Flow velocity

In continuum mechanics the macroscopic velocity, also flow velocity in fluid dynamics or drift velocity in electromagnetism, is a vector field which is used to mathematically describe the motion of a continuum. The length of the flow velocity vector is the flow speed and is a scalar.

Definition

The flow velocity u of a fluid is a vector field

which gives the velocity of an element of fluid at a position and time

The flow speed q is the length of the flow velocity vector

and is a scalar field.

Uses

The flow velocity of a fluid effectively describes everything about the motion of a fluid. Many physical properties of a fluid can be expressed mathematically in terms of the flow velocity. Some common examples follow:

Steady flow

The flow of a fluid is said to be steady if does not vary with time. That is if

Incompressible flow

If a fluid is incompressible the divergence of is zero:

That is, if is a solenoidal vector field.

Irrotational flow

A flow is irrotational if the curl of is zero:

Fluid mechanics

Fluid mechanics is the branch of physics that studies the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. Fluid mechanics has a wide range of applications, including for mechanical engineering, geophysics, astrophysics, and biology. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion. It is a branch of continuum mechanics, a subject which models matter without using the information that it is made out of atoms; that is, it models matter from a macroscopic viewpoint rather than from microscopic. Fluid mechanics, especially fluid dynamics, is an active field of research with many problems that are partly or wholly unsolved. Fluid mechanics can be mathematically complex, and can best be solved by numerical methods, typically using computers. A modern discipline, called computational fluid dynamics (CFD), is devoted to this approach to solving fluid mechanics problems. Particle image velocimetry, an experimental method for visualizing and analyzing fluid flow, also takes advantage of the highly visual nature of fluid flow.

Velocity

The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of its speed and direction of motion (e.g. 7001166666666666666♠60 km/h to the north). Velocity is an important concept in kinematics, the branch of classical mechanics that describes the motion of bodies.

Velocity is a physical vector quantity; both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called "speed", being a coherent derived unit whose quantity is measured in the SI (metric) system as metres per second (m/s) or as the SI base unit of (m⋅s⁻¹). For example, "5 metres per second" is a scalar (not a vector), whereas "5 metres per second east" is a vector.

If there is a change in speed, direction, or both, then the object has a changing velocity and is said to be undergoing an acceleration.

Constant velocity vs acceleration

To have a constant velocity, an object must have a constant speed in a constant direction. Constant direction constrains the object to motion in a straight path thus, a constant velocity means motion in a straight line at a constant speed.

Flow

Flow may refer to:

Science and technology

Relating to the movement of material

Mathematics

Computer science