Cross, Hardy

In contrast to the methods described in Sections III,2 and 3, which are generally applicable to all nonlinear equations, the Hardy-Cross methods have been developed specifically for pipeline network calculations. These methods, devised by Cross (Cl 1) long before the advent of modern computers, are still widely used (D2, D6, G3, G7, H5, II, K8, V2). Although the original publication (Cl 1) is readily accessible to most readers, more concise accounts of these two methods may be found in publications by Fair and Geyer (FI) and Stuckey (S7). 

In principle, the steady-state pipeline network problems can always be solved by the transient solution methods after allowing sufficient time steps for the solution to reach steady state. This possibility was discussed by Nahavandi and Catanzaro (Nl) who made a comparison of a transient solution method with the Cross method of balancing flows (R4). For the particular 35-node and 45-branch hydraulic network problem tested, the transient solution method took 108 seconds as compared with the 134 seconds required by the Hardy-Cross method. (See also Section V,A,2.)... 

Anonymous (1942). Prof. Hardy Cross. Engineering News-Record 128(Feb. 5) 217. P Anonymous (1951). Cross, Hardy. Who s who in America 26 605. Marquis Chicago. Anonymous (1959). Hardy Cross dies. Engineering News-Record 162(Feb.l9) 28. P Cross, H. (1926). Temperature deformations in concrete arehes. ENR 96(5) 190-191. 

Hardy Cross (1885-1959), a structural engineer and university professor whose valuable reflections on the nature of engineering were posthumously published in the book Engineers and Ivory Towers, maintained that engineers are not primarily scientists ... 

Leonard Eaton, Hardy Cross and the Moment Distribution Method, 2001. Hardy-Cross s reputation as a great teacher preceded his invention of the moment distribution method. The dean of his faculty was jealous and tried to remove him for insufficient publishing. He eventually filed a ten-page paper entitled Analysis of Continuous Frames by Distributing Fixed-End Moments. The method was immediately adopted by practising engineers. 

Eaton, L. (2001) Hardy Cross and the Moment Distribution Method. Birkhauser. 

Eaton, L.K. (2001) Hardy Cross and the IVIoment Distribution Method Nexus Network Journai, 3(3) Summer 2001 http //www.nexusjournai.com/Eaton.htmi. 

For a given flow rate at the stack entrance and a known pressure either at the stack inlet or at the stack outlet, it is possible to calculate the flow rate through each of the cells using a method of successive approximations, such as the Hardy-Cross method commonly used for pipe networks [9], or... 

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