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A small family home in Tucson, Arizona has a rooftop area of 2667 square feet, and it is possible to capture rain falling on about 61.0% of the roof. A typical annual rainfall is about 14.0 inches. If the family wanted to install a tank to capture the rain for an entire year, without using any of it, what would be the required volume of the tank in m3 and in gallons? How much would the water in a full tank of that size weigh (in N and in lbf)?

Respuesta :

Answer:

volume  = 53.747 m3 = 14198.138 gal

weight = 526652 N = 118396.08 lbf

Explanation:

We know that volume of water

[tex]volume  =  A'\times H[/tex]

where A' = 61% of A

              [tex] = 0.61\times 2667 = 1626.87 sq ft[/tex]

[tex]volume  =  1626.87 \times (\frac{14}{12} ft)[/tex]

               =1898.015 ft^3

[tex]in\ m^3 = \frac{ 1898.015}{35.315} =   53.7457 m^3[/tex]

[tex]in\ gallon = 1898.015 \times 7.481 = 14198.138 gallon[/tex]

[tex]weight = \rho Vg[/tex]

       [tex]= 1000\times 53.74\times 9.8[/tex]

             =526652 N

[tex]In\ lbf =  \frac{526652}{4.448} = 118396.08 lbf[/tex]

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