# Development and Application of a Novel Non-Iterative Balancing Method for Hydronic Systems
## 3 Theory and Calculations
### Experimental Validation
#### 3.5.2 Comparison between Ratio Method and PFM  
First, a set of target flow rates was defined as well as a balancing tolerance value of \(\pm 10\%\) for individual flow rates, according to the standard requirement (ASHRAE and NEBB [28; 29; 32]) and international commissioning associations such as the Building Services Research and Information Association (BSRIA) [33].  
Nominal pressure drop values of the simulated terminals were defined with reference to typical hydronic terminals, and the determined values were obtained by adjusting the calibrated balancing valves positioned for that purpose.  
This configuration applies to a real case of seven fan coil units (from A2 to D2) characterized by head losses of about 5 kPa with quite different nominal values of flow rate, and one different type (A1) representing a manifold serving an underfloor heating/cooling system whose loss is estimated at 30 kPa. The established flow rates, referring to a working \(\Delta T=5\)\({}^{\circ}\)C, led to heating capacities values consistent with the defined types.  
Table 2 shows the system design configuration and lists the assumed thermal powers, design flow rates, pressure losses, and handwheel position of the drop simulation valve for each thermal unit (TU).  
\begin{table}
\begin{tabular}{c c c c} \hline
**Instrument** & **Model** & **Measuring Range** & **Accuracy** \\ \hline Ultrasonic flow meters at terminals & \begin{tabular}{c} Belimo electronic valves mod. \\ EP015R \\ \end{tabular} & 0–1200 L/h & 6\% of the reading value ranging from 25\% to 100\% of the measuring range. \\ \hline Rotameter flow meters at the pump & \begin{tabular}{c} Frank mod. M350 \\ \end{tabular} & 50 \(\div\) 500 L/h & 8\% of measured value for flow rates between 20\% and 100\% of measuring range according to \\ \hline Pressure probes & \
\begin{tabular}{c} Thermokon mod. DPL1V \\ \end{tabular} & 0 \(\div\) 1 Bar &
\begin{tabular}{c} Declared accuracy 1\%, \\ resolution 0.2 kPa. \\ \end{tabular} \\ \hline \end{tabular}
\end{table}
Table 1: Measurement Equipment, Models, Ranges, and Accuracies.  
Figure 12: Test rig realization.  
As the two methods refer to different flow meter readings, the comparison of the results required an initial consistency check of the measuring instruments. The full test carried out is described in Appendix E. The main result was that in the range of flow values to be considered for comparison, rotameters overestimated the measurement by an average of 4.9% compared with ultrasonic probes (Appendix E Table A1).  
After the adjustment step, the PFM (higher measuring rotameter-referred) is expected to lead to a pump speed that is lower than the velocity obtained after the final adjustment step required by the ratio method procedure (lower measuring MBV-referred). According to the consistency check, the expected difference for pump velocity was about 5%.  
However, although at different final speeds, both methods were expected to reach the same proportion of flow rate values according to the design data; so, the most significant validation resulted from the comparison of final valve positions.  
After conducting the preliminary set-up activities, the two methods were applied in succession. The step-by-step execution of the two procedures is reported in Appendix F.  
At the end of both procedures, the flow values and the positions of all balancing devices as well as the final speed of the pump were registered. It was also verified that both methods led to an effective minimum energy/pressure configuration, with at least one clear path.  
Finally, for each method applied, the number of balancing actions N\({}_{\text{bal}}\) required as well as the number of measurements N\({}_{\text{meas}}\) (including the repositioning of the probe instruments) was determined.