Fluid dynamics is the study of how liquids and gases move, and it helps us understand everything from weather to airplane flight.

Key idea: Fluid dynamics is built on fundamental conservation laws for mass, momentum, and energy, and often uses the idea that fluids are continuous substances.

The basic rules of fluid dynamics come from fundamental laws of physics. These are the laws of conservation of mass, conservation of linear momentum, and conservation of energy. Think of these as unbreakable rules that fluids must follow.

For example, the law of conservation of mass means that fluid cannot just appear or disappear; if you have a certain amount of water flowing into a pipe, the same amount must flow out, unless some is stored or leaks. The law of conservation of linear momentum is like Newton's second law for fluids, explaining how forces make fluids change their motion. The law of conservation of energy means that the total energy in a fluid system stays the same, even if it changes from one form (like movement) to another (like heat).

Scientists also make an important assumption called the continuum assumption. This means they treat the fluid as a continuous substance, like a smooth jelly, rather than a collection of tiny, separate molecules. Even though we know fluids are made of molecules, for most calculations, it is easier and accurate enough to pretend they are perfectly smooth. This allows properties like density and pressure to be defined at every tiny point in the fluid.

Key idea: Complex equations like the Navier Stokes equations are used to model fluid behavior, often requiring simplifications or computer calculations.

To describe how fluids move, scientists use complex mathematical equations. One of the most important sets of equations for many fluids, like air and water, is called the Navier Stokes equations. These equations are very powerful but also very difficult to solve exactly.

Imagine trying to predict every tiny swirl and ripple in a fast moving river. That is how complicated these equations can be. Because they are so hard, scientists often use computers to find approximate solutions, or they simplify the equations for specific situations.

For example, if a fluid is not moving too fast and is not ionized, these equations can describe its flow. When simplified, they can help us solve some basic fluid problems. Besides these, another equation, called a thermodynamic equation of state, is needed to fully describe a fluid's behavior. This equation tells us how pressure relates to other properties like density and temperature. A common example is the ideal gas law, which describes how gases behave under certain conditions.

Key idea: Fluid flows are classified as compressible or incompressible based on whether their density changes significantly during movement.

One important way to classify fluid flows is by whether they are compressible or incompressible. All fluids can be compressed a little bit; if you squeeze a gas or even a liquid, its density will change. However, for many situations, the changes in pressure and temperature are so small that the fluid's density hardly changes at all. In these cases, we can treat the fluid as incompressible.

Think of water flowing through a pipe. Even if the pressure changes a bit, the water's density stays pretty much the same. So, we can treat water as incompressible for most everyday problems. But if you are dealing with a gas moving very fast, like air around a supersonic jet, its density changes a lot, and you must treat it as compressible.

A common misconception is that liquids are always incompressible and gases are always compressible. While liquids are generally much harder to compress than gases, both can be either, depending on the situation. For gases, scientists use a number called the Mach number to decide. If the Mach number is below about 0.3 (meaning the gas is moving much slower than the speed of sound), it can usually be treated as incompressible. Above that, it is considered compressible.

⚠️Watch out: Many people think liquids are always incompressible and gases are always compressible, but whether a fluid is treated as compressible depends on how much its density actually changes under the specific conditions of the flow.

Another way to categorize fluids is by how they respond to forces that try to deform them. Almost all fluids have some stickiness or internal friction, which we call viscosity. This means that if one layer of fluid moves past another, there is a resistance.

Sir Isaac Newton noticed that for many common fluids, like water and air, this resistance (or stress) is directly related to how fast the layers are moving past each other. These are called Newtonian fluids. For these fluids, their stickiness (viscosity) is constant, no matter how fast they are stirred or moved.

However, some fluids are more complicated. These are called non Newtonian fluids. Their stickiness can change depending on how much force is applied. For example, ketchup is a non Newtonian fluid; it is thick in the bottle, but if you shake it hard, it becomes more liquid. Other examples include blood, honey, and some paints. The study of these complex fluids is called rheology.

“For many common fluids, like water and air, their stickiness is constant, no matter how fast they are stirred or moved.”

Key idea: The Reynolds number helps determine if a fluid's motion is dominated by inertial forces (fast, less sticky) or viscous forces (slow, very sticky).

When fluids move, two main types of forces are at play: inertial forces (related to the fluid's mass and how it resists changes in motion) and viscous forces (related to its stickiness or internal friction). The balance between these two forces helps us understand how a fluid will behave.

Scientists use a special number called the Reynolds number to compare these forces. If the Reynolds number is very low, it means viscous forces are much stronger. In these cases, the fluid moves very slowly and smoothly, like honey dripping. This is called Stokes flow or creeping flow, and we can often ignore the inertial forces.

If the Reynolds number is very high, inertial forces are much stronger. The fluid moves quickly, and its stickiness has less effect on the overall motion. In these situations, we sometimes pretend the fluid has no viscosity at all; this is called an inviscid flow. While this simplification makes calculations easier, it is important to remember that even for very fast flows, viscosity is still important near solid surfaces, creating a thin layer called a boundary layer where friction is key.

Fluid flows can also be described as steady flow or unsteady flow. In a steady flow, the fluid properties (like speed, pressure, and density) at any given point do not change over time. Imagine a smooth, constant stream of water from a faucet; if you measure the water speed at one spot, it always stays the same. This makes steady flows much easier to study.

In contrast, an unsteady flow means that these properties change over time at a given point. A good example is a turbulent river with swirling eddies and unpredictable currents. The water speed and direction at any spot would constantly change. While a flow might seem unsteady from one viewpoint, it could be steady from another. For instance, if you are floating in a boat with the current, the water around you might seem steady, even if it is moving fast relative to the riverbank.

Turbulent flow is a common type of unsteady flow. It is characterized by chaotic, swirling motions and apparent randomness. Most flows we see in everyday life, like smoke rising from a fire or air currents around a building, are turbulent. The Navier Stokes equations can describe turbulent flows, but solving them directly for turbulence is incredibly difficult, even for powerful computers. So, scientists often use simplified models to understand and predict turbulence.

“In a steady flow, the fluid properties at any given point do not change over time, making it much easier to study.”