H₂O 179 μm/557 GHz ratio vs. the H₂O 179 μm intensity (expressed in erg s^-1 cm^-2 sr^-1). Theoretical LVG predictions are plotted for volume densities of 10⁵, 10⁶ and 10⁷ cm^-3, and for kinetic temperatures of 300 K (dashed line) and 500 K (full line). Along each curve the N(o-H₂O) column density varies from 10¹² to 10¹⁶ cm^-2 in steps of a factor 10. Open cyan circles refer to intensities measured in a beam of 38′′, equal to the beam size of the 557 GHz observations. Filled red circles plot the unconvolved PACS intensities. The data point for L1448-C is labeled.