Chapter 2 – Why WPM?
Surge Analysis and the Wave Plan Method
Supplementary Material: Example Problems and Solutions
Chapter 2 – Problem 2.16
2.16 Consider a large water distribution network model comprising several thousand pipe elements with diameters ranging from 6” to 72” (150 mm to 1800 mm) having a total length of roughly 1550 km of mostly metallic pipe. There are several pump stations each with multiple pumps connected by short pipe elements similar to those shown in Figure 3.5. The shortest pipe element within the pump station is 1m and the shortest pipe element outside the pump stations is 100m.
a. What is the computational time step that satisfies the necessary CFL condition if the 100m pipe element (shortest pipe element outside the pump stations) and the system average celerity (1000 m/s) are used to determine the computational time step? [Answer: 0.1s]
b. What is the computational time step that satisfies the necessary CFL condition if the shortest pipe element in the entire network and the average celerity (1000 m/s) are used to determine the computational time step? [Answer: 0.001s]
c. Compute the total number of pipe sections in the entire network for a MOC-based solution using the shorter computational time step [Answer: 1.55 million pipe sections]
d. Suppose the total number of pipe sections overwhelms the MOC-based software tool that you are using for surge analysis. Would you be willing to split the model into multiple sub-models, so you can use variable computational time steps to reduce the number of pipe sections? For example, build the main network model (excluding pump stations) using the computational time step associated with 100m long pipe element and build the models within pump stations using the computational time step associated with 1m long pipe element?
e. Under what conditions might it be acceptable to build multiple sub-models of a large network model? In what cases is it clearly unacceptable?
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