Question

54. Every few years, winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s (about 100 mi/h) when the jet stream descends during early spring. Approximately what is the force due to the Bernoulli effect on a roof having an area of 220m2? Typical air density in Boulder is 1.4kg/m3, and the corresponding atmospheric pressure is 8.89×104N/m2. (Bernoulli’s principle as stated in the text assumes laminar flow. Using the principle here produces only an approximate result, because there is significant turbulence.)

Answer 1

For the Bernoulli effect we consider a thin roof, so the heights above and below it can be considered equal and the wind below the roof is stagnant. In this conditions we can solve for the pressure difference over the roof:

(atmospheric pressure is equal and opposite above and below the roof, so it has zero net effect) On the other hand force is just pressure times area: