Everyone, in this video, we're going to start talking about fluids, which is sometimes called fluid mechanics, fluid dynamics, or sometimes just called liquids. Now, the first concept you'll need to know really well is the concept of density. So, we're just going to jump right in and get started.

Liquids and gases are types of what we call fluids. And the reason we use the term fluids is because they often share similar properties. Instead of repeating "liquids and gases" over again, we're just going to call these things fluids. Remember that the main characteristic of fluids is that unlike solids, which always have the same shape, fluids can actually change shape to fill their container. For example, water can fit inside of a cup, and you can pour it out into a bowl, and it'll change shape to fit the container.

You may remember density from an earlier science class. It's basically just a measure of how tightly the molecules are packed inside of a small volume. For example, I've got these two boxes right here. They're identical, which means they have the same exact volume. But in one of them, there are fewer molecules, and in the other, there are more of them, and they're more tightly packed together. So because this one has fewer molecules in the same space, this one has lower density and because this one has a lot of stuff in the same space, this one has high density.

Density itself is represented by the letter that we use is this one over here, which is the Greek letter rho (ρ). The definition of density is that it's the mass (m) divided by the volume (V),m/V. The units for it are kilograms for mass, and for volume, it's cubic meters (m^{3}). The volume of any shape is generally the form of length times width times height.

In many problems, you'll be given the density of a material and the dimensions of a material. Then you can always rearrange to find what the mass is by using the formula m=ρV. Objects of the same material are going to have the same density. Thus, if you have a small block of wood and a big one, they both have the same exact density.

Additionally, you also have a lot of problems in which liquids will mix inside a container and settle into layers. The higher density liquids are going to settle at the bottom. This is because higher density means these things are more compact, and gravity pulls them lower.

Let's run through a quick example. We're going to calculate the total weight of air molecules inside of a really large warehouse. We model this warehouse as a rectangle like this. Its dimensions are 100 meters by 100 meters by 10 meters. We have the density of air and also with gravity as g = 10 m/s^{2}. To calculate the total weight of air, remember that weight is not mass, weight (W) is W=mg. We use the equation for density ρ=mV to find the mass as m=ρV, substitute the values, and we get the weight as 1,225,000 Newtons. That's it for this example, folks. Let me know if you have any questions.