## 2 Materials and Methods
### Calculation of the Required Supplied Airflow  
The air conditioning system plays an important role in every vertical hydroponic crop. First, it allows to maintain proper and regular air circulation inside the farm, but also provides the CO\({}_{2}\) required for plant growth. To analyze the possibility of water recovery the value of treated airflow in air handling unit (AHU) needs to be established. Based on VENTS company materials the required air changes per time unit without any additional CO\({}_{2}\) supplementation is 60 air changes per hour [31]. It needs to be underlined that this amount of air changes per time unit is intended for small grow rooms. To estimate the airflow for the entire hall some fundamental calculations were performed using the assumptions available in the literature. To simplify the calculation, it is assumed, that external CO\({}_{2}\) addition is possible. The effective plant growth cubature is calculated as multiplication of total cultivation area and height of the lights and plants (about 4.0 m).  
Estimation of the air flow assumed that there are constant environmental conditions in the room (\(t_{2o}\) = 23 \({}^{\circ}\)C, \(RH_{2o}\) = 75%). The maximum heat gains (\(Q^{S}\)), and maximum humidity gains are assumed to be assimilated by the air conditioning system. In the hall there are latent heat gains related to the water vapor transport to air from plants (\(Q^{L}_{plant}\)) and sensible heat gains (\(Q^{S}_{plant}\)) due to cyclic (16 h per day) illumination of plants with LED lamps with power equal \(P_{LED}\) = 164 W/m\({}^{2}\). In accordance with the following formula [32], the value of heat gains from LED lamps is calculated as follows:  
\[Q^{S}_{LED}=0.781\cdot P_{LED} \tag{1}\]  
The maximum transpiration stream, and transfer to the internal air is calculated based on a document published by NASA (No. NASA/TP-2015-218570/REV1) [28]. Based on conducted calculations maximum transpiration is equal \(t_{r}\) = 1.97 L/(m\({}^{2}\) day). The value of latent heat from water-to-air transpiration was calculated using the formula, where \(r\) is heat of vaporization (2257 kJ/kg), and \(t_{r}\) is transpiration rate  
\[Q^{L}_{plant}=r\cdot t_{r} \tag{2}\]  
The amount of sensible heat assimilated by plants is estimated using formula [31]:  
\[Q^{S}_{plant}=LAI\cdot p_{a}\cdot c_{p}\cdot\frac{(t_{s}-t_{a})}{r_{a}} \tag{3}\]  
Sensible heat flux depends on a the aerodynamic resistance to heat (\(r_{a}\) = 100 s/m), the difference between the temperature of the transpiring surface (\(t_{s}\)) and in the surrounding air (\(t_{a}\)), \(LAI\) = 3 which is the leaf area index [33], density of the air (\(\rho_{a}\) = 1.20 kg/m\({}^{3}\)), and the specific heat capacity (\(C_{p}\) = 1005 J/(kgK)). The difference between \(t_{s}\) and \(t_{a}\) is assumed to be equal to 0.5 \({}^{\circ}\)C [34]. The summarized heat gains are presented in Table 1. In this case the sensible heat factor (SHF) equals 0.66, hence the airflow was found by choosing the larger one between the airflow calculated basing on the total cooling loads and moisture gains using following equations:  
\[V_{1}=\frac{Q^{S}}{\rho_{a}\cdot c_{p}\cdot\Delta t} \tag{4}\]  
\[V_{2}=\frac{w}{\rho_{a}\cdot\Delta x} \tag{5}\]  
\[V=max(V_{1},V_{2}) \tag{6}\]Considering all assumptions, the required supplied airflows are respectively \(V_{1}=V=28,\)500 m\({}^{3}\)/h and \(V_{2}=17,\)900 m\({}^{3}\)/h. Where \(\Delta t\) is the temperature difference between the supply airflow and exhausted airflow while \(\Delta x\) is the humidity ratio difference between supply airflow and exhausted airflow (g/kg). The \(c_{p}\) is the specific heat capacity of moist air (J/(kgK)), \(\rho_{a}\) is a density of the air (kg/m\({}^{3}\)).