Fluid dynamics

In physics, physical chemistry, and engineering, fluid dynamics is a part of fluid mechanics that studies how fluids like liquids and gases move. It includes areas such as aerodynamics (the study of air moving) and hydrodynamics (the study of water moving).

Fluid dynamics is very useful. It helps us calculate forces and moments on aircraft, figure out how much petroleum moves through pipelines, predict weather patterns, and understand big movements in nature like oceans and the atmosphere.

Solving problems in fluid dynamics usually means finding out properties of the fluid, such as how fast it is moving, its pressure, how heavy it is, and its temperature, all depending on where and when you look. Before the twentieth century, the term "hydrodynamics" was used to mean fluid dynamics, and some names still reflect this today.

Equations

See also: Transport phenomena

Fluid dynamics relies on basic rules called conservation laws. These include keeping track of how much stuff there is, how it moves, and how energy changes. These rules come from classical mechanics and are used even when studying tiny particles or space-time curves.

Fluids are treated as if they fill space completely, even though they are made of tiny particles. This helps scientists study things like how dense a fluid is, how much pressure it has, and how fast it moves.

For many fluids, the Navier–Stokes equations describe how the fluid moves. These are complex math rules that are often solved using computers. Sometimes they can be made simpler to solve more easily.

To fully describe how a fluid behaves, we also need a thermodynamic equation of state. This tells us how pressure changes with other things like temperature and density. One common example is the perfect gas equation:

p = ρ R_u T / M

where p is pressure, ρ is density, T is temperature, R_u is a constant, and M is the molar mass of the gas.

Conservation laws

Three main conservation laws help us understand fluid dynamics. They can be used in two ways: looking at a fixed space or a moving space.

Mass continuity (conservation of mass)

The amount of fluid mass inside a space must match the flow of fluid in and out. This means mass isn’t created or destroyed.

Conservation of momentum

This law tells us that changes in how much motion fluid has inside a space come from fluid flowing in and out, and forces acting on the fluid.

Conservation of energy

Energy can change forms, but the total amount stays the same. This law helps us understand how energy moves and changes in fluids.

Classifications

All fluids can change shape and move, but how they move depends on things like pressure and temperature. Sometimes these changes are small, so we can treat the fluid as if its density stays the same. This makes the math easier.

Fluids can also act differently depending on how they flow. Some, like water and air, follow simple rules where their resistance to flow is steady. Others, like honey or blood, have more complex behaviors. We study these using special tools to understand how they move and change.

The way fluids move can also be calm and steady or wild and turbulent. Scientists use different models to describe these movements, especially when dealing with big objects like airplanes. These models help us understand forces and flows even when the math gets very complex.

Multidisciplinary types

Flows according to Mach regimes

Main article: Mach number

Many flows, like water moving through a pipe, happen at low Mach numbers (subsonic flows). But in aerodynamics and machines that move air, flows often happen at speeds close to or faster than M = 1 (transonic flows), supersonic, or even hypersonic flows. At these high speeds, new things can happen, like changes in the flow or shock waves.

Reactive versus non-reactive flows

Reactive flows are flows where chemicals react. These are important in many areas, like combustion in engines, propulsion devices such as rockets and jet engines, detonations, fires, and even in space science. Besides keeping track of mass, movement, and energy, we also need to watch how different substances change during these reactions.

Magnetohydrodynamics

Main article: Magnetohydrodynamics

Magnetohydrodynamics is the study of how electrically conducting fluids move in electromagnetic fields. Examples include plasmas, liquid metals, and salt water. To understand this, we solve the fluid flow equations together with Maxwell's equations of electromagnetism.

Relativistic fluid dynamics

Relativistic fluid dynamics looks at how fluids move at speeds close to the velocity of light. This area considers effects from both the special theory of relativity and the general theory of relativity. The rules for this are created using Riemannian geometry in Minkowski spacetime.

Fluctuating hydrodynamics

This part of fluid dynamics adds random changes to the normal fluid flow equations to show tiny movements caused by heat. As explained by Landau and Lifshitz, a white noise part from the fluctuation-dissipation theorem of statistical mechanics is added to the viscous stress tensor and heat flux.

Terminology

The idea of pressure is very important when studying how fluids move. Pressure can be found at every point in a fluid, whether it is moving or not. It can be measured using special tools like an aneroid or a mercury column.

In fluid dynamics, there are some special terms that are not used in other areas of fluid study. For example, there are ideas like total pressure and dynamic pressure that come from Bernoulli's equation. These are not the same as regular pressure and cannot be measured with common tools. To make things clearer, many people use the term static pressure when talking about pressure in fluid dynamics. Static pressure is the same as regular pressure and can be found at every point in a flowing fluid.

A special point in a fluid flow where the movement stops next to a solid object is called a stagnation point. The pressure at this point is known as stagnation pressure. These ideas help scientists understand how fluids behave in different situations.

Applications

Fluid dynamics is used in many important ways. It helps us understand how air moves around airplanes and how liquids flow through pipes. Scientists also use it to predict weather and study big movements in the oceans and atmosphere. This knowledge is very useful for many different fields.