No matter where we are, we’re almost always affected by our environment.

Because, we’re affected by the medium that we’re in. Usually that medium is a fluid, like air.

And, to understand how these fluids work, and to be able to optimize our designs, we’re going to need to learn about fluid mechanics. Fluid mechanics explains how the air moves around your car, how food coloring moves through water, making all those pretty patterns. And it explains what makes quicksand act like, well, quicksand.

All of which seems worth knowing, don’t you think? [Theme Music] So far, we’ve talked systems versus their surroundings. We’ve learned that mass and energy cannot be created or destroyed, but that they can be converted. What this means for us as engineers is that, in the real world, we can’t simply focus on what’s going on inside our system.

We need to think about the outside as well. That’s because machines, buildings, even our own bodies, are influenced by their surroundings. To see what I mean, let’s say we’re designing a new car.

We’ve already learned a good deal about engines, so you probably have a decent idea of what should go inside the car. But what about the outside of the car? While a car is moving, it’s going to interact with the fluid that it’s moving through which will be air in most cases.

Unless you’re that Tesla that got sent into space. As the car interacts with the air, the two can affect one another, and this can lead to what we call transfer. You know what transfer is, right?

When something moves, or is moved, from one place to another? There can be a transfer of momentum, or a transfer of heat. Maybe even mass.

But if we’re looking at moving fluids, then we’ll often have a transfer of momentum, which can be better understood with the help of fluid mechanics. Fluid mechanics studies how fluids respond to the forces exerted on them. So how exactly do fluids move?

And how does a particle, or anything for that matter, move within a fluid? To answer these questions, we need to know about stress, strain, and viscosity. Now, if you’ve been a student of physics for any amount of time, I’m sure you’re familiar with stress and strain in the colloquial sense – especially around exam time.

But here, of course, they mean something completely different. Suppose we have a fluid between two flat plates. If we were to move the bottom plate, what would happen to the fluid?

How would it move? Well, at the top and bottom, where the fluid is in contact with the surface, the individual particles of the fluid will go through something called the no-slip condition. In the no-slip condition, a fluid in motion will come to a complete stop at a solid surface and assume a zero velocity relative to the surface.

Basically, the particles of the fluid that are touching the solid will stick to its surface, meaning that they won’t slip. Because of this, the fluid particles in contact with the bottom plate will move with it, while the fluid particles at the top will stay in place with the stationary plate. This is all happening due to stress, the force that’s applied to a cross-sectional area of an object or substance.

If the force is normal, or perpendicular to the surface of the object, then we have normal stress. If it’s parallel, then we have shear stress. You thought I was gonna say “parallel stress,” didn’t you?

We can find stress by taking the applied force and dividing it by our cross-sectional area. Now, once a fluid is stressed, the degree to which it stretches is called strain. Simply put, strain is the deformation that stress causes on a system.

If the deformation causes something in a system to become either shorter or longer, then we can find its strain by taking the change in length and dividing it by the initial length. And this is called normal strain But if the deformation is a change in angle between two segments that had been perpendicular to each other, then we have shear strain. And we can find that by subtracting the change in angle from the original angle, which will either be pi over 2 or 90 degrees, depending on your units.

So all of this is what would happen if our bottom plate was moving. But what if neither plate moved, and we had a pump driving the flow of the fluid between them? Well, the same no-slip condition would apply, so while the fluid moved, its particles at the surface of the two plates would stay stationary.

But another thing that we’d need to take into account is viscosity. Viscosity is essentially a measure of a fluid’s resistance to flow, and it’s often referred to as the thickness of a fluid. For example, water has a low viscosity, since it flows pretty easily, while honey and other thick, sticky fluids have a much higher viscosity.

Some fluids will also thicken when exposed to stress, like when you whisk water mixed with cornstarch. But others will thin out when exposed to stress, like quicksand, which is just water mixed with lots of sand. The great Sir Isaac Newton gave us a way of describing how fluids move with his law of viscosity.

Simply put, this law describes Newtonian fluids as fluids with a viscosity that’s independent of stress. No matter how much stress you put on the fluid, its viscosity never changes. While no real fluid is perfectly Newtonian, many fluids, like air and water, are close enough that we can think of them that way.

