A very simplified schematic of the rain drainage system for a home is shown in Fig. 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. 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 m,
(2) the floor drain has height `h_(2)` = 1.2 m,
(3) pipe M has radius 2.0 cm,
(4) the house has side width w = 40 m and front length L = 70 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?

Explanation

`~~ 2.2` cm/h