# Blast Waves and Scaling Relations

1. Aug 18, 2009

One of the outstanding questions I have in physics relates to scaling relations.

Say you're presented with a problem like: Find X--which has units of y--given that the relevant (dimensional) quantities of this problem are A, B, C, and D. Then you construct a solution using these quantities based not on physical principles, but rather on dimensional analysis!

An examplar of this sort of logic is the Sedov-Taylor solution of exploding bombs/stars in an atmosphere/interstellar medium.

You want to find the radius of the blast given the energy of the explosion and the density of the medium into which the blast wave propagates and you suddenly get:

$$R= \left(\frac{E}{\rho}\right)^{1/5}t^{2/5}$$

I often hear the phrase "self-similar" attached to this sort of conversation. I assume this has something to do with solutions to a certain class of partial differential equations. Can anyone enlighten me?