Using dimensional analysis I estimate that the energy contained in the awful #Beirut explosion was approximately 12 Terajoules = 3 kilotons of TNT. For reference the "Little Boy" dropped on #Hiroshima was ~13-18 kilotons of TNT. #orderofmagnitudephysics

To estimate this, I used the following relationship between the energy of the explosion (E), the radius of the explosion (R), the time since explosion (t), and the density of air (rho).

To determine the exact points in time in milliseconds, I wrote a python script to make subtitles for the video which show the time in milliseconds. I then loaded the video and subtitles into @VlcMediaPlayer. (with help from https://superuser.com/questions/964808/video-player-that-shows-milliseconds?noredirect=1&lq=1)

In order to estimated the explosion radius sizes from the video stills I determined the size of the building next to the explosion using @googlemaps. The orange circle is an estimate where the video above was taken from. The building is 500ft in length.

Using the known density of air at sea level, I plugged in the time and radius estimates from 5 still photos to get 5 energy estimates. I then averaged them to obtain (6.9 + 11.3 + 11.6 + 11.8 + 17.1)/5 = 11.7 TJ = 2.8 ~ 3 kilotons of TNT.

Image 1.

Time: 0.050 ms
Diameter: 215 m
Energy: 6.9 TJ

Image 2:

Time: 0.090 ms
Diameter: 300 m
Energy: 11.3 TJ

Image 3:

Time: 0.130 ms
Diameter: 350 m
Energy: 11.6 TJ

Image 4:

Time: 0.180 ms
Diameter: 400 m
Energy: 11.8 TJ

Image 5:

Time: 0.230 ms
Diameter: 475 m
Energy: 17.1 TJ

This calculation was inspired by G.I. Taylor who originally estimated the energy of the #Trinity atomic bomb in New Mexico in 1945 from 4 still photos of the explosion. http://sites.science.oregonstate.edu/~restrepo/MTH481/Classnotes/GITaylor/GITaylorAnalysis.pdf