Every few years, winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s

Question

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 245 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.)

__________ N

Explanation / Answer

Using Bernoulli's equation

P1 + 0.5*rho*v1^2 + rho*g*h1 = P2 + 0.5*rho*v2^2 + rho*g*h2

P1 - P2 = 05*rho*(v2^2 - v1^2) + rho*g*(h2 - h1)

v2 = 45 m/sec

v1 = 0 m/sec, inside the house

h2 = h1, So h2 - h1 = 0

P1 - P2 = 0.5*rho*v2^2

Now force will be

F = (P1 - P2)*A

F = 0.5*rho*v2^2*A

F = 0.5*1.14*45^2*245

F = 2.83*10^5 N/m^2

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