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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 210 m2? Typical air density in Boulder is 1.14 kg/m3, and the corresponding atmospheric pressure is 8.89 ✕ 10

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Answer:

[tex]F = 2.42*10^5N[/tex]

Explanation:

We can find the solution through Bernoulli's equation for laminar flow,

[tex]P_1+\frac{1}{2}\rho v_1^2 +\rho gh_1 = P_2 +\frac{1}{2}\rho v_2^2 +\rho gh_2[/tex]

We know that the heights are the same, then

[tex]P_1 = \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2} \rho v_2^2[/tex]

[tex]P_1-P_2 = \frac{1}{2} \rho (v^2_2-v^2_1)[/tex]

Pressure is equal to force over Area, so,

[tex]F=\frac{1}{2}\rho(v_2^2-v^2_1)A[/tex]

Our values are,

[tex]\rho = 1.14kg/m^3[/tex]

[tex]v_2 = 45m/s[/tex]

[tex]v_1 = 0[/tex]

[tex]A=210m^2[/tex]

Substituting,

[tex]F= \frac{1}{2}(1.14)(45)^2(210)[/tex]

[tex]F = 2.42*10^5N[/tex]

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