Gesamtfluss

Gesamtfluss is a term used to denote the total amount of a quantity that crosses a boundary or surface per unit time. It represents the aggregate of a flux density over the boundary, capturing the net transfer of the quantity from one side to the other.

Mathematically, if F is a flux density vector field and S is a surface, the total flux through S is Φ = ∬_S F · n dA, where n is the outward normal to S. For a closed surface, this yields the total outward flux. Gauss’s theorem relates this surface flux to the volume integral of the divergence: Φ = ∭_V div F dV. In discrete systems, such as networks, total flow is obtained by summing the flows along all edges that cross a boundary or cut.

Applications span multiple disciplines. In hydrology, the Gesamtfluss corresponds to discharge, for example river or channel flow rate (cubic meters per second). In electromagnetism and heat transfer, it describes electric flux through a surface or heat flux across a boundary. In network analysis and transport problems, it describes the total amount of a commodity, information, or vehicles crossing a boundary between regions.

Computation and units depend on the transported quantity. For liquids, units are cubic meters per second; for mass or energy, units adapt accordingly (kg/s, W, etc.). The concept is distinct from a simple local flux density: Gesamtfluss emphasizes the cumulative crossing of a boundary, and is a key element in continuity relations and conservation laws. See also flux, flux density, divergence, Gauss’s theorem, and continuity equation.