User blog:ThePerpetual/Request 7: Something Witty About Mountains

So basically,

This happens.

Mountain Busting Times A Lot
More specifically, "hundreds upon hundreds." Hundreds, normally, I'd just assume 200 for, but this seems to imply a fair few hundred of these things- furthermore, since we're using absolute minimum for mountain height (610 meters) and a 45 degree slope (below average volume to height ratio), we're more or less taking for granted that not a single mountain in the range will double, triple, etc. our currently assumed volume.

All of this being said, I think that it is relatively fair to assume a total of 400 mountains of our usual size, here.

Also, they're being "popped like balloons": that definitely implies at least violent fragmentation. It could even be pulverization, really, since the "rubble" left over could easily have resulted from the actual earth underneath the mountains, themselves.

Volume of a Mountain, with Radius and Height of 610 meters: 237694000 cubic meters. Or, 2.37694e+14 cubic centimeters.

Multiply this by 400, since 400 mountains, and we get 9.50776e+16 cc.

Violent Fragmentation is 69 J/cc, for stone, while Pulverization is 214 J/cc, so

Lower-End: 9.50776e+16 * 69 = 6.5604e+18 Joules, or 1.568 Gigatons of TNT. Large Mountain level.

Higher-End: 9.50776e+16 * 214 = 2.0347e+19 Joules, or 4.863 Gigatons of TNT.

...that's probably a lot lower than it could be if I were willing to take more liberties

But Wait, There's More-
Of course, there's also the fact that the entire mountain range was swallowed by a raging hurricane wind! So...

First, to find the effective area of the range, I'll figure out the area of a square with side lengths equal to the diameter of the mountain's base: one for each range: hopefully those means seem reasonable...

(Area of a single mountain + Square Base: (610 * 2)^2 = 1742400 sq. meters)

Then, multiply that by 400, to account for the totality of the range-

1742400 * 400 = 696960000 sq. m

...which, uh, as it turns out, making a hurricane of that area does near jack diddly squat. Even if we were to round up to the area of New York City (783800000 m^2), you would get (using 5.89 Joules/cc for instability, which seems to best fit) a total of 3.7043e+16 Joules, or 8.853 Megatons of TNT- barely noticeable from up in the Gigatons range.

Time for the Run-Back
So, thus far it's been a wee bit underwhelming, sure. But! ...well, if we're going to take "converted the clouds into raw energy" | seriously...

Area = 696960000 m^2

Height = 8000 m

Volume of Clouds = 5.57568e+12 cubic meters

Density of Clouds = | 0.5 grams/m^3

Mass of Clouds = 5.57568e+12 * 0.5 = 2.78784e+12 grams, or 2787840000 kg.

So, plug that into the calculator above, and...

2.5056e+26 Joules. Almost exactly 60 Petatons of TNT.

...at least, assuming we can take that literally.

...



Final Results
Mountain Busting Times A Lot: 1.568 - 4.863 Gigatons of TNT, somehow

But Wait, There's More: 8.853 Megatons of TNT

Time For the Run-Back: ~60 Petatons of TNT