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Using Equation Solver Programs to Teach Design of Pipe Networks Introduction Pipe networks are one of the fundamental components in the design of thermal systems. Many universities teach the design of these systems in courses such as Fluid Mechanics or Thermo- Fluid Component Design. Traditionally, the analysis of pipe networks was done using iterative methods, such as the Hardy-Cross method1. However, modern mathematical software such as Mathcad2 and EES3, which include equation solvers, can be used to analyze these systems more efficiently.

The advantage of using software like Mathcad to teach students the design of pipe networks is that students focus in the fundamental concepts rather than in the mathematical solution. To set up the solution to the network problem, they need to enter the correct set of governing equations. Once this is done, the software solves the system of equations and provides them the solution. As a consequence, students spend most of their time analyzing their system rather than computing. This is very useful in design because many changes can be done in a short time to optimize the final design.

The goal of this paper is to describe how the design of pipe networks is taught using the software Mathcad. Three examples that are used in class are discussed. The first is a very simple pipe network that introduces the technique to students. The second example also describes a simple network that shows students how to modify pipe sizes and other parameters to design a stable and controllable network of pipes. The third example discusses the design of a more complex pipe network system, similar to the ones used in hydronic cooling or heating of buildings. The goal of this example is to show students how to design and optimize a complex network of pipes.

Example 1: Analysis of a simple pipe network This simple pipe network is shown in figure 1. The goal of this problem is to calculate pipe flows Q1, Q2, and Q3 in pipes 1, 2, and 3 when the following information is provided: • All pipe sizes and materials • Flow rates coming in or out at points A and B, as shown in the figure Qa = 4 ft3/s A 2 C Q2

Q1 Q3 1 3

B Qb=1 ft3/s

Figure 1. Analysis of a Simple Network

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Bravo, R. (2006, June), Using Equation Solver Programs To Teach Design Of Pipe Networks Paper presented at 2006 Annual Conference & Exposition, Chicago, Illinois. 10.18260/1-2--979