Bond graphs [21] are based on modeling energy flow, power, between system components and inherently enforce continuity of power and conservation of energy. This provides a systematic framework for building consistent and well constrained models of dynamic physical systems across multiple domains (e.g., electrical, mechanical, hydraulic). They rely on effort variables to represent generalized voltage, pressure, temperature, etc., and on flow variables to represent generalized current, volume flow, entropy flow, etc. The product of effort and flow represents power, and, therefore, each power connection (bond) has these two variables associated with it. The topological character of bond graphs allows for compositional modeling and makes them directly applicable to qualitative processing. This renders them useful in situations where precise numerical information may not be available. However, analytic system models derived from bond graphs are also amenable to quantitative simulation and analysis. Furthermore, bond graphs embody a direct relation between state variables and physical component parameters, and their causality constraints provide the mechanisms for effective and efficient diagnosis. Finally, in previous work we have shown that bond graphs can be extended to systematically facilitate structural changes in model configurations [10, 13, 16].
To illustrate, we derive the bond graph model for a simple
bi-tank system illustrated in Fig. 4.
First, common pressure, effort, points are identified as 0-junctions.
These junctions represent a general form of Kirchhoff's current law,
i.e., effort on all connections is the same and the flows have to
sum to 0 (e.g., an electrical parallel connection).
In this system, the two important pressures are the ones at the
bottom of the tanks, 
and 
. A 0-junction defines
each of these variables and connects to the storage elements that
represent the tank capacities, 
and 
.
The Bernoulli outflow resistances
are modeled by two dissipators as well, where their outflow depends
on the pressure at the bottom of the tanks.
The two
0-junctions exchange fluid via a common volume flow, flow,
connection, the
1-junction, and the dissipative element R is connected to this
junction to represent the
pressure drop across the connecting pipe.
The flow variable 
, represents the corresponding volume flow.
Note that 1-junctions represent a general form of Kirchhoff's voltage
law, i.e., the flow through all connections is the same and efforts
have to sum to 0 (e.g., an electrical series connection).
The inflow into the left tank is
independent of its pressure at the bottom, and, therefore, it is
represented as an ideal flow source.
Figure 4: The bi-tank system and its bond graph model.