## 3 Results and Discussion
Constant \(A_{1}\) for mass gain, water gain, moisture content increase, and volume increase was described using Equation (5):  
\[A_{1}=A_{1,0}+\frac{\frac{M_{\rm w}}{m_{d}}}{a_{1}+a_{2}\frac{M_{\rm w}}{m_{d}}} \tag{5}\]  
where \(a_{1}\) and \(a_{2}\) constants. Constant \(A_{1}\) for fry matter loss was determined with Equation (6):\[\frac{1}{A_{1}}=\left(\frac{1}{A_{1}}\right)_{0}+\frac{\frac{m_{d}}{M_{w}}}{a_{1}+a _{2}\frac{m_{d}}{M_{w}}} \tag{6}\]  
where \(a_{1}\) and \(a_{2}\) are constants. Constant \(A_{2}\) for all investigated variables (mass gain, dry matter loss, water gain, moisture content increase, and volume increase) was calculated applying Equation (7):  
\[\frac{1}{A_{2}}=\left(\frac{1}{A_{2}}\right)_{0}+\frac{\frac{M_{w}}{m_{d}}}{a_{1 }+a_{2}\frac{M_{w}}{m_{d}}} \tag{7}\]  
where \(a_{1}\) and \(a_{2}\) are constants. In Equations (5)-(7), \(M_{w}\) is the mass of rehydrating water at the beginning of the rehydration, and \(m_{d}\) is the mass of dried red beets at the beginning of the rehydration. When there is a lack of rehydrating water (\(M_{w}=0\)), it turns out from Equation (5) that \(A_{1}=A_{1,0}\). Taking into account the results from the experiments (Table 2 and Figure 2a,c-e), it can be assumed that \(A_{1,0}=0\). As far as Equation (6) was concerned, it can be counted that for the amount of rehydrating water \(M_{w}\)\(\rightarrow\)\(\infty\), \(1/A_{1}=(1/A_{1})_{0}\). Experimental results (Table 3 and Figure 2b) allowed for the acceptation that \((1/A_{1})_{0}=0\). It can be deducted from Equation (4) that when there is not any rehydrating water (\(M_{w}=0\)), the process of rehydration cannot be conducted and therefore \(X_{e}=X_{0}\) under which situation \(1/A_{2}=0\). Considering this in Equation (7), it can be accepted that \((1/A_{2})_{0}=0\). The results of the impacts of the solid-to-liquid ratio on the Peleg model constants are presented in Tables 3-5 and in Figures 2 and 3. Table 3 presents the values of the constants in Equation (5) for \(A_{1}\) (mass gain, water gain, moisture content increase, and volume increase), in Equation (6) for \(A_{1}\) (dry matter loss), and in Equation (7) for \(A_{2}\), and statistical tests of developed Equations (5)-(7) are shown in Table 4. It can be noticed that the values of the coefficient of determination R\({}^{2}\) varied between 0.8957 and 0.9654 for Peleg rate constant \(A_{1}\) and between 0.9845 and 0.9977 for the Peleg capacity constant \(A_{2}\). As far as the root mean square error (RMSE) was concerned, it can be stated that its values were within \(2\times 10^{-5}\) to 0.2320 for \(A_{1}\) and within 0.0182 to 39.3976 for \(A_{2}\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & **Statistical** & \multirow{2}{*}{**Mass Gain**} & **Dry Matter Loss** & **Water Gain** & **Moisture Content Increase** & **Volume Increase** \\  & & & & **Loss** & **Mean** & **Mean** & **Mean** \\ \hline \multirow{2}{*}{\(A_{1}\)} & R\({}^{2}\) & 0.8957 & 0.9350 & 0.9040 & 0.9571 & 0.9654 \\  & RMSE & 0.0002 & \(4\times 10^{-5}\) & 0.0001 & 0.2320 & \(2\times 10^{-5}\) \\ \multirow{2}{*}{\(A_{2}\)} & R\({}^{2}\) & 0.9904 & 0.9845 & 0.9977 & 0.9860 & 0.9920 \\  & RMSE & 39.3976 & 0.0182 & 3.4162 & 0.9160 & 29.7406 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical tests of Equations (5)–(7) applied to determine the Peleg model parameters.