momentumbalansen

Momentumbalansen, or the momentum balance, is the principle that the total linear momentum of a physical system is conserved in the absence of external forces. In practical terms, it relates how momentum changes inside a region to the forces acting on that region and to the flow of momentum across its boundary. The concept is foundational in physics and engineering, underlying Newton’s laws and the behavior of fluids, solids, and granular media.

In continuous-media form, the momentum balance can be written in both integral and differential forms. The integral form for a control volume states that the time rate of change of momentum inside the volume plus the net flux of momentum across the surface equals the sum of external forces acting on the volume. Symbolically, d/dt ∫CV ρv dV + ∮S ρv (v · n) dA = ∑F_ext, where ρ is density, v is velocity, and n is the surface normal. The differential form expresses the local balance as ∂(ρv)/∂t + ∇ · (ρ v ⊗ v) = ∇ · σ + ρ g, with σ the stress tensor and g body forces per unit mass.

This balance underpins the Navier–Stokes equations for fluids and the equations of motion in solid mechanics. It also leads to impulse–momentum relations used in collision and propulsion problems. In engineering, momentumbalansen is applied to aerodynamics, hydraulics, vehicle safety, and many areas of fluid-structure interaction, where external forces, pressure, viscous stresses, and momentum flux determine system dynamics.