The factory, at an elevation of 58.0 m, draws from a circular, constant-area tank (T-1) at a base elevation of 90.0 m with a minimum water elevation of 99.0 m, an initial water elevation of 105.5 m, a maximum water elevation of 106.0 m, and a diameter of 10.0 m. The Hardy Cross method can be used to calculate the flow distribution in a pipe network.A pump station is designed to supply water to a small linen factory. In fact, it is possible to intentionally leave off decimals in the early iterations of the method to run the calculations faster. As long as the last few iterations are done with attention to detail, the solution will still be correct. If the method is followed correctly, the proper flow in each pipe can still be found if small mathematical errors are consistently made in the process. Subsequent mistakes in calculation are also iteratively corrected. The Hardy Cross method iteratively corrects for the mistakes in the initial guess used to solve the problem. Without the Hardy Cross methods, engineers would have to solve complex systems of equations with variable exponents that cannot easily be solved by hand. The Hardy Cross method is useful because it relies on only simple mathematics, circumventing the need to solve a system of equations. The method of balancing flows uses an initial guess that satisfies continuity of potential over each loop and then balances the flows until continuity of flow is also achieved at each junction.Īdvantages of the Hardy Cross method Simple mathematics Method of balancing flows (section incomplete) Continue from step 3 until the change in flow is within a satisfactory range.If the change in flow is negative, apply it to all pipes of the loop in the clockwise direction. If the change in flow is positive, apply it to all pipes of the loop in the counter-clockwise direction.The general relationship between head loss and flow is: The Hardy Cross method allows for any of these relationships to be used. In the case of water flow through pipes, a number of methods have been developed to determine the relationship between head loss and flow. The method also assumes that the relation between flow rate and head loss is known, but the method does not require any particular relation to be used. The Hardy Cross method assumes that the flow going in and out of the system is known and that the pipe length, diameter, roughness and other key characteristics are also known or can be assumed. Each method starts by maintaining either continuity of flow or potential, and then iteratively solves for the other. Hardy Cross developed two methods for solving flow networks. 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). 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.
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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 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." Derivation The moment distribution method was used to determine the forces in statically indeterminate structures and allowed for engineers to safely design structures from the 1930s through the 1960s, till the computer oriented methods. 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. 2.3 Method of balancing flows (section incomplete).The method was later made obsolete by computer solving algorithms employing the Newton–Raphson method or other numerical methods that eliminate the need to solve nonlinear systems of equations by hand. 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 introduction of the Hardy Cross method for analyzing pipe flow networks revolutionized municipal water supply design. 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 forces in statically indeterminate structures. 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 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.