# Development and Application of a Novel Non-Iterative Balancing Method for Hydronic Systems
## Appendix B Analysis of Cases Where the Farthest Terminal Is Not the Most Disadvantaged
### Determination of the MD Terminal in Manifold-Based or Reverse Return Configurations  
Firstly, the disadvantaged terminal can be identified in every configuration by the designer during sizing activity. Whatever the procedure of identification, this terminal will assume the role of \"reference\" or \"index\" and will be chosen as the starting terminal as discussed in the paper.  
In the absence of the appropriate design documentation, it will still be possible to identify the disadvantaged terminal, provided that at least all design flow rates are known.  
The determination of the MD terminal can be experimentally carried out in a manner that depends on the availability of terminal flow sensors or a single sensor at the pump (or common section).  
1. Having individual flow meters available on each terminal user, it is enough to carry out a preliminary measurement with all valves fully open. The most disadvantaged terminal can be found by calculating the characteristic ratio \(\dot{Q}_{Measured}/\dot{Q}_{Nominal}\) for each path and choosing the one with the lowest value as commonly practiced when using the traditional Ratio Method (see Appendix A.2).
2. Alternatively, by using a single flow meter at the pump, different sub cases must be considered: (i) if the terminals are same model and size and connected by piping have similar length, there is no reason why the \(\dot{Q}_{Measured}\) flow can vary, then the MD terminal is by definition the one with the greatest \(\dot{Q}_{Nominal}\) flow rate value, and there's actually no need for measurements; this case also arises when terminals of the same size have so significant pressure losses that the path's differences are negligible. (ii) if the design flow rate values of the users are the same but path lengths are different, the flow rate of each terminal can be measured by running the pump at a constant speed and fully opening/measuring only one path at a time closing the others. The calculation of the ratio \(\dot{Q}_{M}/\dot{Q}_{N}\) allows the terminals to be sorted and the MD to be identified. (iii) if both lengths and flow rates of each path/terminal are different, the previous test, to be exhaustive, must be conducted by imposing a constant manifold pressure; this requires a pressure detection across supply and return sections of the manifold. That pressure detection can also be used as pressure reference for control loop in PFM procedure.  
The reverse return configuration presents quite an analogy with the already discussed main manifold-based case; the working pressure of each user is invariant because of the connection, and the different allocation of line drop losses between supply and return are composed in such a way as to be self-compensating. This makes this type of circuitry assimilable to the manifold-based circuit and can be approached in the same way, simply by identifying the MD terminal as previously described and starting from that; in the absence of a manifold, the pressure measurement related to the (iii) case can be performed directly across one of the connected terminals.  
Frequent is also the hybrid case of a main manifold with the departure of distributed lines (e.g., risers serving radiators or fancoils) or the case of a primary distribution serving zone manifolds in sequence with direct/reverse return as shown in Figure A2.  
In these cases, local zone manifolds represent complex users which can be conceptually replaced by equivalent users having the total flow rate and design pressure head of the manifold and whose size of which is not related to the position, but generally depends on the heat loads of each zone; in these situations, it can easily happen that the farthest manifold is not also the MD one.