Fluid Mechanics; Lift Force on a Roof; Bernoulli's Equation

[AdkinsJr]

Homework Statement

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, $$v_1$$.

Homework Equations

Bernoulli's Equation:
$$P_1+\frac{1}{2}\rho v_1^2+\rho gy_1= P_2+\frac{1}{2}\rho v_2^2+\rho gy_2$$

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 $$y_1=y_2$$. I'm also assuming that the velocity of the air inside the house is zero, $$v_2=0$$. So I can rearrange Bernoulli's equation:

$$P_2-P_1=\frac{1}{2}\rho v_1^2$$

I think that the net force should be:

$$\Sigma F=(P_2-P_1)A-Mg=\frac{1}{2}\rho v_1^2A-Mg$$

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.

 

[ehild]

That roof does not float in the air, but is supported by the walls. I am sure the problem means the net force from air. ehild

 

[AdkinsJr]

That roof does not float in the air, but is supported by the walls. I am sure the problem means the net force from air.


ehild

lol, yeah that's probably true for most roofs.

It turns out that my first instinct was correct, I just need to find the net force from air as you say. When I first made the calculation I obtained a number slightly greater than the value given in the back of the book, it turns out that the density of air is either 1.29 kg/m^3 or 1.20 kg/m^3 depending on varying conditions, I was using the former.