= Two-plume three-layer displacement ventilation
{title2=$g_1'/g_2'=(\psi+\psi^{2/3})/(1+\psi)$}
Two independent point-source <pure plumes> with $\psi=B_1/B_2<1$ remove lower-layer volume $Q=C(B_1^{1/3}+B_2^{1/3})h_1^{5/3}$. If plume 1 feeds the middle layer, its reduced gravity is $g_1'=B_1/[CB_1^{1/3}h_1^{5/3}]$. The upper outflow carries both sources, so $g_2'=(B_1+B_2)/Q$, yielding the displayed ratio. Opening flow is driven by the integrated hydrostatic head $g_1'(h_2-h_1)+g_2'(H-h_2)$. A plume crossing the lower interface has altered buoyancy relative to its new ambient and must be continued with nonzero incoming mass and momentum fluxes rather than reset as a zero-flux pure plume.
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