analogy in scientific theories

from http://www.repairfaq.org/REPAIR/F_appfaq1.html:

The easiest way to explain basic electrical theory without serious math
is with a hydraulic analogy. This is of the plumbing system in your house:

Water is supplied by a pipe in the street from the municipal water company
or by a ground water pump. The water has a certain pressure trying to
push it through your pipes. With electric circuits, voltage is the analog
to pressure. Current is analogous to flow rate. Resistance is analogous
the difficulty in overcoming narrow or obstructed pipes or partially open
valves.

Intuitively, then, the higher the voltage (pressure), the higher the
current (flow rate). Increase the resistance (partially close a valve or
use a narrower pipe) and for a fixed voltage (constant pressure), the
current (flow rate) will decrease.

With electricity, this relationship is what is known as linear: double the
voltage and all other factors remaining unchanged, the current will double
as well. Increase it by a factor of 3 and the current will triple. Halve
the resistance and for a constant voltage source, the current will double.
(For you who are hydraulic engineers, this is not quite true with plumbing
as turbulent flow sets in, but this is just an analogy, so bear with me.)

I intend to expose this analogy formally, i.e. electrical and hydraulic circuits are different kinds of models of the same abstract formal theory.