Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
Concept
Flow velocity
Summary
In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the flow velocity vector is the flow speed and is a scalar.
It is also called velocity field; when evaluated along a line, it is called a velocity profile (as in, e.g., law of the wall).
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.
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:
That is, if is an irrotational vector field.
A flow in a simply-connected domain which is irrotational can be described as a potential flow, through the use of a velocity potential with If the flow is both irrotational and incompressible, the Laplacian of the velocity potential must be zero:
Vorticity
The vorticity, , of a flow can be defined in terms of its flow velocity by
If the vorticity is zero, the flow is irrotational.
Potential flow
If an irrotational flow occupies a simply-connected fluid region then there exists a scalar field such that
The scalar field is called the velocity potential for the flow. (See Irrotational vector field.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Ontological neighbourhood