= Pure plume balance
{title2=$M^{5/2}=5FQ^2/(8\alpha)$}
For the constant-entrainment axisymmetric plume equations $Q'=2\alpha\sqrt M$, $M'=FQ/M$ with $F>0$, pure balance means $M^{5/2}=5FQ^2/(8\alpha)$ at every height. This is a similarity relation between fluxes, not a requirement that the physical source have zero radius. A finite source on this curve is represented by a <plume virtual origin>. For fluxes normalized by pi and top-hat fields, the same relation is $g'b/w^2=8\alpha/5$.
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