Tornado energy

Most energy of a tornado is energy of motion: kinetic energy. From physics you may remember that the kinetic energy (KE) is

KE = 1/2 m v^{2}

where

m = mass (of air in tornado)

v = velocity (wind velocity in tornado).

Let's assume that wind velocity is typical of an F3 tornado, around 300 km/hr. So

v = 300 km hr^{-1} = 80 m s^{-1}

To get the mass, recall that m = r V, where r = density and V = volume. The appropriate density is that of air: r = 1 kg m^{-3}.

To estimate the volume, make a simplifying assumption: approximate the tornado shape by a vertical cylinder with height h and radius r. The volume of the cylinder is

V = p r^{2} h

Assume the cylinder is 1 km in height and 1 km in radius.

Substituting volume and density into the equation for mass, then substituting for mass in the expression for kinetic energy,

KE = 1/2 p r^{2} h v^{2}

= 1/2 p (10^{3} m)^{2} (10^{3} m) (80 m s^{-1})^{2}

= 3 x 10^{12} J = 3 x 10^{19} ergs

This energy is quite small in comparison with the energy of other phenomena we have studied (e.g. earthquakes and volcanic eruptions). Nevertheless, tornadoes are destructive because this energy is concentrated into a very small region, compared with the large regions that earthquakes and volcanoes affect.