Net force on roof from wind? Using Bernoulli's eq?

AI Thread Summary
To calculate the net force on a roof from wind blowing at 24 m/s over an area of 300 m², Bernoulli's equation is applied. The pressure difference between the still air inside the building and the wind creates a net force. Using the density of air (1.293 kg/m³), the calculations yield a force of approximately 111,715.2 N/m², which may differ from the study sheet's answer of 108,000 N/m² due to rounding. The left side of Bernoulli's equation represents the wind speed, while the right side reflects the pressure in still air. Understanding these concepts is crucial for accurately determining the forces acting on structures due to wind.
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Homework Statement


If wind blows at 24 m/s over your house, what is the net force on the roof if its area is 300 m squared?


Homework Equations


Bernoulli's equation? P1+1/2pv1sqrd+pgy1=P2+1/2pv2sqrd+pgy2


The Attempt at a Solution


Really didn't know where to go with this. I remembered my teacher mentioning that Bernoulli's equation was relevant. Tried plugging in the numbers, but didn't have any success. Any help would be extremely appreciated, as I have a final on this tomorrow morning. Thanks
 
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In case of a horizontal roof, the terms containing the height y will cancel in Bernoulli's equation. The wind blows above the roof, the pressure is lower there than below the roof, in the building, where the air is in rest. If Po is the pressure of the air in rest, P+1/2 d v2=Po. The total force on the roof is (Po-P)A, (A is the area of the roof). You need the density of air (d). ehild
 
Thank you so much for your help.
from bernoulli's I get to .5(d)(v1sqrd)=P2-P1. Once I plug in my numbers: .5(1.293)(576)=372.384. Then multiplied by the area: 372.384(300)= 111715.2 N/msqrd. For some reason the study sheet has the answer as 108000 N/msqrd, but maybe this could just be rounding.
Conceptually, I'm wondering so on the left side of the equation is the wind blowing 24m/s, while on the right side it is stopped? Thank you so much, you have been monumentally helpful.
 
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