If the house is in size, estimate the weight of the roof. Assume the roof is not nailed down. ?

A 200 wind blowing over the flat roof of a house causes the roof to lift off the house.





PLEASE HELP! i need this by tomorrow.If the house is in size, estimate the weight of the roof. Assume the roof is not nailed down. ?
I assume the wind speed of 200 means 200 mph (a category 5 hurricane). This is equivalent to 320 kph or 90 m/s.





The wind speed causes a difference in pressure between air above the roof and air in the house.





From Bernoulli's equation, this difference is 1/2 x density of air x square of wind speed.





Air density is about 1.2 kg/m^3, so pressure difference is





1/2 x 1.2 x 90^2 = 4860 N/m^2, or approx. 5000 N/m^2





Estimate the size of the roof as 10 m x 10 m = 100 m^2.





So the force lifting the roof = Pressure Difference x Area = 5000 x 100 =5 x 10^5 N.





Assuming that the roof only just lifts off, this is also the weight of the roof.





Is this estimate reasonable? Assume the roof is made of wood with average density 500 kg/m^3 and is 1 m thick. (Density of water is 1000 kg/m^3.) Then its volume would be 1m x 100 m^2 = 100 m^3 and its weight would be





500 kg/m^3 x 100 m^3 x 10 N/kg = 5 x 10^5 N.





This agrees with the estimate from windspeed.





(10 N/kg is the conversion factor from kg to N.)