# Humidity Conditions of Aerated Concrete Walls Depending on the Type of Finishing Coating
## 2 Materials and Methods
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**City** & **Rostov-on-Don** & **Voronezh** & **Novosibirsk** & **Vorkuta** \\ \hline Average temperature of the & & & & \\ heating period th\({}_{\text{p}}\), \({}^{\circ}\)C & \(-0.1\) & \(-2.5\) & \(-8.1\) & \(-9.5\) \\ Terms of use & A & A & A & A \\ Duration of the heating & & & & \\ period Zh\({}_{\text{p}}\), days & & & & \\ Average monthly relative & & & & \\ air humidity during the & & & & \\ coldest month, \% & & & & \\ Heating degree days & 3337 & 4275 & 6238 & 8791 \\ Monthly average & & & & \\ temperatures used in & & & & \\ the calculations: & & & & \\ October & 9.6 & 6.6 & 2.6 & \(-4.2\) \\ November & 3.4 & 0 & \(-7.3\) & \(-12.8\) \\ December & \(-1.2\) & \(-4.8\) & \(-14.4\) & \(-16.7\) \\ January & \(-3.8\) & \(-7.4\) & \(-17.6\) & \(-20.4\) \\ February & \(-3.0\) & \(-7.0\) & \(-15.8\) & \(-20.0\) \\ March & 2.4 & \(-1.3\) & \(-8.0\) & \(-14.2\) \\ April & 10.9 & 8.4 & 2.7 & \(-9.4\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Design climatic parameters. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Aerated Concrete Grade**} \\ \cline{2-5}
**City** & **D350** & **D400** & **D500** & **D600** \\ \hline Vorkuta & 0.60 & 0.65 & 0.80 & 0.95 \\ Novosibirsk & 0.45 & 0.50 & 0.65 & 0.75 \\ Voronezh & 0.40 & 0.40 & 0.50 & 0.60 \\ Rostov-on-Don & 0.35 & 0.35 & 0.45 & 0.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Thickness of the aerated concrete layer, m.  
After that, according to the calculated values for the temperatures \(\tau_{xi}\), the values for the maximum elasticity of the water vapor \(E_{i}\) are calculated using the formulas:  
\[E_{xi}=610.5\exp\left(\frac{17.269\cdot\tau_{xi}}{237.3+\tau_{xi}}\right),\ \tau_{xi}\geq 0\ ^{ \circ}\mathrm{C} \tag{2}\]  
\[E_{xi}=610.5\exp\left(\frac{21.875\cdot\tau_{xi}}{265.5+\tau_{xi}}\right),\ \tau_{xi}\leq 0\ ^{ \circ}\mathrm{C} \tag{3}\]  
Using the thermodynamic analogy, the values for the actual elasticity of the water vapor at the boundaries of the individual layers \(e_{x}\), Pa, should be determined by the formula:  
\[e_{xi}=e_{int}-(e_{int}-e_{out})\frac{R_{xi}^{p}}{R_{0}^{p}} \tag{4}\]  
where \(e_{int}\) is the actual water vapor pressure of the indoor air, Pa;  
\(e_{out}\) is the actual water vapor pressure of the outdoor air, Pa;  
\(R_{0}^{p}\) is the total actual reduced vapor permeability resistance in the outer wall, m\({}^{2}\cdot\)h\(\cdot\)Pa/mg; and  
\(R_{xi}^{p}\) is the total vapor permeability resistance, starting from the internal air to a given section in the thickness of the outer wall, m\({}^{2}\cdot\)h\(\cdot\)Pa/mg. Then, using the empirical method, the outside air temperature \(t_{out}\) was chosen, at which the following condition was fulfilled in the enclosure in one of the layers:  
\[e_{xi}\approx E_{xi} \tag{5}\]  
This temperature is called the temperature at which condensation begins \(t_{b,c}\). When the outside temperature \(t_{out}\) drops below this value, the conditions for the formation of condensate are created in the outer wall. When the outside temperature \(t_{out}\) rises above this value, the conditions for the formation of condensate will not be created in the outer wall (Figure 2). To calculate the amount of condensate formed in a given month, the following method was employed. The amount of condensate falling per hour (mg/m\({}^{2}\cdot\)h) was determined, using the formula, by the average temperature in the calculated month:  
\[G_{c}^{h}=G_{hyd}^{h}-G_{dry}^{h} \tag{6}\]  
Figure 2: Method for determining the temperature at the onset of condensation \(t_{b,c}\): (**a**) \(t_{out}=t_{b,c}\): (**b**) \(t_{out}<t_{b,c}\); (**c**) \(t_{out}>t_{b,c}\).