The eminent British fluid dynamicist G. I. Taylor deduced the energy release \(E\) from the first atomic explosion simply by dimensional analysis. This was strictly classified information, but Taylor showed that those well versed in dimensional analysis have access to such confidential information!

A shock wave of radius \(R\) is produced by the explosion and \(R\) increases as a function of time, \(t\). Taylor showed that

\[R=C E^{1 / 5} t^{2 / 5} ho^{-1 / 5}\]

Verify his result, which was based on dimensionless analysis. The energy release was classified information but from the pictures of the explosion \(R\) vs. \(t\) could be plotted on a \(\log -\log\) scale and the plot should have a slope of \(2 / 5\). The estimate of the energy release can then be obtained from the intercept of this graph. Taylor assumed the constant \(C\) above to be nearly one (this value was based on a similar model problem) and estimated the energy release. His estimate was in close agreement with the classified value.