Hydraulic Analogy for Inductive Electric Elements

Conference Paper (PDF Available) · September 2010with 136 Reads
Conference: Advanced Aspects of Theoretical Electrical Engineering Sozopol '2010 Sozopol, Bulgaria, At Sozopol, Bulgaria
Abstract
This document presents а new hydraulic model of coil and transformer. The method of hydraulic analogies is very useful to explain physical phenomena in area of electrical circuits, because hydraulic models have a lower level of abstraction.
Advanced Aspects of Theoretical Electrical Engineering Sozopol '2010 19.09.10 – 22.09.10, Sozopol, Bulgaria
Hydraulic Analogy for Inductive Electric Elements
George Popov1), Rumen Trifonov2)
1) Computer Science Department, Technical University of Sofia, Kl. Ohridsky Str,No.8, 1000,
Bulgaria, phone: +3592 965-22-24, e-mail: popovg@tu-sofia.bg
2) Computer Science Department, Technical University of Sofia, Kl. Ohridsky Str,No.8, 1000,
Bulgaria, phone: +3592 965-22-24, e-mail: r_trifonov@tu-sofia.bg
Abstract: - This document presents а new hydraulic model of coil and transformer. The
method of hydraulic analogies is very useful to explain physical phenomena in area of
electrical circuits, because hydraulic models have a lower level of abstraction.
Key-Words: - electric circuits, electric chain, hydraulic model, coil, transformer
1. Introduction
Use of the hydraulic analogies to explain circuits and electronic circuits has many
advantages: things are dealt with at a lower level of abstraction, as are associated with
clear concepts of learner, to summarize the common phenomena in nature, it is
possible to transfer knowledge and skills from one area to another, etc.
There are large known analogies between electric and hydraulic circuits:
pressure - potential;
difference in pressure - tension;
flow - current;
narrowing of the tube - resistance;
pump - electric current generator;
tower pressure - voltage generator;
valve - diode;
quantity of water - capacity.
It is interesting to note that there are hydraulic models of bipolar and field
transistors, to whom are applicable some fundamental equations of electronics!
The abstract expression of electrical parameters by analogy has another useful
side - it can be clarified Precedents factors and to derive appropriate mathematical
formulas. Another useful part is the use of the developed mathematical apparatus for
electrical circuits for the study of other phenomena.
It is obvious that, first and second Kirchhoff laws apply to hydraulic circuits. Also
Ohm's law formula for the resistance
S
l
R
ρ
=
, where ρ is resistivity, l - length, and S -
the intersection of the tube.
Advanced Aspects of Theoretical Electrical Engineering Sozopol '2010 19.09.10 – 22.09.10, Sozopol, Bulgaria
At Fig.1 is given a famous analogy of E.Aiseberg, where a capacitor is
discharged through the resistance. Fig.2 shows charging of capacitor by current
generator.
Fig.1.Discharging of capacitor Fig.2. Charging of capacitor
In Fig. 3 is given an analogy of a hydraulic vibrator circuit with its fluctuations. If
there is parallel included a voltmeter to this resonant circuit we will be monitor a
voltage's resonance.
Contrary, if there is connected serially an ampermeter in this circuit; we will see a
resonance of currents.
Sometimes there is very difficult to explain these things to students in electrical
engineering.
Fig.3 A model LC circuit
In Fig. 4 shows the passage of alternating current in through a capacitor, here can
be explained the role of the decoupling capacitor in electronic circuits. At Fig. 5 is
shown that the two series connected capacitors have less capacity of each of them.
Fig.4. Fig.5
Advanced Aspects of Theoretical Electrical Engineering Sozopol '2010 19.09.10 – 22.09.10, Sozopol, Bulgaria
From the foregoing it appears that the only model of the coil is not sufficiently
adequate. At Fig.3 phenomenon of inductance is modeled by the fluid inertia in the
extended tube.
In this case cannot be modeled impact parameter L of the bobbin. Nor can realize
a transformer, to model phenomena such as reaction of the current of the anchor and
etc.
1. Modeling of Inductance
If in the analogy (used in Fig.3) It can replace an hydraulic coil with propeller
with flywheel, there will have a more adequate model of the phenomenon inductance.
It is clear that the resulting model has more adequate properties of these of real
bobbin. The device resists any change to the current like real bobbin: when current
increases the device make a resistance and when the current slows device supports it.
Fig.6 A hydraulic model of the bobbin
The analogy is also another area - in the coils the electrical energy is converted
into magnetic field, in the model - the energy of a moving fluid converts into kinetic
energy.
The inductance of the bobbin depends on the actual number of coils and the
parameter L, associated with ferromagnetic core, but here this is modeled with
number of blades and mass flywheel M.
A parasitic resistance R of the bobbin is expressed through resistance tubes and
bearings in the model.
If two hydraulic bobbins are contacted with a common axis, there is obtained a
device with similar parameters of the real transformer:
a means for galvanic decoupling (splitting of fluid - flows);
transformer current and voltage (flow, pressure)
transformer of impedances (momentum, force);
a device with Inductive character.
The coefficient of transformation can be realized by different number and shape
of blades or by mechanical gearbox system.
This model of the transformer has only one drawback - work with both AC and
DC.
Advanced Aspects of Theoretical Electrical Engineering Sozopol '2010 19.09.10 – 22.09.10, Sozopol, Bulgaria
A better model of transformer is shown at Fig.7, where two pipes (cylinders) have
pistons connected together. They pass the AC fluid movements. To model the
inductance and allowing to pass DC, parallel to them are connected two coils (like
these at Fig. 6).
Fig.7 A hydraulic model of transformer
The model would be more appropriate if the relationship between the two pistons
is made through first-generation lever. By this way it can model dephasing between
output and input voltage.
Transformation ratio can be altered by varying the intersection of the cylinders
and pistons.
3. Conclusions
Such devices are commonly used in hydraulic machines, but the idea here is to
enrich the hydraulic circuits of analogies. This article may be written at the level of
differential equations where there is such a similarity, but this should be the next step
in the process of didactic teaching of the discipline, i.e. harmony in physics,
respectively in the nature.
4. References
[1] E. Aisberg, Le Transistor? ...Mais C Est Très Simple!, Societe Des Editions Radio - 1969
[2] E. Aisberg La Radio ? Mais C Est Très Simple, Dunod - 14/10/1998
[3] Popov G., Hydraulic Models of Inductive Elements, Symposium of metrology, Sozopol,
2006
[4] E. Laclais. Alarme? Pas de panique! Guide de l’installation reussie, PubliTronic , Pais-
Bas, Avril, 1995.
[5] http://en.wikipedia.org/wiki/Hydraulic_analogy
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