Question

Meteorologists measure the pressure inside a category 5 hurricane to be 0.97 atm very close to the ground (sea level). What is the wind speed of the hurricane? You can assume that the density of air is 1.29 kg/m3 and the pressure outside the hurricane is 1 atm.

Answer 1

Let the pressure inside the hurricane is P1 = 0.97 atm

= 0.97 * 1.013 * 10⁵ Pa

= 0.982 * 10⁵ Pa

Let the pressure outside the hurricane is P2 = 1 atm

= 1.013 * 10⁵ Pa

The two things we can observe here are that

1. Pressure outside the hurricane region is normal atmospheric pressure just above the surface of the earth

2. Pressure inside the hurricane is less than normal atmospheric pressure. Low pressure region can be associated to the hurricane.

Density of the air is d = 1.29 kg/m³

Let the speed of the air inside the hurricane be v1

Speed of the air outside the hurricane is v2

Now we can solve the problem using the Bernoulli's equation

P1 + 1/2 * d v1² + d g h1 = P2 + 1/2 * d v2² + d g h2  

Here as we consider the air flow at heights very near to the earth surface , we can take h1 = h2 = 0

And also flow of the air outside the hurricane is very gentle and slow. So speed of the air outside the hurricane is very low compared to the speed of the air inside the hurricane. Then we can neglect the term 1/2 d v2² as it will be too small compared to 1/2 d v1²

The remaining equation will be

P1 + 1/2 * d * v1² = P2

P2 - P1 = 1/2 * d * v1²

v1² = 2* ( P2 - P1 ) / d

v1 = [ 2 * { ( 1.013 - 0.982 ) * 10⁵ } / 1.29 ]

= ( 0.0607 * 10⁵ / 1.29 )

= ( 0.0471 * 10⁵ )

= 4711.62

= 68.64 m/s

= 247.104 km/hr

So the wind travels nearly at a speed of 250 km per hour in the hurricane.