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= Hydraulic analogy =
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Introduction
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The electronic�hydraulic analogy (derisively referred to as the
drain-pipe theory by Oliver Lodge) Paul J. Nahin, 'Oliver Heaviside:
The Life, Work, and Times of an Electrical Genius of the Victorian
Age', JHU Press, 2002
page 59 is the most widely used analogy for "electron fluid" in a
metal conductor. Since electric current is invisible and the
processes at play in electronics are often difficult to demonstrate,
the various electronic components are represented by hydraulic
equivalents. Electricity (as well as heat) was originally understood
to be a kind of fluid, and the names of certain electric quantities
(such as current) are derived from hydraulic equivalents. As with all
analogies, it demands an intuitive and competent understanding of the
baseline paradigms (electronics and hydraulics).
Paradigms
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There is no unique paradigm for establishing this analogy. Two
paradigms can be used to introduce the concept to students using
pressure induced by gravity or by pumps.
In the version with pressure induced by gravity, large tanks of water
are held up high, or are filled to differing water levels, and the
potential energy of the water head is the pressure source. This is
reminiscent of electrical diagrams with an up arrow pointing to +V,
grounded pins that otherwise are not shown connecting to anything, and
so on. This has the advantage of associating electric potential with
gravitational potential.
A second paradigm is a completely enclosed version with pumps
providing pressure only and no gravity. This is reminiscent of a
circuit diagram with a voltage source shown and the wires actually
completing a circuit. This paradigm is further discussed below.
Other paradigms highlight the similarities between equations governing
the flow of fluid and the flow of charge. Flow and pressure variables
can be calculated in both steady and transient fluid flow situations
with the use of the hydraulic ohm analogy. Hydraulic ohms are the
units of hydraulic impedance, which is defined as the ratio of
pressure to volume flow rate. The pressure and volume flow variables
are treated as phasors in this definition, so possess a phase as well
as magnitude.
A slightly different paradigm is used in acoustics, where acoustic
impedance is defined as a relationship between pressure and air speed.
In this paradigm, a large cavity with a hole is analogous to a
capacitor that stores compressional energy when the time-dependent
pressure deviates from atmospheric pressure. A hole (or long tube) is
analogous to an inductor that stores kinetic energy associated with
the flow of air.
A circuit was used to model feedback stabilization of a hydrodynamic
plasma instability in a magnetic mirror In this application, the
effort was to keep the plasma column centered by applying voltages to
the plates, and except for the presence of turbulence and non-linear
effects, the plasma was an actual electric circuit element (not really
an analog).
Voltage, current, and charge
==============================
In general, electric potential is equivalent to hydraulic head. This
model assumes that the water is flowing horizontally, so that the
force of gravity can be ignored. In this case, electric potential is
equivalent to pressure. The voltage (or voltage drop or 'potential
difference') is a difference in pressure between two points. Electric
potential and voltage are usually measured in volts.
Electric current is equivalent to a hydraulic volume flow rate; that
is, the volumetric quantity of flowing water over time. Usually
measured in amperes.
Electric charge is equivalent to a quantity of water.
Basic circuit elements
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Image:Electrionics Analogy - Pipe (Wire).svg|'Conducting wire:' a
simple pipe.
Image:Electrionics Analogy - Reduced Pipe (Resistor).svg|'Resistor:' a
constricted pipe.
File:1-1111 CU-solderfitting-type 5130-22.jpg|'Node in Kirchhoff's
junction rule:' A pipe tee filled with flowing water.
A relatively wide pipe completely filled with water is equivalent to
conducting wire. When comparing to a piece of wire, the pipe should
be thought of as having semi-permanent caps on the ends. Connecting
one end of a wire to a circuit is equivalent to un-capping one end of
the pipe and attaching it to another pipe. With few exceptions (such
as a high-voltage power source), a wire with only one end attached to
a circuit will do nothing; the pipe remains capped on the free end,
and thus adds nothing to the circuit.
A resistor is equivalent to a constriction in the bore of the pipe
which requires more pressure to pass the same amount of water. All
pipes have some resistance to flow, just as all wires have some
resistance to current.
A node (or junction) in Kirchhoff's junction rule is equivalent to a
pipe tee. The net flow of water into a piping tee (filled with water)
must equal the net flow out.
File:CapacitorHydraulicAnalogyAnimation.gif|'Capacitor:' a flexible
diaphragm sealed inside a pipe.
File:Hydraulic inductor model.svg|'Inductor:' a heavy paddle wheel or
turbine placed in the current.
File:Axial compressor.gif|'Voltage or current source:' A dynamic pump
with feedback control.
A capacitor is equivalent to a tank with one connection at each end
and a rubber sheet dividing the tank in two lengthwise (a hydraulic
accumulator). When water is forced into one pipe, equal water is
simultaneously forced out of the other pipe, yet no water can
penetrate the rubber diaphragm. Energy is stored by the stretching of
the rubber. As more current flows "through" the capacitor, the
back-pressure (voltage) becomes greater, thus current "leads" voltage
in a capacitor. As the back-pressure from the stretched rubber
approaches the applied pressure, the current becomes less and less.
