Estimate the air pressure inside a category 5 hurricane, where the wind speed is 270 km/h (Figure 1). Express your answer to two significant figures and include the appropriate units.

Question

Estimate the air pressure inside a category 5 hurricane, where the wind speed is 270 km/hkm/h (Figure 1).

Express your answer to two significant figures and include the appropriate units.

Answer 1

The pressure inside a hurricane can be estimated using Bernoulli’s equation in still air ( v₀=0_,  P₀=1.013*10⁵ N/m²) and in the hurricane (P₁, V₁) at the same height (h). Air density is 1.29 kg/m³.

P₀ +(1/2)ρ(v₀)² + ρgh = P₁ +(1/2)ρ(v₁)² + ρgh; after canceling ρgh and using v₀=0, P₀=1.013*10⁵ N/m²

P₁= P₀ -(1/2)ρ(v₁)² =1.013*10⁵ N/m²  - (1.29/2 kg/m3)(270000/3600 m/s)²= 1.013*10⁵ N/m²  -48.375 N/m²  = 101,251.625≈1.0125*10⁵ N/m²