Wind blows over the top of a 10.0 m tall chimney at 12.7 m/s. The air at the bottom of the chimney is stationary. What is the difference in air pressure between the top and bottom of the chimney?

Answer 1

This is an application of Bernouli's law which states

P₁ + 1/2dv₁² + dgh₁ = P₂ + 1/2dv₂² + dgh₂ where P is pressure, d is density, v is velocity, and h is height. The subscript 1 refers to the bottom of the chimney.

Rearranging P₁ - P₂ = 1/2dv₂² - 1/2dv₁² + dgh₂ - dgh₁.

The velocity at the bottom of the chimney is zero, so - 1/2dv₁² = 0 so the equation becomes

P₁ - P₂ = 1/2dv₂² + dg(h₂ - h₁) = 1/2 x 1.20 kg/m³ x 12.7² m²/s² + 1.20 kg/m³ x 9.8m/s^-2 x (10.0 - 0) = 214 N/m².

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