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Every few years, winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s (about 100 mph) 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 230 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 assumes a laminar flow. Using the principle here produces only an approximate result, because there is significant turbulence.)

Answer :

boffeemadrid

Answer:

265477.5 N

Explanation:

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

v = Velocity of wind = 45 m/s

A = Area = 230 m²

From Bernoulli's principle we have the relation

[tex]P_1+\frac{1}{2}\rho v_1^2 +\rho gh_1 = P_2 +\frac{1}{2}\rho v_2^2 +\rho gh_2\\\Rightarrow 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 230\\\Rightarrow F=265477.5\ N[/tex]

Force due to the jet stream on the roof is 265477.5 N

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