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 225 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.)

Answer 1

Answer:

F = 260 kN

Explanation:

given,                                

speed = 45 m/s            

Area = 225 m²                    

air density = 1.14 Kg/m³                

Atmospheric pressure =  8.89 ✕ 10⁴ N/m²

Using  Bernoulli equation          

assuming the level is same        

$P_1 - P_2 = \dfrac{1}{2}\rho V^2$

$\Delta P= \dfrac{1}{2}\rho V^2$          

$\Delta P= \dfrac{1}{2}\times 1.14 \times 45^2$

$\Delta P=1154.25\ Pa$

Force = Pressure x area              

Force =1154.25 x 225        

F = 259706.25 N                              

F = 260 kN