## 3 Results
### Permeability  
Equation (5) adequately reproduces the relationship between the pressure drop across the pad and inlet air velocity, as is shown in Figure 12 for the \(BC\) pad. In this case, the permeability (\(K\)) and the Forchheimer coefficient (\(\beta\)) of the equation were estimated for each water flow used. To obtain a universal expression to compute the pressure drop across the pad as a function of the inlet air velocity and the water flow, the permeability and the Forchheimer coefficient were considered proportional to water flow, as \(K(Q)=\frac{1}{J_{1}+J_{2}Q}\) and \(\beta(Q)=(g_{1}+g_{2}Q)\). Two additional cases were evaluated: assuming that the permeability was water flow dependent or that the Forchheimer coefficient was water flow dependent. The goodness of the fitted equations was compared through the coefficient of determination (R\({}^{2}\)) and the RMSE. The best values were obtained when the permeability was considered constant and the Forchheimer coefficient as a function of the water flow. Figure 13 compares Equation (5) fitted to each water flow when the permeability and the Forchheimer coefficient were considered as constants (solid line), and fitted to all the  
Figure 11: Normalized pressure drop as a function of water flow for an air velocity of 1 m s\({}^{-1}\). The colour bars correspond to different water flows: blue: \(Q=2\) L min\({}^{-1}\) m\({}^{-1}\), red: \(Q=6.2\) L min\({}^{-1}\) m\({}^{-1}\) and orange: \(Q=10\) L min\({}^{-1}\) m\({}^{-1}\). Figure 10: Normalized pressure drop as a function of inlet air velocity (\(u\)) for a constant water flow of 6.2 L min\({}^{-1}\) m\({}^{-1}\). The colour bars corresponds to different air velocities: blue: \(u=0.5\) m s\({}^{-1}\), red: \(u=1.0\) m s\({}^{-1}\), orange: \(u=1.5\) m s\({}^{-1}\) and magenta: \(u=2\) m s\({}^{-1}\). Figure 9: Pressure drop across the pads studied for a fixed value of inlet air velocity (\(u=1\) m s\({}^{-1}\)) and water flow (\(Q=6.2\) L min\({}^{-1}\) m\({}^{-1}\)). experimental data (asterisk markers), considering the permeability as a constant and the Forchheimer coefficient as a function of the water flow. There was no visible difference between them for \(u<1.0\) and a slight deviation for higher \(u\) was detected. Table 12 summarizes the \(g\)'s coefficients, R\({}^{2}\), RMSE, permeability and the Forchheimer coefficient for a water flow of 6.2 L min\({}^{-1}\) m\({}^{-1}\) for comparison purposes. As the pad is constantly wetted, the water forms a thick layer over the material, which affects the flow of air, increasing \(\Delta P\). However, the permeability could be considered constant, while the Forchheimer coefficient changes with the water flow. The coefficient \(g_{2}\) shows the effect of the water flow over \(\Delta P\). For the cellulose material, this parameter is small. For the \(CS_{1}\) and \(BC\) materials this parameter presents significant influence as was shown previously in Figure 11. \begin{table}
\begin{tabular}{l c c c c c} \hline
**Pad** & \(g_{1}\) & \(g_{2}\) & \(R^{2}\) & **RMSE [Pa]** & \(K\) [m\({}^{2}\)] & \(\beta\)**(6.2) [m\({}^{-1}\)]** \\ \hline \(CL\) & 20.8546 & 0.2351 & 0.9997 & 0.18166 & \(1.3959\times 10^{-6}\) & 22.31 \\ \(CS_{1}\) & 946.7572 & 72.6893 & 0.9988 & 1.36296 & \(1.0108\times 10^{-7}\) & 1397.4 \\ \(CS_{2}\) & 551.5387 & 39.3833 & 0.9995 & 1.05007 & \(3.6648\times 10^{-7}\) & 795.7 \\ \(BC\) & 891.2264 & 82.1001 & 0.9991 & 1.63633 & \(2.4308\times 10^{-7}\) & 1400.2 \\ \(PS_{1}\) & 358.6404 & 17.9078 & 0.9995 & 0.90228 & \(1.4939\times 10^{-7}\) & 469.7 \\ \(PS_{2}\) & 287.9664 & 9.8696 & 0.9993 & 0.85144 & \(2.6975\times 10^{-7}\) & 349.2 \\ \hline \end{tabular}
\end{table} 
Table 12: Permeability (\(K\)) and coefficients used to compute the Forchheimer coefficient as a function of water flow (\(\beta(Q)=(g_{1}+g_{2}Q)\)) in Equation (5). The coefficient of determination (\(R^{2}\)) and the Root Mean Square Error (RMSE [Pa]) of the fitted equation are presented.