Non-Newtonian fluids, on the other hand, don’t follow the law of viscosity. Their viscosity can change under stress, and therefore their strain can, too. A non-Newtonian fluid will actually thicken or thin out if you apply a force to it, which is exactly what happens when you step into quicksand.

The stress of you stepping onto it makes it become less viscous. And then you’re in trouble. Now, there’s still the matter of how one fluid moves within another fluid.

And to understand that, we should turn to the work of British engineer Osborne Reynolds. In 1868, just a year after graduating college, Reynolds became the first professor of engineering at Owens College in Manchester. He spent much of his career studying fluid mechanics, and one of his greatest contributions was his work on fluid flow patterns.

In 1883, Reynolds conducted an experiment that revealed there are two main types of flow in a pipe: laminar and turbulent. This experiment was so influential that the device that he used to conduct it was still used well into the 21st century. In his experiment, Reynolds used a colored fluid with the same density of water, and injected a very thin stream of it into a large transparent tube with water flowing through it.

When he injected the dye into slow-moving water, the flow of the dye maintained its place and pattern in the center of the water. We call this laminar flow. But when Reynolds injected the dye into water that was moving fast, the dye spread out and diffused, mixing with the water and coloring it.

This is called turbulent flow. Those were the two main types of flow that Reynolds found, but we also have something called transitional flow. Transitional flow is a mixture of laminar and turbulent flow.

It often has turbulence in the center of the pipe, and laminar flow near the edges. Reynolds’ experiment allowed him to determine when the transition would occur from laminar to turbulent, giving us the quantity we now know as the Reynolds number. We can find the Reynolds number for the flow of a fluid in a pipe by taking the diameter of the pipe and multiplying it by the velocity of the fluid and the density of the fluid, then dividing all of that by the viscosity of the fluid.

Now, the value we get for our Reynolds number will be dimensionless, meaning there are no units attached to it, but it can tell us a lot about the movement of a fluid. It lets us know how predictable, or chaotic, our fluid flow will be. That’s because we can look at the Reynolds number as a ratio of inertial forces to viscous forces.

Inertial forces represent the driving kinetic movement of the fluid, which result in chaotic flow movement, like the swirling motion of eddies and vortices. Viscous forces represent resistance to flow and are more likely to provide slow, steady motion. So the more powerful your viscous forces are, the slower and more controlled the fluid’s motion will be.

The higher your inertial forces are, the more chaotic your flow will be. Therefore, a low Reynolds number represents laminar flow, while a high Reynolds number represents turbulent flow. In a pipe, laminar flows will usually have a Reynolds number lower than 2100, while turbulent flows will usually be higher than 4000.

And a Reynolds number between these two values typically represents transitional flow. Understanding fluid mechanics allows us to use and apply equipment for fluid flow, like pumps and pipes. And we can also apply this knowledge so we can better understand how things move inside a fluid.

Like that new car we’re designing. If we’re testing our new car in a wind tunnel, we’ll want to see how the air around the car is moving and design our vehicle to account for the flow. The more resistance our cars have from the air, the harder it is to go faster and the more fuel they’ll need to use to travel at a given speed.

This is why understanding fluid flow is so important. So remember, it’s not just the system that matters, but also the surroundings. Today was all about fluid mechanics.

We talked about the different scales that we work with as engineers as well as mass and energy transfers. We learned about the no-slip condition and the different types of stress and strain that we’ll encounter. Newton’s law of viscosity gives us a way to describe fluid movement, and Reynold’s number helps in determining the difference between laminar and turbulent flow.

I’ll see you next time, when we’ll learn even more about fluid flow and some of the equipment behind momentum transfer. Crash Course Engineering is produced in association with PBS Digital Studios. You can head over to their channel to check out a playlist of their amazing shows, like The Art Assignment, The Origin of Everything, and Physics Girl.

Crash Course is a Complexly production and this episode was filmed in the Doctor Cheryl C. Kinney Studio with the help of these wonderful people. And our amazing graphics team is Thought Cafe.