Calculating Rainfall Rate for Basement Flooding Risk | Bernoulli's Equation"

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Homework Statement

A very simplified schematic of the rain drainage system for a home is shown. Rain falling on the slanted roof runs off into gutter around the roof edge it then drains through downspouts into a main drainage pipe M below the basement which carries the water to an even larger pipe below the street. Apply the following:

1.)the downspouts have h1= 11m
2.)the floor drain has height h2=1.2m
3.)pipe M has radius 3cm
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

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.

Homework Equations

p+ .5 rho v^2+rho gh=p+.5 rho v^2+rho gh
AV=av

The Attempt at a Solution

A=a so V=V

 

[mb218]

I also figured out that the v at the end of the pipe of length h1= 146 cm/s by using v^2=v0^2+2gh