6533b7d2fe1ef96bd125ea03

RESEARCH PRODUCT

Flux of a Vector Field

Manuel MaestreAntonio Galbis

subject

Physics::Fluid DynamicsPhysicssymbols.namesakeField (physics)Mathematical analysisGaussian surfacesymbolsFluxVector fieldElectric fluxVector calculusMagnetic fluxVector potential

description

In this chapter we concentrate on aspects of vector calculus. A common physical application of this theory is the fluid flow problem of calculating the amount of fluid passing through a permeable surface. The abstract generalization of this leads us to the flux of a vector field through a regular 2-surface in \(\mathbb{R}^3\). More precisely, let the vector field F in \(\mathbb{R}^3\) represent the velocity vector field of a fluid. We immerse a permeable surface S in that fluid, and we are interested in the amount of fluid flow across the surface S per unit time. This is the flux integral of the vector field F across the surface S

yearjournalcountryeditionlanguage
2012-01-01
https://doi.org/10.1007/978-1-4614-2200-6_4