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`Communicated by S.
Casado (LABEIN)`

The system under consideration has 27 equations and 27 unknowns with
several parameters whose value is only known approximately. Two kind of
unknowns are considered:

- the pressures: .
- the flows: .

The total degree of the equations is equal
to one or two. These come from two different physical conditions: flow
equilibrium in the different components of the electric-hydraulic circuit
and pressure value in every node of such a diagram. The flow equilibrium
equations are:
and the pressure equations are:

The initial data is given by the knowledge of the pressure and flow at the
entry node:
In this case, only real solutions are
required.