# Fluid

In physics, a **fluid** is a substance that continually deforms (flows and cannot resist deformation) under applied shear stress or external force. Fluids include gases, liquids, and plasma.

All fluids are compressible (that is, their density increases under increasing pressure) to some extent, but liquids are much less compressible than gases and are generally considered incompressible. Even gases may be treated as incompressible provided the airflow speeds involved are not high.

For subsonic airflow over an airplane below about 150 m/s (492 ft./s or about 336 mph), air may be treated as incompressible, i.e., the density remains the same throughout the flow. At higher speeds, the effects of compressibility must be taken into account.

## Fluid mechanics

**Fluid mechanics** is one of the oldest and broadest fields of engineering. It deals with the properties and behavior of fluids, i.e., liquids and gases at rest (fluid statics) or in motion (fluid dynamics). Because of their ability to flow, liquids and gases have many properties in common not shared by solids.

**Fluid statics** includes the study of pressure, density, Pascal’s law, and Archimedes’ principle. **Fluid dynamics** includes the study of streamlines (see streamlining), Bernoulli’s law, and the propagation of waves.

Engineers use fluid mechanics in the design of bridges, dams, and ships. Physicists use it in studying the structure of the atomic nucleus, and astronomer uses it to explain the spiral structure of some galaxies.

The study of fluids in motion, or fluid dynamics, makes up the more significant part of fluid mechanics. Branches of fluid dynamics include hydrodynamics (study of liquids in motion) and aerodynamics (study of gases in motion) as well as vortex dynamics, gas dynamics, computational fluid dynamics (CFD), convection heat transfer, flows of turbomachinery, acoustics, bio-fluids, physical oceanography, atmospheric dynamics, wind engineering, and the dynamics of two-phase flows. The modern design of aircraft, spacecraft, automobiles, ships, land and marine structures, power and propulsion systems or heat exchangers relies on a clear understanding of the relevant fluid mechanics.

## Fluid flow

A **fluid flow** may be described in two different ways: the Lagrangian approach (named after the French mathematician Joseph Louis Lagrange), and the Eulerian approach (named after Leonhard Euler, a famous Swiss mathematician).

In the Lagrangian approach, one particle is chosen and is followed as it moves through space with time. The line traced out by that one particle is called a particle pathline.

A Eulerian approach is used to obtain a clearer idea of the airflow at one particular instant. One can look at a “photograph” of the flow of, for instance, surface ocean currents at a particular fixed time. The entire flow field is easily visualized. The lines comprising this flow field are called streamlines (see streamlining).

Thus, a pathline refers to the trace of a single particle in time and space, whereas a streamline presents the line of motion of many particles at a fixed time. The question of whether particle pathlines and streamlines are ever the same is considered next.

Of primary importance in understanding fluid movements about an object is the concept of a steady flow. On a windy day, a person calls the wind steady if, from where she stands, it blows continuously from the same direction at a constant speed. If, however, the speed or direction changes, the wind is “gusty” or unsteady. Similarly, the flow of a fluid (both liquid and air) about an object is steady if its velocity (speed and direction) at each point in the flow remains constant – this does not necessarily require that the velocity be the same at all points in the fluid.

This means that for unsteady flows, particle pathlines (the Lagrangian point of view) and streamlines (the Eulerian approach) are not equivalent. For a steady flow, however, a particle pathline and streamline are equivalent, and the Lagrangian point of view is the same as the Eulerian approach for flow visualization.

As well as steady or unsteady, fluid flow can be rotational or irrotational. If the elements of fluid at each point in the flow have no net angular (spin) velocity about the points, the fluid flow is said to be irrotational. One can imagine a small paddle wheel immersed in a moving fluid. If the wheel translates (or moves) without rotating, the motion is irrotational. If the wheel rotates in a flow, the flow is rotational.

According to a theorem of Hermann von Helmholtz, a German physicist who contributed much to theoretical aerodynamics, assuming zero viscosity, if a fluid flow is initially irrotational, it remains irrotational. In real life, viscosity effects are limited to a small region near the surface of the airfoil and in its wake. Most of the flow may still be treated as irrotational.

