Hardy Cross method

The Hardy Cross method is an iterative method for determining the flow in pipe network systems where the inputs and outputs are known, but the flow inside the network is unknown. The method was first published in November 1936 by its namesake, Hardy Cross, a structural engineering professor at the University of Illinois at Urbana–Champaign. The Hardy Cross method is an adaptation of the Moment distribution method, which was also developed by Hardy Cross as a way to determine the moments in indeterminate structures.

The introduction of the Hardy Cross method for analyzing pipe flow networks revolutionized municipal water supply design. Before the method was introduced, solving complex pipe systems for distribution was extremely difficult due to the nonlinear relationship between head loss and flow. The method was later made obsolete by computer solving algorithms employing the Newton-Raphson method or other solving methods that prevent the need to solve nonlinear systems of equations by hand.

In 1930, Hardy Cross published a paper called "Analysis of Continuous Frames by Distributing Fixed-End Moments" in which he described the moment distribution method, which would change the way engineers in the field performed structural analysis. The moment distribution method was used to determine the moment distributions in indeterminant concrete structures and allowed for engineers to safely design structures from concrete from the 1930s to 1960. In November 1936, Cross applied the same geometric method to solving pipe network flow distribution problems, and published a paper called "Analysis of flow in networks of conduits or conductors."

The Hardy Cross method is an application of continuity of flow and continuity of potential to iteratively solve for flows in a pipe network. In the case of pipe flow, conservation of flow means that the flow in is equal to the flow out at each junction in the pipe. Conservation of potential means that the total directional head loss along any loop in the system is zero (assuming that a head loss counted against the flow is actually a head gain).

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