= Plume-fed doorway ventilation
{title2=$z_i^5=(8/27)\gamma^3W^2(D-z_i)^3$}
For a <pure plume> with $g'_p=\gamma B^{2/3}z^{-5/3}$, a steady sharp interface at $z_i$ has $Q_p=B^{1/3}z_i^{5/3}/\gamma$ and warm-layer <reduced gravity> $g'=B/Q_p$. A freely discharging upper doorway of height $D$ and width $W$ has available head $D-z_i$. Equating plume supply to the <broad-crested weir> flux gives the displayed implicit height relation, with $0<z_i<D$. Warm air above the doorway stores heat but adds no available head at its crest in this uniform-layer model.
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