  Original and improved version of the Hardy Cross iterative method with
related modifications are today widely used for calculation of fluid flow
through conduits in loops-like distribution networks of pipes with known node
fluid consumptions. Fluid in these networks is usually natural gas for
distribution in the municipalities, water in waterworks or hot water in
district heating system, air in the case of ventilation systems in buildings or
mines, etc. Since, the resistances in these networks depend of flow, problem is
not linear like in electrical circuits, and iterative procedure must be used.
In both version of the Hardy Cross method, in original and in the improved one,
initial results of calculation in iteration procedure is not flow, but rather
the correction of flow. Unfortunately, these corrections should be added to or
subtracted from a flow calculated in previous iteration according to complicate
algebraic rules. After the here presented node-loop method, final results in
each of the iterations is flow directly rather than flow correction. In that
way complex algebraic scheme for sign of flow correction is avoided, while the
final results still remain unchanged. Numbers of required iterations for the
same results are comparable with the improved Hardy Cross method.
