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The density-related, Landau and Lifshitz hydrostatic "pressure" p(ρ,T), appearing in the modern literature on the stresses in polarizable fluids, and known also as the Abraham-Becker hydrostatic "pressure", is examined in a thought experiment. Fluid in a rectangular channel is put through a cyclic magnetization and dilatation process at constant temperature. A very direct solution for p(ρ,T) is obtained using the concepts of lumped-parameter electromechanics. The properties of this "pressure" as a carrier of density information and as a contributor to the stresses are illustrated.