Question

Estimate the air pressure inside a category 5 hurricane, where the wind speed is 350 km/h (Figure 1) .

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

Answer 1

Given,

speed = 350 km/hr = 97.22 m/s

We need to determine the pressure inside the hurricane.

We know from Bernaulli's equation that:

P1 + 1/2 v1² + h1 g = P2 +  1/2 v2² + h1 g

Let us consider 1 for outside hurricane and 2 for inside.

At sea level, P1 = atmosphereic pressure = 1.05 x 105 Pa ;

v1 = 0 and h1 = 0 ; h2 = 0 (its also at sea level) and we have v2 = 97.22 m/s

then the equation reduces to:

P1 = P2 +  1/2 v2²

P2 = P1 - 1/2 v2² = 1.01 x 10⁵ Pa - 1/2 x 1.29 kg/m³ x (97.22 m/s )²

P2 = 9.5 x 10⁴ Pa

Hence, air pressure inside hurricane = P2 = 9.5 x 10⁴ Pa.