(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to find the net force acting on a flat squared roof with area A while the wind is blowing outside at some velocity, [tex]v_1[/tex].

2. Relevant equations

Bernoulli's Equation:

[tex]P_1+\frac{1}{2}\rho v_1^2+\rho gy_1= P_2+\frac{1}{2}\rho v_2^2+\rho gy_2[/tex]

3. The attempt at a solution

The roof is flat, so the air pushing up from the inside is at the same depth as the air pushing down on the outside, so [tex]y_1=y_2[/tex]. I'm also assuming that the velocity of the air inside the house is zero, [tex]v_2=0[/tex]. So I can rearrange Bernoulli's equation:

[tex]P_2-P_1=\frac{1}{2}\rho v_1^2[/tex]

I think that the net force should be:

[tex]\Sigma F=(P_2-P_1)A-Mg=\frac{1}{2}\rho v_1^2A-Mg[/tex]

M is the mass of the roof. The problem is that I cannot find the mass, nor is it given. I"m told the that the roof is has an area of 225m and the wind is 100 mph. I convert the airspeed to meters-per-second, which is about 44.70 m/s. I can plug these numbers in, along with the known density of air, but it doesn't do any good if I don't know M.

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# Homework Help: Fluid Mechanics; Lift Force on a Roof; Bernoulli's Equation

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