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Mercury column problem of ideal gas state equation
(1) Gas pressure P0 when not inverted+pressure P0 when ρ GH is inverted.

(p0+ρgh)s(l-h)=p0sl

L=p0/(ρg)+h

(2) suppose that h can be added.

(P0+ρGH)s(L-H)=[P0+ρg(H+H)]s(L-H-H)

The solution is h = l-2h-P0/ρ g.

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