Estimate the air pressure inside a category 5 hurricane, where the wind speed is 300 km/h (Fig. 10–52).

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Inside the hurricane, we have the air moving with some speed v 2 and some pressure P 2 that we have to find and outside the hurricane, there is v 1 and atmospheric pressure. v 1 is zero—the air's not moving over here— and so the pressure is just gonna be atmospheric pressure and y 2 and y 1 are the same— we are comparing two points at the same altitude. So this Bernoulli's equation reduces to... you get rid of all these terms because y 2 and y 1 are the same so that means these two terms are equal so they cancel away, you can subtract them both from both sides. And then v 1 is zero so this term is gone so we have P 2 plus one-half density times v 2 squared equals P 1 which is P a for atmospheric pressure. So we take this term to the right hand side and P 2 then is P a minus one-half ρv 2 squared. So that's 1.013 times 10 to the 5 pascals minus one-half times 1.29 kilograms per cubic meter times 300 kilometers per hour times 1000 meters per kilometer times 1 hour for every 3600 seconds and that gives us meters per second and square that speed and here's what it looks like in the calculator— that conversion is the same as dividing by 3.6 by the way— and we end up with 9.7 times 10 to the 4 pascals is the pressure inside the hurricane.