Question

Every few years, winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s (about 100 mi/h) when the jet stream descends during early spring. show answer No Attempt Approximately what is the force due to the Bernoulli effect on a roof having an area of 205 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 assumes a laminar flow. Using the principle here produces only an approximate result, because there is significant turbulence.)

Answer 1

Answer:

The force exerted on the roof is $F =2.37*10^{5}N$

Explanation:

From the question we are told that

      The speed of the wind is $v = 45.0 m/s$

       The area of the roof is $A = 205 m^2$

       The air density of Boulder is $\rho = 1.14 kg / m^3$

        The atmospheric pressure is $P_{atm} = 8.89 * 10^{4} N/ m^2$

For a laminar flow the Bernoulli’s principle is  mathematically represented as

            $P_1 + \frac{1}{2} \rho v_a ^2 + \rho g h_a = P_2 + \frac{1}{2} \rho v_b ^2 + \rho h_b$

Where  $v_1$ is the  speed of air in  the building

             $v_b$ is the speed of air outside the building

             $P_1 \ and \ P_2$ are the pressure of inside and outside the house

             $h_a \ and \ h_b$ are the height above and  below the roof

Now for  $h_a = h_b$

            The above equation becomes

                 $P_1 + \frac{1}{2} \rho v_a ^2 = P_2 + \frac{1}{2} \rho v_b ^2$

                 $P_1 - P_2 = \frac{1}{2} \rho (v_b^2 - v_a^2)$

Since pressure is mathematically represented as

           $P = \frac{F}{A }$

The above equation can be written as

             $F = \frac{1}{2} \rho ( v_b^2 - v_a ^2 ) A$

The initial velocity is 0

    Substituting value  

                $F = \frac{1}{2} (1.14) [(45^2 - 0^2 ) ](205)$

                $F =2.37*10^{5}N$