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

Answer 1

`F = 2.42*10^5N`

Step-by-step explanation:

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

`P_1+(1)/(2)\rho v_1^2 +\rho gh_1 = P_2 +(1)/(2)\rho v_2^2 +\rho gh_2`

We know that the heights are the same, then

`P_1 = (1)/(2)\rho v_1^2 = P_2 + (1)/(2) \rho v_2^2`

`P_1-P_2 = (1)/(2) \rho (v^2_2-v^2_1)`

Pressure is equal to force over Area, so,

`F=(1)/(2)\rho(v_2^2-v^2_1)A`

Our values are,

`\rho = 1.14kg/m^3`

`v_2 = 45m/s`

`v_1 = 0`

`A=210m^2`

Substituting,

`F= (1)/(2)(1.14)(45)^2(210)`

`F = 2.42*10^5N`