408-The Hardy Cross Method and its Successors in Water Distribution Modeling
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This course teaches the following specific knowledge and skills:
1. Hydraulic concepts necessary for understanding various pipe network analysis methods
2. The history behind the development of the Hardy Cross method
3. The basic principles the Hardy Cross method is based on and the step-by-step procedures used for pipe network analysis
4. The differences between the Hardy Cross and Modified/Improved Hardy Cross methods
5. Some of the advantages and disadvantages of using the Hardy Cross method
6. The differences between loop methods, node methods, flow methods, and gradient/node-loop methods for analyzing pipe networks
7. The basic concept of the Newton-Raphson method
8. The basic concept and application of the Linear Theory method
9. The basic concept and application of the Gradient method
10. A timeline of water distribution modeling advances from 1960 to 2020
11. The head loss methods and hydraulic balancing methods used by common hydraulic modeling software programs
12. Introduces leading modeling software developers, programs, and their basic capabilities
Water distribution system models have become very important and practical tools for civil engineers. Models are often used to optimize the design of new distribution systems or analyze major extensions or modifications to existing distribution systems. Computer models help engineers answer many common questions. For example, what is the maximum fire flow at a given point in the system? How long can that fire flow be provided for? What size pipe installation would be necessary between two points in a system to increase the pressure at one of the points to the minimum pressure required? If a subdivision or commercial development is built, will adequate pressures and flows exist? If not, what length and size of water mains must be upgraded by the developer to allow for the proposed construction?
In the 1930s the Hardy Cross method provided a breakthrough in pipe network analysis. Later, the advent of the modern computer allowed for analysis of even larger distribution systems using the method. Despite the development of more efficient computer algorithms, the Hardy Cross method remains the pipe network analysis method taught to most undergraduate civil engineering majors.
This course covers the history, basic principles, assumptions, step-by-step procedures, advantages, and disadvantages for solving pipe network problems using the Hardy Cross method. The three predominate analysis methods used by water distribution modeling software over the past 40 years are introduced and explained (the Newton-Raphson, Linear Theory, and Gradient methods). At the end of the course material a summary of some popular public-domain and commercial hydraulic models is presented. A total of ten example problems and solutions are included throughout the course to reinforce learning. The primary audiences for this course are consulting and municipal engineers in the water resource and environmental fields.
Other Courses by Kelly McAtee, PE, LEED A.P.
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