Suppose a flat roof has a surface area of 1.08000×102 m2. Presume the air inside

Question

Suppose a flat roof has a surface area of 1.08000×102 m2. Presume the air inside the building (and under the roof) is at atmospheric pressure, 1.01325×105 Pa, and that the air racing across the top of the roof is at a pressure of 9.97446×104 Pa.

What is the force with which the air inside the house pushes the roof upward? (please calculate this to 5 significant digits)

What is the force with which the air outside the house pushes the roof downward? (again, calculate this value to 5 significant digits)

The lift force takes into account the combination of these two forces. What is the lift force acting on the roof?

Explanation / Answer

(a)

Expression for pressure:

P = F/A

Rearrange the equation,

F = PA

F = (1.01325 X 105)(1.08000×102 m2)

F = 1.0943 x 107 N

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(b)

Again use the same equation,

F = PA

F = (9.97446×104 Pa)(1.08000×102 m2)

F = 1.0772x 107 N

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(c)

The lift force takes into account the combination of these two forces

The difference gives the answer

1.0943 x 107 N - 1.0772x 107 N = 1.7068x 105 N

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