A very simplified schematic of the rain drainage system for a home is shown in t

Question

A very simplified schematic of the rain drainage system for a home is shown in the 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 the figure, a floor drain in the basement is also connected to drainage pipe M. Suppose the following apply: 1. the downspouts have height h1 = 12 m, 2. the floor drain has height h2 = 1.0 m, 3. pipe M has radius 2.7 cm, 4. the house has side width w = 35 m and front length L = 49 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 the basement?

Explanation / Answer

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