It is dimensional analysis provided you can justify that the constant should approximately be 1. This is what G. I. Taylor did for the fireball of the trinity t

It is dimensional analysis provided you can justify that the constant should approximately be 1. This is what G. I. Taylor did for the fireball of the trinity test. And apparently it does end up being close to 1. I do worry about the accuracy of this a bit, but looks like it could in theory work.