Fluid mechanics

Fluid mechanics is a major branch of physics. It focuses on the mechanics of fluids and the forces acting upon them. In this context, a fluid is any substance that can flow. This includes liquids, gases, and even plasmas. The field is a subdiscipline of continuum mechanics. This means scientists model matter from a macroscopic viewpoint. They look at the big picture rather than individual atoms. This approach allows them to treat matter as a continuous substance. This makes it possible to study how large systems behave.

Scientists divide this field into two primary branches. The first is fluid statics, also known as hydrostatics. This branch studies fluids that are at rest in stable equilibrium. It explains common phenomena, such as why atmospheric pressure changes with altitude. It also explains why oil and wood float on water. The second branch is fluid dynamics. This is the study of fluids in motion. It examines how forces cause liquids and gases to flow. To solve problems in dynamics, scientists calculate properties like velocity, pressure, density, and temperature. These values change based on both space and time.

Fluid dynamics contains several specialized subdisciplines. Aerodynamics is the study of air and other gases in motion. Hydrodynamics is the study of liquids in motion. These fields use empirical laws derived from measuring actual flows. These measurements help solve practical problems in many industries. For example, aerodynamics helps engineers calculate the forces on an aircraft. Hydrodynamics can help determine the mass flow rate of petroleum through a pipeline. These studies are essential for predicting weather patterns and understanding nebulae in space.

Fluid mechanics has a very long history of discovery. The study began at least as far back as ancient Greece. Archimedes investigated buoyancy and formulated Archimedes' principle. This is often considered the first major work on the subject. Later, Iranian scholars Abu Rayhan Biruni and Al-Khazini used experimental methods. During the Renaissance, Leonardo da Vinci made important observations and experiments. Isaac Newton investigated viscosity, which is a fluid's resistance to flow. In 1739, Daniel Bernoulli introduced mathematical fluid dynamics in his work, Hydrodynamica.

Many mathematicians later advanced the field through complex equations. Claude-Louis Navier and George Gabriel Stokes developed the Navier–Stokes equations. These differential equations describe the force balance at a specific point in a fluid. They describe how momentum changes in response to pressure and viscosity. Because these equations are mathematically complex, they are hard to solve. Most complex cases, like turbulence in weather systems, require computers. This modern approach is called computational fluid dynamics, or CFD. Scientists also use particle image velocimetry to visualize fluid flow.

When studying fluids, scientists use the continuum assumption. This is an idealization where fluids are treated as continuous. Even though fluids are made of molecules, we act as if they are a solid mass. This works well unless the scale is extremely small. To check if this assumption is valid, scientists use the Knudsen number. This is the ratio of the molecular mean free path to the system's scale. If the number is below 0.1, the continuum hypothesis works well. If it is larger, scientists must use statistical mechanics instead.

Fluids are also categorized by how they react to force. A Newtonian fluid is named after Isaac Newton. In these fluids, the shear stress is linearly proportional to the velocity gradient. This means the fluid will continue to flow regardless of the forces applied. Water is a common example of a Newtonian fluid. In contrast, some fluids are described as viscous or inviscid. An inviscid fluid has no viscosity, which is an idealization used in math. Most real-world fluids are viscous, especially near solid surfaces in a boundary layer.

Fluid mechanics connects to many different scientific disciplines. It is used in mechanical, aerospace, civil, chemical, and biomedical engineering. It is also vital to geophysics, oceanography, and meteorology. In medicine, it helps doctors understand blood pressure. It even applies to social sciences through crowd dynamics. By understanding these principles, we can model everything from explosions to traffic engineering. The field remains an active and essential part of modern science.