Calculating Pressure Force on a Storefront Window | Tornado Physics Problem"

[notsam]

Homework Statement

A tornado wind of 200km/h blows across the face of a store front window. Estimate the force on the 2m X 3m window due to the difference in air pressure inside and outside the window. Assume the store is airtight so the inside pressure remains at 1.0 atm.

Homework Equations

Unknown

The Attempt at a Solution

PLEASE help. I honestly have no idea how to even start this problem, or what equation to use.

 

[Filip Larsen]

You may want to look in your textbook for Bernoulli's equation.

 

[notsam]

I'm sorry I DO NOT understand this. So .5pv^2+pgz+p=constant. I see where the velocity plugs in...but what about the dimmensions for the window?

 

[Filip Larsen]

Assuming constant height you can use Bernoulli's equation to calculate the drop in static pressure when the wind blows across the window, that is, from

$$p_0 = const = p_1 + \rho v^2/2$$

where p₀ = 1 atm, you can find the pressure difference between the inside (p₀) and outside (p₁) of the window and convert that to an equivalent force over the window area.

 

[notsam]

Ok ok, so basically since the window isn't breaking that is why I can set it equal to it? Oh and then I convert pressure to force?

 

[Filip Larsen]

The left and right side of the last equation I gave represent the total pressure at two different points on the same stream line, and that is why you can equate them.

Strictly speaking we then assume that the streamline starts inside the store, gets accelerated by the tornado and then ends up passing outside the store window. If you are uncomfortable with that assumption, you may equally well assume that the stream line starts at a different place than inside the store, but with same static pressure (and height) and zero velocity.

And yes, once you have a pressure differential over the window and you know the area of the window you can calculate the net force of this pressure difference.