|
Your illustration is certainly sobering, but most likely not quite correct. It would be absolutely correct if the lake had vertical sides like a cylinder, but it doesn't, the bottom slopes just a few degrees from horizontal.
Since I'm a math nut, I tried to find the volume of a hypothetical lake in the shape of an inverted cone, whose base is a perfect circle with an area of 630 square miles and whose sides slope at an angle of 10 degrees. The base would therefore be a circle with a radius of about 14.161 miles or 74,770 feet, rounded to the nearest foot. The height of the cone would be 74,770 x tan(10 deg) or 13,184 feet to the nearest foot. The volume of the cone, IIRC, is (1/3)x(r squared)x(h), or 24,568,616,477,867 cubic feet. That's for the whole cone, mind you.
Next, we find the volume of a cone in exactly the same shape, but with a height two feet shorter. The height is therefore 13,182 feet, the corresponding radius is 13,182/(tan(10deg)), or 74,759 feet. This leads to a smaller cone with a volume of 24,557,662,107,914 cubic feet, a difference of 10,954,369,953 cubic feet, or about one third of what you calculated.
So instead of 514 towers full of water, it would only take 160 towers worth. Having said all that, it still scares the crap out of me.
Peace.
|