Air pressure with Bernoulli's equation

[pompey]

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?

 

[gmax137]

I do not have the cited textbook, so I can't give any specific advice on the questions. However, there are many "Bernoulli" threads here on PF, anyone interested could do a search. Or maybe start here:

https://www.physicsforums.com/threads/fluid-mechanics-flow-through-a-pipe-bernoulli-equation.437040/

Be sure to look at the "Suggested For:..." threads at the bottom of the link. This is a really useful feature.

 

[gmax137]

We also have an Insights article on Demystifying Bernoulli's equation.

https://www.physicsforums.com/insights/demystifying-the-often-misunderstood-bernoullis-equation/

 

[Astronuc]

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., P_i - P_o, across a pipe (or tube) wall, or P_o - P_i, 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.