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

The force exerted on the roof is
`F =2.37*10^(5)N`

Step-by-step 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 + (1)/(2) \rho v_a ^2 + \rho g h_a = P_2 + (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 + (1)/(2) \rho v_a ^2 = P_2 + (1)/(2) \rho v_b ^2`

`P_1 - P_2 = (1)/(2) \rho (v_b^2 - v_a^2)`

Since pressure is mathematically represented as

`P = (F)/(A )`

The above equation can be written as

`F = (1)/(2) \rho ( v_b^2 - v_a ^2 ) A`

The initial velocity is 0

Substituting value

`F = (1)/(2) (1.14) [(45^2 - 0^2 ) ](205)`

`F =2.37*10^(5)N`