We can model the water consumption $\dot{m}_{w}$ of a simple humidifier using the following equations:
\begin{align} \eta_{hum} & = {T_{db,i} - T_{db,o} \over T_{db,i} - T_{wb,i}} \\ h_{o} & = h_{i} \\ \dot{m}_{w} & = \dot{m}_{a}(w_{o} - w_{i}) \end{align}
where the subscripts $i$ and $o$ denote the entrance and exit of the humidifier respectively, $\eta_{hum}$ is the efficiency of the humidifier, $T_{db}$ and $T_{wb}$ are the dry and wet bulb temperatures of the air respectively, $h$ and $w$ are the enthalpy and humidity ratio of the air respectively, and $\dot{m}_{w}$ and $\dot{m}_{a}$ are the mass flow rate of the water and air respectively.
We can fix $\eta_{hum}$, $\dot{m}_{a}$, and the atmospheric air pressure to study just the effects of the temperature and humidity of the entering air on the water consumption.
I created this psychometric chart with four different air conditions to see if I could pinpoint one thermodynamic property of the entering air that would be responsible for the water consumption, but the story seems to be a bit more complicated than that. The relative humidity $\phi$ appears to be the property with the highest correlation with water consumption, but higher relative humidities don't always result in lower water consumptions.
What is the full story?
