Vektinnflyt

Vektinnflyt is a term used in Norwegian-language contexts to describe the inflow of a vector field into a defined region. It is closely related to the standard notion of flux in vector calculus, but emphasizes the direction of crossing the region’s boundary into the interior.

Formal definition: Let F be a vector field defined on a region V with boundary ∂V and outward unit normal n. The flux across ∂V is Φ = ∬_{∂V} F · n dS. The inflow, or vektinnflyt, is Φ_in = ∬_{∂V} F · (−n) dS = −Φ. Equivalently, using inward normal n_in, Φ_in = ∬_{∂V} F · n_in dS. The value is positive when more field enters the region than leaves.

Relation to the divergence theorem: The divergence theorem states Φ_out = ∬_{∂V} F · n dS = ∭_V (∇·F) dV. Therefore the inflow is Φ_in = −Φ_out = −∭_V (∇·F) dV. In a volume where ∇·F is positive, net inflow tends to be negative (more leaving).

Examples and interpretation: In fluid dynamics, vektinnflyt describes the rate at which fluid mass or momentum enters a control volume. In electromagnetism, it can represent the inward flow of a field. It is a boundary-oriented quantity that supports conservation analysis and system modeling.

See also: Flux, Divergence, Control volume, Continuity equation.