When the flow rate of the pump is fixed, it is possible, with the addition of multiple fixed flow rate pumps to produce a system where the in-flow and out-flow of a particular node are not the same and this would result in an invalid system where a flow balance could never be achieved.

The fixed flow rate pump defines the flow rate and this cannot vary to give a flow / pressure balance within the system, so some other part of the system must be allowed to vary. If flow control valves are also used, at least one flow path must have no control device fitted. If all flow paths are controlled, it will not be possible to solve the system, and in this case the system is termed over-controlled. 

If a pump with a fixed flow rate is used on a ‘main line’ that branches to other paths with flow control valves then at least one path on the branch lines must have no flow control valve. The flow rate along this path will be set to the difference between the total flow in all other paths and the flow rate produced by the fixed flow rate pump.

Flow control valves need to have a positive pressure at their inlet that is sufficient to meet the system pressure losses after the flow control valve (through pipe friction, fittings, components, changes in elevation) plus the pressure loss that the flow control valve itself needs to introduce to achieve a balance within the pipe system. If the required pressure cannot be achieved, it will not be possible to solve the system.