Abstract
The original and improved versions of the Hardy Cross iterative method with related modifications are today widely used for the calculation of fluid flow through conduits in loop-like distribution networks of pipes with known node fluid consumptions. Fluid in these networks is usually natural gas for distribution in municipalities, water in waterworks or hot water in district heating systems, air in ventilation systems in buildings and mines, etc. Since the resistances in these networks depend on flow, the problem is not linear like in electrical circuits, and an iterative procedure must be used. In both versions of the Hardy Cross method, in the original and in the improved one, the initial result of calculations in the iteration procedure is not flow, but rather a correction of flow. Unfortunately, these corrections should be added to or subtracted from flow calculated in the previous iteration according to complicated algebraic rules. Unlike the Hardy Cross method, which requires complicated formulas for flow corrections, the new Node-loop method does not need these corrections, as flow is computed directly. This is the main advantage of the new Node-loop method, as the number of iterations is the same as in the modified Hardy Cross method. Consequently, a complex algebraic scheme for the sign of the flow correction is avoided, while the final results remain accurate.
Highlights
Since the resistances in a network of pipes for distribution of fluids depend on flow, the problem is not linear as in Direct Current (DC) electric circuits
The aforementioned algebraic rules for the correction of flow calculated as an intermediate step in an iterative procedure can be found in the reference book [4]. These rules can be used for both versions of the Hardy Cross method, and for a general node-oriented method in which the correction of pressure is calculated as an intermediate step rather than as a correction of flow
The main advantage of the novel node-loop method is that flow in each pipe can be calculated directly, which is not possible for the original Hardy Cross nor the improved Hardy Cross methods (Figure 4)
Summary
Since the resistances in a network of pipes for distribution of fluids depend on flow, the problem is not linear as in Direct Current (DC) electric circuits. The improved Hardy Cross method [2], as an intermediate step determines corrections for each loop but treats the whole network system simultaneously, and applies this correction to compute the new flow in each conduit, as in the original version [1]. It is more efficient, but the intermediate step in calculations is not eliminated. The original Hardy Cross method can be expressed using matrix calculations with no effects on the final results [8]
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