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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.

Psychometric chart and property values

What is the full story?

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higher ambient temperature means higher water consumption and so does lower relative humidity. There are air conditioning handbooks which explain all this in detail. Try the one published by Trane.

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