Vector Analysis Versus Vector Calculus pp 107-126 | Cite as

# Flux of a Vector Field

## Abstract

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*

## Keywords

Unit Normal Vector Canonical Basis Measurable Subset Permeable Surface Linear Isomorphism## Preview

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