A very simplified schematic of the rain drainage system for a home is shown in Figure. Rain falling on the slanted roof runs off into gutters around the roof edge; it then drains through downspouts (only one is shown) into a main drainage pipe M below the basement, which carries the water to an even larger pipe below the street. In Figure a floor drain in the basement is also connected to drainage pipe M suppose the following apply:
1. The downspouts have height h1 = 11 m,
2. The floor drain has height h2 = 1.2 m,
3. Pipe M has radius 3.0 cm,
4. The house has side width w = 30 m and front length L = 60 m,
5. All the water striking the roof goes through pipe M,
6. The initial speed of the water in a downspout is negligible,
7. The wind speed is negligible (the rain falls vertically). At what rainfall rate, in centimeters per hour, will water from pipe M reach the height of the floor drain and threaten to flood thebasement?

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January 18, 2011

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