Thus capacitors "filter out" constant pressure differences and slowly
varying, low-frequency pressure differences, while allowing rapid
changes in pressure to pass through.
An inductor is equivalent to a heavy paddle wheel placed in the
current. The mass of the wheel and the size of the blades restrict the
water's ability to rapidly change its rate of flow (current) through
the wheel due to the effects of inertia, but, given time, a constant
flowing stream will pass mostly unimpeded through the wheel, as it
turns at the same speed as the water flow. The mass and surface area
of the wheel and its blades are analogous to inductance, and friction
between its axle and the axle bearings corresponds to the resistance
that accompanies any non-superconducting inductor. An alternative
inductor model is simply a long pipe, perhaps coiled into a spiral for
convenience. This fluid-inertia device is used in real life as an
essential component of a hydraulic ram. The inertia of the water
flowing through the pipe produces the inductance effect; inductors
"filter out" rapid changes in flow, while allowing slow variations in
current to be passed through. The drag imposed by the walls of the
pipe is somewhat analogous to parasitic resistance. In either model,
the pressure difference (voltage) across the device must be present
before the current will start moving, thus in inductors, voltage
"leads" current. As the current increases, approaching the limits
imposed by its own internal friction and of the current that the rest
of the circuit can provide, the pressure drop across the device
becomes lower and lower.
An ideal voltage source (ideal battery) or ideal current source is a
dynamic pump with feedback control. A pressure meter on both sides
shows that regardless of the current being produced, this kind of pump
produces constant pressure difference. If one terminal is kept fixed
at ground, another analogy is a large body of water at a high
elevation, sufficiently large that the drawn water does not affect the
water level. To create the analog of an ideal current source, use a
positive displacement pump: A current meter (little paddle wheel)
shows that when this kind of pump is driven at a constant speed, it
maintains a constant speed of the little paddle wheel.
Other circuit elements
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Image:Electrionics Analogy - Valve (Diode, conducting).svg|A simple
one-way ball-type check valve, in its "open" state acts as a diode in
its conducting state.
Image:Electrionics Analogy - Pressure-activated valve
(Transistor).svg|A pressure-actuated valve combined with a one-way
check valve acts as a (field-effect) transistor.
Image:Electrionics Analogy - Valve (Diodes comparison).svg|Like a
one-way check valve, a diode blocks current that flows the wrong way.
Current that flows the right way goes through almost unchanged.
Image:Electrionics Analogy - Example Circuit.svg|A simple A/C circuit
consisting of an oscillating pump, a "diode" valve, and a "capacitor"
tank. Any kind of motor could be used here to drive the pump, as long
as it oscillates.
A diode is equivalent to a one-way check valve with a slightly leaky
valve seat. As with a diode, a small pressure difference is needed
before the valve opens. And like a diode, too much reverse bias can
damage or destroy the valve assembly.
A transistor is a valve in which a diaphragm, controlled by a
low-current signal (either constant current for a BJT or constant
pressure for a FET), moves a plunger which affects the current through
another section of pipe.
CMOS is a combination of two MOSFET transistors. As the input
pressure changes, the pistons allow the output to connect to either
zero or positive pressure.
A memristor is a needle valve operated by a flow meter. As water
flows through in the forward direction, the needle valve restricts
flow more; as water flows the other direction, the needle valve opens
further, providing less resistance.
Principal equivalents
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EM wave speed (velocity of propagation) is equivalent to the speed of
sound in water. When a light switch is flipped, the electric wave
travels very quickly through the wires.
Charge flow speed (drift velocity) is equivalent to the particle speed
of water. The moving charges themselves move rather slowly.
DC is equivalent to the a constant flow of water in a circuit of
pipes.
Low frequency AC is equivalent to water oscillating back and forth in
a pipe
Higher-frequency AC and transmission lines is somewhat equivalent to
sound being transmitted through the water pipes, though this does not
properly mirror the cyclical reversal of alternating electric current.
As described, the fluid flow conveys pressure fluctuations, but fluids
do not reverse at high rates in hydraulic systems, which the above
"low frequency" entry does accurately describe. A better concept (if
sound waves are to be the phenomenon) is that of direct current with
high-frequency "ripple" superimposed.
