Question

Hurricanes can involve winds in excess of 130 km/h at the outer edge.

a) 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/m3) of radius 84 km and height 4.8 km .

b) Make a crude estimate of the angular momentum of such a hurricane.

Answer 1

Hurricanes can involves winds in excess of 120 km/h. make crude estimate of (a) the energy, (b) angular momentum. Approximate the hurricane as a rigidly uniform cylinder of air (density 1.3 kg/m3) of radius 100 km and height 4.0 km.

The first thing to do is to estimate the mass of air involved in the hurricane.

Mass = density×volume of cylinder

= (1.3 kg/m3)(pr2h)

= (1.3 kg/m3)(p(100,000 m)2(4000 m)

= 1.63×10^14 kg.

For a rigid cylinder the moment of inertia about the center is

I = ½ MR2

= ½ (1.63×1014 kg)(100,000 m)2

= 8.17×10^23 kg×m2

a. The energy is in the form of rotational KE.

KEr = ½ Iw2 where w = v/r = 36.1 m/s/100,000m = 3.61×10-4 rad/s since v = 130 km/h = 36.1 m/s.

Thus KEr = ½ (8.17×10^23 kg×m2)(3.61×10-4 rad/s)^2

= 5.32×10^16

b. The angular momentum

L = Iw = (8.17×10^23 kg×m2)(3.61×10^-4 rad/s)

=2.95x10^20 kg×m2