The radius of a hurricane is about 500km. The wind speed near the center (eye) w

Question

The radius of a hurricane is about 500km. The wind speed near the center (eye)
whose radius is estimated at 25km, reached 250km / h. The air inlet from the edge of the hurricane towards the eye and the rotation of the system conserves angular momentum.

a)Estimate the wind speed near the edge of the hurricane.

b)Calculate the pressure in the eye of the hurricane if the pressure near the edge is approximately one atmosphere.

c)If the kinetic energy of the winds when reaching the eye of the hurricane becomes potential energy determine how high up the air goes.

Explanation / Answer

given that radius of haricane r = 500km wind speed v = 250 km/h for a particle a distance r from the axis the angular momentum is L = mvr a+ from the angular momemtum the product of hte radius and speed is constant , so the speed at the rim is about 250 km/h * 30km/ 350km = 21.42 km/h b) the pressure i slower at the eye by an amount         p = 1/2 * 1.2 kg / m3 ( (250 km/h)2 - ( 21.42 km/h)2 ) ( 1m/s/ 3.6 km/h)2 = 2.8 * 103 pa c)   from the equation of kinematics                v2 = 2gh             h = v2 /2g               = ( 250 km/h)2 / 2 * 9.8 m/s2              = ( 250 * 5/18 m/s)2 / 2 * 9.8 m/s2             = 246m              = ( 250 * 5/18 m/s)2 / 2 * 9.8 m/s2             = 246m

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