at which the object moves through the fluid?
- The drag force is proportional to the square root of the speed.
- The drag force is proportional to the speed.
- Below a certain speed, the drag force is proportional to the square root of the speed, but above this speed, the drag force is proportional to the speed.
- Below a certain speed, the drag force is proportional to the speed, but above this speed, the drag force is proportional to the square of the speed.
- The drag force is proportional to the square of the speed.
We know that, for fluids, at low speeds and at high speeds.
The drag force is not a constant proportion. It is not proportional to either the speed or the square of the speed at all times: it changes. It cannot be A, B, or E then.
Below a certain speed, the drag force is smaller, being only proportional to , but is not lower than . It cannot be the square root of . It cannot be C then.
The correct answer is thus D: Below a certain speed, the drag force is proportional to the speed, but above this speed, the drag force is proportional to the square of the speed.
Example 2: Graphical Representation of Drag Force Speed Relation on an Object Traveling through a Fluid
Which of the following most correctly shows how the drag force exerted by a fluid on an object moving through the fluid varies with the speed at which the object moves through the fluid?
At low speeds, . At high speeds, .
Graph A shows drag force increasing at a slower and slower rate as speed increases. The shape of the graph indicates that this is a situation where the drag force is proportional to the square root of speed, so it cannot be this one.
Graph B shows a drag force perfectly proportional to speed, but we know that it changes, so it cannot be this one either.
Graph D shows a drag force that does change with speed, starting as a line then gradually curving. However, we know that as speed increases, drag force should be increasing with a faster squared relationship, not a slower one.
Graph C correctly shows a drag force proportion that starts as a line and increases faster to become a squared proportion at higher speed. Graph C is the correct answer.
When stirring a fluid, its internal friction can prevent portions of it from mixing if it is viscous enough. Observe the diagram below showing the honey and water broken down into three different layers.
If we were to drop in some small green beads to both vials and stir them briefly, we would see the following.
The beads mix between the layers more easily in the less viscous water than in the honey. When layers are able to mix easily through stirring, this chaotic motion is described as turbulent.
The internal friction of the honey makes the layers more distinct and less likely to change. Change in a fluid due to some outside force is called deformation, and more viscous fluids are resistant to it.
Let’s look at some examples.
Example 3: Fluid Resistance to Deformation
If a fluid increases in viscosity, in which of the following ways does this change the fluid’s resistance to deformation?
- The resistance of the fluid to deformation is not affected.
- The fluid has greater resistance to deformation.
- The fluid has less resistance to deformation.
A fluid with a greater internal friction produces a greater drag force on anything attempting to change it. Resistance to deformation must change with viscosity, so the answer is not A.
Deformation means changing shape due to an outside force, and more internal friction means a fluid will hold its shape more easily. Thus, a viscous fluid will have greater resistance to deformation, not less.
The correct answer is B.
Example 4: Spinning Disk Oil Deformation
Thin layers of equal area and thickness of two different-colored oils are placed onto the central region of the top surface of two identical solid disks, as shown in the diagram. The disks are then rotated with equal angular velocities and the oils spread over the surfaces of the disks. The oils have the same density but different viscosities. Which of the oils has the greater viscosity?
- The yellow oil has the greater viscosity.
- The orange oil has the greater viscosity.
- Both oils have the same viscosity.
A more viscous fluid has a greater resistance to deformation. The two oils start with the same shape, but at the end of the same rotation, they have different shapes. They must have different viscosities, so the answer is not C.
The yellow oil’s shape has changed considerably more than the orange oil, meaning the yellow oil has less viscosity than the orange one. The correct answer is thus B, the orange oil has the greater viscosity.
The viscosity of a fluid, how it deforms and at what speeds it changes the drag force are of interest to engineering, where efficiency must be maximized. Machines that involve the use of fluid can be carefully planned out with specific values of viscosity to ensure proper operation.
Let’s look at an example.
Example 5: Lubricating a Cylinder with Vertical Reciprocal Motion
A piston undergoes vertical reciprocal motion within a cylinder in an engine, as shown in the diagram. Where there is contact between the piston and the cylinder, friction is produced. The friction can be reduced by coating the cylinder with a lubricating fluid. If the lubricating fluid used has a low viscosity, which of the following most correctly explains why parts of the cylinder will not retain sufficient lubrication?
- The lubricant will mainly stick only to the lower face of the cylinder.
- The lubricant will flow from the closed end of the cylinder toward the open end of the cylinder more than in the opposite direction.
- The lubricant will flow from the open end of the cylinder toward the closed end of the cylinder more than in the opposite direction.
- The lubricant will mainly stick only to the upper face of the cylinder.
- The lubricant will flow toward the center of the piston more than in the opposite direction.
A low-viscosity lubricant would not stick at all, to either the lower or the upper face of the cylinder, only pooling at the bottom of the inside. This is not ideal, as the idea is to lower the friction between the piston and the cylinder along its entire length. Answers A or D are not it.
A low-viscosity lubricant would be able to flow more toward the center of the piston but will also flow just as easily in the other direction, back toward the walls. The answer is not E.
Imagine a high-viscosity fluid like honey. It would get stuck all over the inside of the piston and resist the pull of gravity more easily.
If, instead of honey, the fluid was water, it would start on the sides of the cylinder just like the honey but would easily flow to the closed end of the cylinder due to gravity, along the inside near the bottom.
This presents a problem as the idea is to lubricate the entire cylinder, but a low-viscosity fluid would soon not sufficiently reduce friction near the open end of the cylinder, as it would flow toward the closed end due to gravity.
The correct answer is C.
When we talk about the viscosity of fluids, we do not just mean liquids; gases have internal friction too, though it is much less. It is still enough to create a drag force on objects moving through it, more commonly known as air resistance. This is just from air being a fluid, meaning this drag does not come from a wind moving the air in a particular direction.
As an object, such as the car in the diagram above, travels through air, it experiences a drag force. You can feel this force wanting to slow you down if you ever stick your hand out a car window when it is moving.
The proportions that drag force has with speed still hold with air, meaning it begins to increase with a squared relationship past certain speeds. This is why breaking speed records is so difficult, because every additional kilometre per hour gained requires exponentially more force to counteract the drag force.
Consider the difference between a car that travels at 10 m/s and another that travels at 20 m/s.
The drag force, , is more proportional to at the lower speed of 10 m/s, but it gets closer to being proportional to at the higher speed of 20 m/s. This means that the car requires more power and thus more fuel as it goes faster and faster. So while going at a higher speed means getting to a location faster, it also makes the car much more fuel inefficient.
Viscosity is also an important consideration in medical practices, as humans have many different fluids inside them. For example, blood is more viscous than water. When it leaves a human body, it begins to rapidly clot in a process called coagulation, increasing viscosity even more.
This is usually very helpful, as it forms a barrier to prevent more blood from leaving a wound, but blood continues to clot even when outside of the body. This means that when donating blood, the clots increase the viscosity to such a point that it would become impossible to use the blood after a certain point.
It would not be able to flow into or out of a blood bag very well at all, and it would actively harm someone if given to them (injecting yourself with honey is not good, no matter how much like blood it is)! To solve this, anticoagulants such as citrate are added to blood bags to ensure the viscosity does not increase too much. This allows the blood to flow easily out of the bag into a recipient’s body.
Let’s summarize what we have learned in this explainer.
- Viscosity is the magnitude of internal friction of a fluid.
- Objects moving through a fluid experience a drag force from friction, .
- At low speeds, . At high speeds, .
- Fluids with greater viscosity have greater resistance to deformation.