Wikipedia:WikiProject Fluid dynamics/Top draft

Fluid mechanics is the study of the macroscopic physical behaviour of fluids. Fluids are specifically liquids and gases though some other materials and systems can be described in a similar way. The solution of a fluid dynamic problem typically involves calculating for various properties of the fluid, such as velocity, pressure, density, and temperature, as functions of space and time.

Fluid mechanics has a wide range of applications. For example, it is used in calculating forces and moments on aircraft, the mass flow of petroleum through pipelines, and in prediction of weather patterns. Fluid mechanics offers a mathematical structure that underlies these practical discipines which often also embrace empirical and semi-empirical laws, derived from flow measurement, to solve practical problems.

The concept of a fluid is surprisingly general. For example, some of the basic mathematical concepts in traffic engineering are derived from considering traffic as a continuous fluid.

The continuity assumption

Gases and liquids are composed of molecules which collide with one another and with solid objects. The continuity assumption, however, considers fluids to be continuous, making it a subdiscipline of continuum mechanics. That is, properties such as density, pressure, temperature, and velocity are taken to be well-defined at infinitely small points, and are assumed to vary continuously from one point to another. The discrete, molecular nature of a fluid is ignored.

The reliability of this continuity premise is assessed using the Knudsen number. Physical systems with Knudsen numbers at or above unity require the use of statistical mechanics, which itself provides the underlying physics of fluids which is an input to fluid mechanics.

Continuum mechanics	Solid mechanics: the study of the physics of continuous solids with a defined rest shape.	Elasticity: which describes materials that return to their rest shape after an applied stress.
		Plasticity: which described materials that permanently deform after a large enough applied stress.	Rheology: the study of materials with both solid and fluid characteristics
	Fluid mechanics	Non-Newtonian fluids
		Newtonian fluids

The important distinction between Newtonian and Non-newtonian fluids is discussed further in the article on viscosity.

Overview of fluid mechanics

Fluid mechanics	Fluid statics
	Fluid dynamics	Laminar flow	Newtonian fluids	Ideal fluids	Incompressible flow
					Compressible flow
				Viscous fluids
					Computational fluid dynamics
					Solutions for specific regimes
			Non-Newtonian fluids	Rheology
		Turbulence

Foundations of fluid mechanics

The foundational axioms of fluid mechanics are the conservation laws, specifically, conservation of mass, conservation of momentum (also known as Newton's second law), and conservation of energy. These are based on classical mechanics and are violated in relativistic mechanics.

These basic laws are used, along with empirical experience, to derived the basic laws of fluid statics. This then provides a basis through which fluid dynamics can be developed through the introduction of interial effects.

The simplest problems of fluid dynamics are those that set all changes of fluid properties with time to zero. This is called steady flow, and is applicable to a large class of problems, such as lift and drag on a wing or flow through a pipe.

Laminar versus turbulent flow

Turbulence is flow dominated by recirculation, eddies, and apparent randomness. Flow in which turbulence is not exhibited is called laminar.

It is believed that turbulent flows obey similar equations to the laminar case. However, the flow is so complex that it is not possible to solve turbulent problems from first principles with the computational tools available today or likely to be available in the near future. Turbulence is instead modeled using one of a number of turbulence models and coupled with a flow solver that assumes laminar flow outside a turbulent region.

Newtonian versus non-Newtonian fluids

Sir Isaac Newton showed how stress and the rate of change of strain are related in a simple was for many familiar fluids, such as water and air. These Newtonian fluids are characterised by a simple viscosity.

However, some other materials, such as milk and blood, and also some plastic solids, have more complicated non-Newtonian stress-strain behaviours. These are studied in the sub-discipline of rheology.

Compressible versus incompressible Flow

A fluid problem is called compressible if changes in the density of the fluid have significant effects on the solution. If the density changes have negligible effects on the solution, the fluid is called incompressible and the changes in density are ignored.

In order to determine whether to use compressible or incompressible fluid dynamics, the Mach number of the problem is evaluated. As a rough guide, compressible effects can be ignored at Mach numbers below approximately 0.3. Nearly all problems involving liquids are in this regime and modeled as incompressible.

The incompressible Navier-Stokes equations are simplifications of the Navier-Stokes equations in which the density has been assumed to be constant. These can be used to solve incompressible problems.

Viscous versus inviscid flow

Viscous problems are those in which fluid friction has an important effect on behaviour. Problems for which friction can safely be neglected are called inviscid.

Inviscid flow is governed by the Euler equations for which there are many simple solution methods depending on what specific assumptions can be made. In addition, the boundary condition of the equations is that flow is stationary normal to a solid surface.

Viscous flows are governed by the Navier-Stokes equations which must satisfy the stricter boundary condition that flow is stationary both normal and tangential to a solid surface. These are nonlinear differential equations that typically need to be solved using the techniques of computational fluid dynamics.

The Reynolds number can be used to evaluate whether viscous or inviscid equations are appropriate to the problem. High Reynolds numbers indicate that the inertial forces are more important than the viscous forces. However, even in high Reynolds number regimes certain problems require that viscosity be included in a thin boundary layer, even where the Euler equations are used for the flow distant from a body.

The Navier Stokes equations can be applied to a vast range of problems.

Solutions of the Navier-Stokes equations for specific regimes	Flow past solid bodies: Drag (force), Lift (force)	Rigid bodies	Steady flow:	Low Reynolds number: Stokes flow
				High Reynolds number: Boundary layers
			Unsteady flow: Flow-induced vibration
		Elastic bodies: Aeroelasticity
	Free-surface flows: surface waves etc solitons
	Buoyancy effects
	Rotating frames: with particular applications to meteorology and oceanography

History

Main article: History of fluid mechanics

Applications

Fluid phenomena

The following observed fluid phenomena can be characterised and explained using fluid mechanics: