The bedroom and bathroom windows are perpendicular to the ground and the sunroof is parallel to the ground.  Which of the window openings has the greatest flux?At one point during a rain storm,...

The bedroom and bathroom windows are perpendicular to the ground and the
sunroof is parallel to the ground.  Which of the window openings has the
greatest flux?

At one point during a rain storm, the rain is falling at a constant rate of n
drops per square meter at an angle of 60 with respect to the horizontal
direction.  Unfortunately Ted has left three windows open: (1) the sunroof on his
car that measures 0.6 m by 0.3 m, (2) his bathroom window that measures 0.6 m
by 0.2 m; and (3) his bedroom window that measures 0.6 m by 0.3 m.

Asked on by tagnaouti

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quantatanu | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The larger the angle with the plane of the surface the higher is the flux, another factor is higher the surface area higher is the flucx, 

precisely, 

flux = area * Sin[angle with the surface]   [cosine, if you measure

                                                             angle with normal to the

                                                             surface]

 

Abed = area of bedroom window = 0.6 m by 0.3 m

                                               = 0.18 m^2

Abath = area of bathroom window = 0.6 m by 0.2 m

                                                 = 0.12 m^2

Aroof = area of sunroof                =  0.6 m by 0.3 m

                                                 = 0.18 m^2


As the rain falls at an angle 60 degrees with the ground so

angle of rain with sunroof = 60 deg

angle with bathroom window=angle with bedroom window = 30 deg 

(assuming bedroom and bathroom windows are along the same side)

Then 

Flux through sunroof = Aroof * Sin[60]* n drops

                              = 0.18 * 0.866

                              = 0.155 * n  drops

Flux through bedroom window = Abed * Sin[30]* n drops

                               = 0.18 * 0.5

                               = 0.09 * n drops 

                              

Flux through bathroom window = Abath * Sin[30]* n drops

                                      = 0.12 * 0.5

                                      = 0.06 * n drops

so flux through sunroof is the greatest.     

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