Strömungsstrom

Strömingsström is a term used in fluid dynamics to denote the local transport of fluid mass or volume through a region of space, often described as the flow flux density. In mathematical form, the mass flux density is J = ρ v, where ρ is the fluid density and v is the velocity vector. The magnitude of J represents the mass flow per unit area, while the volumetric flux is simply v when density is normalized or treated separately. Across a surface with unit normal n, the mass flow rate is given by ∫ J · n dA, and the volumetric flow rate is ∫ v · n dA.

Incompressible flows, where ρ is constant, satisfy the continuity equation ∇·v = 0, meaning the net flux out of any closed surface balances the flux in. The Strömingsström concept is closely tied to the idea of flux continuity: the divergence of the flux density J is equal to the negative rate of change of stored mass, ∂ρ/∂t + ∇·J = 0.

The concept also connects to streamlines and stream functions. For steady, two-dimensional, incompressible flow, there exists a stream function ψ whose contours are streamlines. The velocity components can be expressed in terms of ψ, and the local Strömingsström aligns tangent to streamlines, illustrating how flow carries material along these paths.

Applications of Strömingsström appear across engineering and physics, including pipe and open-channel hydraulics, meteorology, and blood flow analysis. Practically, it underpins the calculation of mass and volume flow rates through surfaces, ducts, or vessels, using either direct measurements of velocity fields or integral forms over cross-sectional areas.