Will the Unsecured Shed Roof Withstand the Storm Winds?

[vu10758]

Homework Statement

Someone is putting a small shed in their backyard. The roof is not nailed down so gravity alone is holding it down. The wind suddenly flows across the top of the roogf at 20 m/s. The air inside the shed is 1.01 x 10^15 Pa, the normal atmospheric pressure. The roof has an area of 16m^2 and a mass of 250 kg. Density of air is 1.29 kg/m^3. Will the roof fly off?

Homework Equations

The Attempt at a Solution

The answer is that the roof will fly off.

In order for this to be true, pressure inside plus gravity must be greater than pressure outside.

Pushing down I have Pressure_up = 1.01 x 10^5 Pa.

I know that Pressure_down = mg/A + P_wind

I know this must be less than 1.01 x 10^5

However, what is the formula for Pressure_wind? I know the faster the wind, the smaller the pressure. I know formulas such as p + .5*density*v^2 + density*g*y, but it seems like a higher velocity would yield a higher pressure with this formula. It shouldn't be that way. What am I doing wrong?

 

[AlephZero]

What is "p + .5*density*v^2 + density*g*y" equal to?

If you use the equation correctly, you will find higher velocity does give lower pressure.