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 equation on a roof having an area of 220m^2? Typical air density in Boulder is 1.14kg/m^3, and the corresponding atmospheric pressure is 8.89×10^4N/m^2. (Bernoulli’s principle as stated in the assumes laminar flow. Using the principle here produces only an approximate result, because there is significant turbulence.)

a) 1.2 x 10^5 N
b) 2.4 x 10^5 N
c) 3.6 x 10^5 N
d) 4.8 x 10^5 N

Answer 1

Using Bernoulli's principle, with given wind speed, air density, and atmospheric pressure, we calculate the force on a 220 m² roof to be approximately 2.4 x 10⁵ N, which corresponds to option b.

Step-by-step explanation:

The student's question pertains to the application of Bernoulli's principle in determining the force exerted on a roof by wind in Boulder, Colorado. Bernoulli's equation relates the speed of a fluid, its density, and pressure, and can be used to estimate the force on a surface in windy conditions. Using the given wind speed of 45.0 m/s, air density of 1.14 kg/m³, and atmospheric pressure of 8.89×10⁴ N/m², we can calculate the pressure difference caused by the wind. This pressure difference applies over the roof's area of 220 m² to yield the force.

According to Bernoulli's equation, the wind speed contributes to a decrease in pressure on the roof. The equation for this is P + \(0.5 \times \rho \times v^2\), where P is atmospheric pressure, \rho is the density of air, and v is the wind speed. Calculating the pressure difference due to wind, and multiplying by the area of the roof will give us the force. The correct option should reflect the force estimate after these calculations. After appropriate substitutions and calculations, we find that the answer is option b) 2.4 x 10⁵ N.