Question

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 1

265477.5 N

Step-by-step explanation:

`\rho` = 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

`P_1+(1)/(2)\rho v_1^2 +\rho gh_1 = P_2 +(1)/(2)\rho v_2^2 +\rho gh_2\\\Rightarrow P_1-P_2=(1)/(2)\rho v^2\\\Rightarrow \Delta P=(1)/(2)1.14* 45^2\\\Rightarrow \Delta P=1154.25\ Pa`

Force is given by

`F=PA\\\Rightarrow F=1154.25* 230\\\Rightarrow F=265477.5\ N`

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