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Every few years, winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s (about 100 miles per hour) 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 235 m2? Typical air density in Boulder is 1.14 kg/m3, and the corresponding atmospheric pressure is 8.89 ✕ 104 N/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.)

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boffeemadrid

Answer:

271248.75 N

Explanation:

[tex]\rho[/tex] = Density of air = 1.14 kg/m³

v = Velocity of wind = 45 m/s

A = Area = 235 m²

From Bernoulli's principle we have the relation

[tex]P_1-P_2=\frac{1}{2}\rho v^2\\\Rightarrow \Delta P=\frac{1}{2}1.14\times 45^2\\\Rightarrow \Delta P=1154.25\ Pa[/tex]

Force is given by

[tex]F=PA\\\Rightarrow F=1154.25\times 235\\\Rightarrow F=271248.75\ N[/tex]

Force due to the jet stream on the roof is 271248.75 N

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