# Development and Application of a Novel Non-Iterative Balancing Method for Hydronic Systems
## 5 Discussion  
Regarding the terminal valve positions, the fact that B2 and C2 showed positions that differed by 14% and 17%, respectively, at the ends of the two procedures deserves further investigation: the assessment that needs to be made is firstly whether the difference in flow rate is expected to be greater or less than the difference in valve stroke. Since the valves used in the balancing test rig were control valves, the factors that must be considered for this analysis derive from the theory describing the flow rate/position relationship for this type  
Figure 13: Final valve configurations after application of ratio and PF methods. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Design Data**} & \multicolumn{3}{c}{**Ratio Method**} & \multicolumn{3}{c}{**Progressive Flow Method**} \\ \hline \multirow{3}{*}{ \begin{tabular}{c} **Terminal** \\ **Unit** \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} **Design** \\ **Flow Rate** \\ **[l/h]** \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} **Valve** \\ **Opening** \\ **[\%]** \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} **Final** \\ **Pump** \\ **Speed** \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} **Flow Rate** \\ **[l/h]** \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} **Valve** \\ **Sum of MBV** \\ **[l/h]** \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} **Value** \\ **[l/h]** \\ \end{tabular}  } & \multirow{3}{*}{\ \begin{tabular}{c} **Final** \\ **Opening** \\ **[\%]** \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} **Flow Rate** \\ **[l/h]** \\ \end{tabular}  } \\ \hline A1 & 200 & 100\% & & & 100\% & & \\ \hline A2 & 300 & 55\% & & & 60\% & & \\ \hline B1 & 300 & 100\% &  
of valve. These factors are represented by (i) the inherent characteristics of the valves used, (ii) the degree of openness of the valves in which the behavior is to be analyzed, and (iii) the value of the Authority parameter assumed by the valves with respect to the controlled circuit. These valves are designed to maintain equipercentage behavior in the upper half of the opening and the authority calculation gives a value for both in the range of 0.2-0.3. In accordance with ASHRAE [30] and as shown in Figure 14; considering an Authority value within the range [0.2-0.3] (or, in percentage, [20-30%]), the flow rate variations related to the difference in the opening respectively between 92% and 75% and between 70% and 54%, were expected to be lower than 10%, as highlighted by the red and green reference quotas. As for the speed rotation of the pump and referring to the previously expressed considerations, the difference must be consistent with the difference in measurements obtained by the instruments taken as the reference instruments for each method; the value obtained by applying the PFM method based on rotameters led to a rotation speed of \((80-85)/80\times 100\)\(=-6.25\%\) lower than that obtained with the terminal ultrasonic probe-based ratio method, in good agreement with the 4.9% difference verified by carrying out preliminary consistency tests between the two measuring instruments (Appendix E, Table A1). After discussing the PFM from the theoretical point of view and its experimental validation, it is considered useful to investigate its practical advantages. A first evaluation was made by simply comparing the overall N\({}_{\text{meas}}\) and N\({}_{\text{bal}}\) required by the application on the test rig; the values were compared with the ones obtained through application of the PFM, see Table 4.  
The PFM proved to be more efficient, both in terms of the actions required for balancing and in terms of movement of the measurement probes; the advant \begin{table}
\begin{tabular}{c c c c} \hline \hline
**N** & **Ratio Method** & **PFM** & **Difference** \\ \hline N\({}_{\text{meas}}\) & 27 & 14 & \(-48\%\) \\ \hline N\({}_{\text{bal}}\) & 22 & 13 & \(-41\%\) \\ \hline \hline \end{tabular}
\end{table}