Halliday, Resnick & Walker — Fluids: Problem 66

66 A very simplified schematic of the rain drainage system for a home is shown in Fig. 14-45. 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. 14-45, 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 \(2.0 \text{ cm}\), (4) the house has side width \(w = 40 \text{ m}\) and front length \(L = 70 \text{ m}\), (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?