Air pressure with Bernoulli's equation

In summary: So, one can think about pressures in terms of "geopotentials" (potentials relative to some reference surface), or "pressure coordinates." Hope that helps.
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pompey
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Nevermind, I think I figured out why I needed to set P2 = 0 in the first problem. Actually, what I needed to do was set P2 = 1 atm, and when I calculated force, I needed to use F = (P2 - P1) * A to get the right answer.

So just ignore this...but here's the post anyway:

For anyone who has the book, giancoli 5th ed, pg 306 number 39 and 41.

Question 1: If wind blows at 30 m/s over your house, what is the net force on the flat roof if its area is 240 m^2.

Question 2: Estimate the air pressure at the center of a hurricane with wind speed of 300 km/h at the center.

For question 1 and 2, using bernoulli's equation, and setting y1=y2=0, we have:

P1 + 1/2*d*v1^2 = P2 + 1/2*d*v2^2 where d = density of air = 1.29 kg/m^3

For question 1, if we set P2 = 0 and v2 = 0, and v1 = 30 m/s, I get the right answer. I solve for P1 and then for the force, I just say F = P1 * A where A = 240m^2.

But for question 2, if I do the same thing, with P2 = 0 and v2 = 0 and v1 = 300 km/h = 83 m/s, I do not the right answer. But, if I set P2 = 1 atm, I get the right answer.

Can someone explain how to solve these two questions?
 
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It's important to have both/all the pressures be in absolute pressure. Sometime pressure is given as gage (or gauge) pressure, which is relative to 1 atm. For absolute pressure, the reference is 0, or pure vacuum.

Also, once can consider differential pressure, e.g., Pi - Po, across a pipe (or tube) wall, or Po - Pi, depending on the type of problem. One might calculate the tension in a pipe/tube wall, or collapse potential. Sign convention is important with respect to calculated stresses.

It's a bit like a ground reference in electrical circuit potentials.
 

1. What is Bernoulli's equation and how does it relate to air pressure?

Bernoulli's equation is a fundamental principle in fluid dynamics that describes the relationship between fluid velocity and pressure. In simple terms, it states that as the velocity of a fluid increases, the pressure decreases. This can be seen in the context of air pressure, as air moving at a higher velocity, such as in a fast-moving stream of air, will have lower pressure than still air.

2. How is air pressure affected by the shape and size of an object?

The shape and size of an object can significantly affect air pressure around it. For example, an object with a curved surface, such as an airplane wing, can create an area of low pressure on top and high pressure on the bottom, which creates lift. Similarly, a smaller object will experience more significant changes in air pressure than a larger object due to the air having to move around it with a greater velocity.

3. Can Bernoulli's equation explain why airplanes can fly?

Yes, Bernoulli's equation is a crucial principle in explaining how airplanes can fly. The shape of the wings creates a difference in air pressure, with lower pressure on top and higher pressure on the bottom, which creates lift. This lift allows the airplane to overcome the force of gravity and stay in the air.

4. How does air pressure change with altitude?

As altitude increases, air pressure decreases. This is because there is less air above, and therefore, less weight pushing down on the air below. The decrease in air pressure with altitude is exponential, meaning that the higher the altitude, the more significant the change in air pressure will be.

5. Can Bernoulli's equation be applied to gases other than air?

Yes, Bernoulli's equation can be applied to any fluid, including gases other than air. It is a fundamental principle in fluid dynamics and can be used to analyze the behavior of any fluid, as long as it is in motion. However, the equation may need to be modified for different types of gases or fluids, depending on their properties.

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