Inductive spark used in induction coils is similar to water hammer,
caused by the inertia of water
Equation examples
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Some examples of analogous electrical and hydraulic equations:
!type !hydraulic !electric !thermal !mechanical
|quantity |volume V [m3] |charge q [C] |heat Q [J] |momentum P [Ns]
|quantity flux |Volumetric flow rate \Phi_{V} [m3/s] |current I
[A=C/s] |heat transfer rate \dot{Q} [J/s] |force F [N]
|flux density |velocity v [m/s] |current density j [C/(m2·s) = A/m²]
|heat flux \dot{Q}' [W/m2] |stress \sigma [N/m2 = Pa]
|potential |pressure p [Pa=J/m3=N/m2] |potential \phi [V=J/C=W/A]
|temperature T [K] |velocity v [m/s=J/Ns]
|linear model |Poiseuille's law \Phi_{V} = \frac{\pi r^{4}}{8 \eta}
\frac{\Delta p^{\star}}{\ell} |Ohm's law j=-\sigma \nabla \phi
|Fourier's law \dot{Q}'=\kappa \nabla T |dashpot \sigma = c \Delta v
If the differential equations have the same form, the response will be
similar.
Limits to the analogy
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If taken too far, the water analogy can create misconceptions. For it
to be useful, one must remain aware of the regions where electricity
and water behave very differently.
Fields (Maxwell equations, Inductance): Electrons can push or pull
other distant electrons via their fields, while water molecules
experience forces only from direct contact with other molecules. For
this reason, waves in water travel at the speed of sound, but waves in
a sea of charge will travel much faster as the forces from one
electron are applied to many distant electrons and not to only the
neighbors in direct contact. In a hydraulic transmission line, the
energy flows as mechanical waves through the water, but in an electric
transmission line the energy flows as fields in the space surrounding
the wires, and does not flow inside the metal. Also, an accelerating
electron will drag its neighbors along while attracting them, both
because of magnetic forces.
Charge: Unlike water, movable charge carriers can be positive or
negative, and conductors can exhibit an overall positive or negative
net charge. The mobile carriers in electric currents are usually
electrons, but sometimes they are charged positively, such as the
positive ions in an electrolyte, the H+ ions in proton conductors or
holes in p-type semiconductors and some (very rare) conductors.
Leaking pipes: The electric charge of an electrical circuit and its
elements is usually almost equal to zero, hence it is (almost)
constant. This is formalized in Kirchhoff's current law, which does
not have an analogy to hydraulic systems, where the amount of the
liquid is not usually constant. Even with incompressible liquid the
system may contain such elements as pistons and open pools, so the
volume of liquid contained in a part of the system can change. For
this reason, continuing electric currents require closed loops rather
than hydraulics' open source/sink resembling spigots and buckets.
Fluid velocity and resistance of metals: As with water hoses, the
carrier drift velocity in conductors is directly proportional to
current. However, water only experiences drag via the pipes' inner
surface, while charges are slowed at all points within a metal, as
with water forced through a filter. Also, typical velocity of charge
carriers within a conductor is less than centimeters per minute, and
the "electrical friction" is extremely high. If charges ever flowed
as fast as water can flow in pipes, the electric current would be
immense, and the conductors would become incandescently hot and
perhaps vaporize. To model the resistance and the charge-velocity of
metals, perhaps a pipe packed with sponge, or a narrow straw filled
with syrup, would be a better analogy than a large-diameter water
pipe. Resistance in most electrical conductors is a linear function:
as current increases, voltage drop increases proportionally (Ohm's
Law). Liquid resistance in pipes is not linear with volume, varying as
the square of volumetric flow (see Darcy-Weisbach equation).
Quantum Mechanics: Solid conductors and insulators contain charges at
more than one discrete level of atomic orbit energy, while the water
in one region of a pipe can only have a single value of pressure. For
this reason there is no hydraulic explanation for such things as a
battery's charge pumping ability, a diode's depletion layer and
voltage drop, solar cell functions, Peltier effect, etc., however
equivalent devices can be designed which exhibit similar responses,
although some of the mechanisms would only serve to regulate the flow
curves rather than to contribute to the component's primary function.
In order for the model to be useful, the reader or student must have a
substantial understanding of the model (hydraulic) system's
principles. It also requires that the principles can be transferred to
the target (electrical) system. Hydraulic systems are deceptively
simple: the phenomenon of pump cavitation is a known, complex problem
that few people outside of the fluid power or irrigation industries
would understand. For those who do, the hydraulic analogy is amusing,
as no "cavitation" equivalent exists in electrical engineering. The
hydraulic analogy can give a mistaken sense of understanding that will
be exposed once a detailed description of electrical circuit theory is
required.
One must also consider the difficulties in trying to make an analogy
match reality completely. The above "electrical friction" example,
where the hydraulic analog is a pipe filled with sponge material,
illustrates the problem: the model must be increased in complexity
beyond any realistic scenario.
See also
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*Fluidics
*Hydraulic circuit
*Mechanical-electrical analogies
*Bond graph
External links
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*
[
http://faraday.physics.utoronto.ca/IYearLab/Intros/DCI/Flash/WaterAnalogy.html
Animation]
* Hydraulic Analogy for Inductive Electric Elements
[
https://www.researchgate.net/publication/295812753_Hydraulic_Analogy_for_Induct
ive_Electric_Elements]
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Original Article:
http://en.wikipedia.org/wiki/Hydraulic_analogy
