Hurricanes can involve winds in excess of 120 km/h at the outer edge.
Make a crude estimate of the energy of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 kg*m^3 of radius 120 km and height 4.5 km.
Make a crude estimate of the angular momentum of such a hurricane.
To estimate the energy and angular momentum of a hurricane, let's make a few assumptions:
1. The hurricane can be approximated as a rigidly rotating uniform cylinder of air.
2. The density of air within the cylinder is uniform and equal to 1.3 kg/m^3.
3. The radius of the hurricane is 120 km (or 120,000 meters).
4. The height of the hurricane is 4.5 km (or 4,500 meters).
5. The wind speed at the outer edge is in excess of 120 km/h (or 33.3 m/s).
Now, let's calculate the energy and angular momentum.
1. Energy of the Hurricane:
To estimate the energy, we can calculate the kinetic energy of the rotating air within the hurricane. The kinetic energy is given by the formula:
KE = (1/2) * mass * velocity^2
To calculate the mass, we need to find the volume of the cylinder and multiply it by the density:
Volume = π * radius^2 * height
Mass = Volume * density
Now, substituting the values:
Volume = π * (120,000)^2 * 4,500
≈ 678,447,423,428 m^3
Mass = 678,447,423,428 * 1.3
≈ 880,976,553,357 kg
Velocity = 33.3 m/s
KE = (1/2) * 880,976,553,357 * (33.3)^2
≈ 7.09 x 10^14 Joules
Therefore, the estimated energy of the hurricane is approximately 7.09 x 10^14 Joules.
2. Angular Momentum of the Hurricane:
The angular momentum of the rotating air within the hurricane can be calculated using the formula:
L = moment of inertia * angular velocity
Since we're assuming the hurricane can be approximated by a uniform cylinder, the moment of inertia (I) can be given by:
I = (1/2) * mass * radius^2
Now, substituting the values:
I = (1/2) * 880,976,553,357 * (120,000)^2
≈ 1.274 x 10^18 kg * m^2
Angular Velocity = velocity / radius
= 33.3 / 120,000
= 2.775 * 10^-4 rad/s
L = 1.274 x 10^18 * 2.775 * 10^-4
≈ 3.53 x 10^13 kg * m^2/s
Therefore, the estimated angular momentum of the hurricane is approximately 3.53 x 10^13 kg * m^2/s.
Figure the mass of air: density*piR^2*h watch units.
Then figure moment of inertia
Finally, energy 1/2 I w^2 and momentum I w