A simplifying argument often used to aid in understanding basic ideas about fluid flow is that of one-dimensional fluid flow. Flows may be considered one-dimensional where the flow parameters (for example density, velocity, temperature, pressure) vary as a function of one spatial variable (for example, length) and variations in the other two spatial dimensions (i.e., y and z) are negligible by comparison.

Simplifying assumptions about fluids are made: the first is that fluid is considered to be inviscid (no viscosity); the second is that it is incompressible. Further, the flow is considered steady and one-dimensional. Fluids with these characteristics are said to be ideal fluids or perfect fluids. Once solutions of problems relating to the lift and drag of ideal fluids, or the inviscid flow, have been made, a solution of the viscous flow in the thin boundary layer allows the effects of skin friction drag to be calculated.

### Laminar fluid flow

**Laminar flow** is non-turbulent flow in smooth parallel (non-intersecting) paths in layers that have different velocities. There are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids.

The term laminar flow describes one of the three types (the other two are transitional and turbulent) of behavior that a boundary layer can exhibit.

When a fluid (such as air) moves (or flows) past a solid surface, such as an airplane wing, a thin layer develops adjacent to the surface where frictional forces tend to retard the motion of the fluid. This layer is defined as the boundary layer.

In general, the most desirable state is one with a high degree of laminar flow, i.e., exhibits a low degree of friction drag. In particular, a high degree of laminar flow reduces the amount of fuel consumed by an aircraft and also increases its flight range.

### Laminar-turbulent transitional fluid flow

The process of a laminar fluid flow becoming turbulent is known as a **laminar-turbulent transition** (or **transitional flow**). The main parameter characterizing transition is the Reynolds number.

Each of these flows behaves in different manners in terms of their frictional energy loss while flowing and have different equations that predict their behavior. Transition is often described as a process proceeding through a series of stages. “Transitional flow” can refer to transition in either direction, that is laminar-turbulent transitional or turbulent-laminar, transitional flow.

### Turbulence or turbulent fluid flow

**Turbulence** (or **turbulent flow**) is a flow regime characterized by low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time. A flow that is not turbulent is called laminar flow. The (dimensionless) Reynolds number characterizes whether flow conditions lead to laminar or turbulent flow.

The flow of water over a simple smooth object, such as a sphere, illustrates it. At very low speeds the flow is laminar; i.e., the flow is smooth (though it may involve vortices on a large scale). As the speed increases, at some point, the transition is made to turbulent (“chaotic”) flow. In turbulent flow, unsteady vortices appear on many scales and interact with each other. Drag due to boundary layer skin friction increases.

The structure and location of boundary layer separation often change, sometimes resulting in a reduction of overall drag. Because the laminar-turbulent transition is governed by Reynolds number, the same transition occurs if the size of the object is gradually increased, or the viscosity of the fluid is decreased, or if the density of the fluid is increased.

## Superfluid (state of matter)

**Superfluidity** is a special quantum state of matter in which a substance (called **superfluid**) flows with zero viscosity (without loss of kinetic energy), by the absence of entropy and by having infinite thermal conductivity. The superfluids, if placed in a closed path, can flow infinitely without friction.

Superfluids have many unusual properties. They behave like typical components of solutions, with all the properties associated with normal fluid and superfluid components. Therefore it is impossible to set a temperature gradient in a superfluid, as it is impossible to set a potential difference in a superconductor.

Superfluidity was discovered by Pëtr Leonidovič Kapica, John F. Allen, and Don Misener in 1937. The study of superfluids is called quantum hydrodynamics.

### Superfluid applications

An important application of superfluids is in dilution coolers.

In the field of chemistry, superfluid helium-4 has been successfully used in spectroscopy techniques as a quantum solvent. Called Superfluid Helium Droplet Spectroscopy (SHeDS), it is of enormous interest in the study of gas molecules; since a single molecule solvated in a superfluid medium benefit from freedom of rotation: in this way, the molecule behaves as it would in the gaseous phase.