Halliday, Resnick & Walker — Fluids: Problem Problem_72

A very simplified schematic of the rain drainage system for a home is shown in Fig. 14.35. 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 Fig. 14.35, a floor drain in the basement is also connected to drainage pipe M. Suppose the following apply: (1) the downspouts have height \( h_1 = 11 \text{ m} \), (2) the floor drain has height \( h_2 = 1.2 \text{ m} \), (3) pipe M has radius \( 3.0 \text{ cm} \), (4) the house has side width \( w = 30 \text{ m} \) and front length \( L = 60 \text{ m} \), (5) all the water striking the roof goes through pipe M, (6) the initial speed of the water in a downspout is negligible, and (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?