Kanaalreciprocity

Kanaalreciprocity is a principle in hydraulic network theory describing a symmetry property of transfer relations between points in a canal or canalized flow system. In a network that obeys linear, time-invariant hydraulics, the influence of a unit head difference between point A and point B is indistinguishable from the influence of a unit head difference between B and A. Practically, kanaalreciprocity implies that the transfer impedance or conductance between two nodes is symmetric.

The concept draws on general reciprocity theorems from physics and electrical network theory, adapted to canal networks and irrigation systems. It provides a useful check on models and can simplify analysis by allowing the interchange of source and sink locations without changing the predicted exchanges of flow and head.

Mathematically, for a passive, linear hydraulic network with nodal heads h and flows q, the relation q = G h holds, where G is the conductance matrix. Kanaalreciprocity requires G to be symmetric, i.e., G_ij = G_ji. This symmetry arises under conditions of linear head-loss relations, steady-state operation, and no active components that add or remove energy in a way that would break reciprocity.

Limitations include nonlinear flow behavior, turbulence, variable cross-sections, and active devices such as pumps or turbines, which can violate reciprocity. In real-world networks, kanaalreciprocity is an approximation used for model validation, sensitivity analysis, and certain design optimizations where linear assumptions are reasonable. See also reciprocity (physics), hydraulic network theory, and electrical network reciprocity.