At a basic level, matter is often sorted into solids, liquids, and gases. Fluid mechanics simplifies this a bit. It groups liquids and gases together under one umbrella: fluids. What do a stream of water and the air you're breathing have in common? They both flow.

This ability to flow is the defining characteristic of a fluid. A solid, like a block of wood, will resist a force trying to change its shape. If you push on the side of it, it might move, but it won’t continuously deform. A fluid, on the other hand, will. If you drag your hand through water, the water moves out of the way and keeps moving as long as you apply force. It has no fixed shape of its own and will take the shape of whatever container it's in.

This leads to a key distinction. Solids resist shear stress by deforming to a fixed point. Fluids resist the rate of deformation. Think about stirring honey versus stirring water. The honey feels thicker because it offers more resistance to your stirring motion. This property is called viscosity.

Another important property is density, which is the mass of the fluid packed into a given volume. We represent it with the Greek letter rho, $\rho$. A cubic meter of water is much heavier than a cubic meter of air because water is far denser.

Finally, there's pressure. In a static fluid, pressure is the force exerted by the fluid on a surface, spread out over the area of that surface. It acts in all directions at once. When you dive into a pool, the pressure you feel in your ears comes from the weight of all the water above you.

Even though fluids are made of countless individual molecules constantly bumping into each other, it's impractical to track every single one. Instead, in fluid mechanics, we usually treat the fluid as a continuum. This is an assumption that the fluid is a continuous substance, without any gaps.

This allows us to talk about properties like density and velocity at a specific point in the fluid, rather than worrying about individual molecules. The continuum assumption works incredibly well as long as we are looking at scales much larger than the distance between molecules, which is almost always the case in engineering and physics.

When fluids move, they can do so in different ways. The flow can be smooth and orderly, like a slow-moving river. This is called laminar flow, where the fluid moves in parallel layers with little to no mixing. The layers slide past one another smoothly.

On the other hand, the flow can be chaotic and irregular, like a raging waterfall or smoke rising from a chimney. This is turbulent flow. It’s characterized by eddies and swirls, and it causes the fluid properties to fluctuate rapidly at any given point.

Whether a flow is laminar or turbulent has a massive impact on things like drag on a vehicle or the way pollutants spread in the atmosphere. The transition between these two states is one of the most complex and important topics in all of fluid dynamics.

The behavior of fluids is governed by a few fundamental physical laws that you might already know. These principles form the bedrock of fluid mechanics.

First is the conservation of mass. This is a simple but powerful idea: mass cannot be created or destroyed. For a fluid, this means that if you have flow going into a defined volume, the same amount of mass must either flow out or accumulate inside. The net mass flow into a volume equals the rate of increase of mass within that volume.

Second is the conservation of momentum, which is essentially Newton's Second Law of Motion ($F=ma$) applied to fluids. This principle states that the rate of change of momentum of a fluid is equal to the net forces acting on it. These forces include pressure, viscosity (friction), and gravity.

Finally, there's the conservation of energy. The total energy of a fluid, which includes kinetic energy (from motion), potential energy (from height), and internal energy (from temperature), is conserved. Energy can change forms, for instance from potential to kinetic as water flows downhill, but the total amount remains constant, aside from any work done on the fluid or heat added to it.

These three conservation laws are the starting point for deriving the complex equations, like the Navier-Stokes equations, that allow us to model and predict how fluids will behave in nearly any situation imaginable.