a) Values of N_H2O for ΔV = 100 km s^-1 as a function of τ₁₀₀, for T_dust = 55 K (red) and 75 K (blue), required to account for the observed averaged L_H2O/L_IR ratios in HII-mild AGN sources (as given by Y13). Models both without (squares) and with (triangles) collisional excitation are shown. In the latter models, T_gas = 150 K, and n_H2 = 5 × 10⁴−3 × 10⁵ cm^-3 for T_dust = 55−75 K, respectively. The large filled symbols indicate the best fit models to the averaged SLED. Panels b)− e) compare in detail the four models with τ₁₀₀ = 0.1 (both with and without collisions) with the observed values (black circles) in HII-mild AGN sources (both the normalized flux ratios (SLED) and the L_H2O/L_IR ratios, Y13, for lines 2−6). In panels b) and d), the models indicate the values of L_H2O/L_IR for ΔV = 100 kms^-1. Lines 1, 7, and 8 are excluded from the comparison because of their low detection rates (Y13).