DICLIB.COM
AI-based language tools

All tools Subscription Contact Us

Enter a word or phrase in any language 👆

Language:

Translation and analysis of words by artificial intelligence

On this page you can get a detailed analysis of a word or phrase, produced by the best artificial intelligence technology to date:

how the word is used
frequency of use
it is used more often in oral or written speech
word translation options
usage examples (several phrases with translation)
etymology

What (who) is irrotational flow - definition

CONCEPT IN VECTOR CALCULUS

Irrotational; Irrotational field; Gradient field; Potential vector field; Conservative field; Curl free field; Curl-free vector field; Irrotational vector field; Irrotational flow; Irrotational Flow

$The above vector field <math>\mathbf{v} = \left( - \frac{y}{x^2 + y^2},\frac{x}{x^2 + y^2},0 \right)</math> defined on <math>U = \R^3 \setminus \{ (0,0,z) \mid z \in \R \}</math>, i.e., <math>\R^3</math> with removing all coordinates on the <math>z</math>-axis (so not a simply connected space), has zero curl in <math>U</math> and is thus irrotational. However, it is not conservative and does not have path independence.$

Irrotational

·adj Not rotatory; passing from one point to another by a movement other than rotation;

- said of the movement of parts of a liquid or yielding mass.

Conservative vector field

In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property that its line integral is path independent; the choice of any path between two points does not change the value of the line integral.

https://en.wikipedia.org/wiki/Conservative_vector_field

Laplace equation for irrotational flow

DIFFERENTIAL EQUATION IN FLUID MECHANICS

Laplace’s equation for irrotational flow

Irrotational flow occurs where the curl of the velocity of the fluid is zero everywhere. That is when

https://en.wikipedia.org/wiki/Laplace_equation_for_irrotational_flow

Wikipedia

Conservative vector field

In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property that its line integral is path independent; the choice of any path between two points does not change the value of the line integral. Path independence of the line integral is equivalent to the vector field under the line integral being conservative. A conservative vector field is also irrotational; in three dimensions, this means that it has vanishing curl. An irrotational vector field is necessarily conservative provided that the domain is simply connected.

Conservative vector fields appear naturally in mechanics: They are vector fields representing forces of physical systems in which energy is conserved. For a conservative system, the work done in moving along a path in a configuration space depends on only the endpoints of the path, so it is possible to define potential energy that is independent of the actual path taken.

https://en.wikipedia.org/wiki/Conservative vector field