Winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s (about 101 mi/h)

Question

Winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s (about 101 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 67 m2. Typical air density in Boulder is 1.10 kg/m3, and the corresponding atmospheric pressure is 8.86x10^4 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.)

Explanation / Answer

Bernoulli's Equation indicates tha tpressure difference between
inside the house {Air Velocity = 0} and outside the house, just
above the roof {Air Velocity = 45.0 m/sec}, is given by (where
height difference is considered negligible between inside &outside):

By Bernoullis theorem :-
=>P1 + h1dg + 1/2dv1^1 = P2 + h2dg + 1/2dv2^2
=> P1- P2 = 1/2dv^2 {as h1 = h2}
=>?P = 1/2 x 1.10 x (45)^2
=>?P = 1113.75 Pa
By P = F/A
=>F = PA = 1113.75 x 67 = 74621.25 N

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