Hydraulic analogy
Encyclopedia
The electronic–hydraulic analogy (derisively referred to as the drain-pipe theory by Oliver Heaviside
) 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 component
s 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. Like all analogies, it demands an intuitive and competent understanding of the baseline paradigm
s (electronics and hydraulics).
Applications:
Flow and pressure variables can be calculated in fluid flow network with the use of the hydraulic ohm analogy.
The method can be applied to both steady and transient flow situations.
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Wire
s : A relatively wide pipe completely filled with water is equivalent to a piece of 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 forcibly 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.
Electric potential
: Equivalent to pressure
.
Voltage
: Also called potential difference. A difference in pressure between two points. Or in open hydraulic troughs and tanks, a difference in water height or "head". Usually measured in volts.
Electric charge
: Equivalent to a quantity of water.
Current
: Equivalent to a hydraulic volume flow rate; that is, the volumetric quantity of flowing water over time. Usually measured in amperes.
Ideal voltage source
: 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.
Ideal current source
: 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.
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Resistor
: 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 like all wires have some resistance to current.
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Diode
: Equivalent to a one-way check valve
with a slightly leaky valve seat. Like 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.
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Capacitor
: 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 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.
Inductor
: 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.
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Transistor
: 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
: A combination of two MOSFET
transistors. As the input pressure changes, the pistons allow the output to connect to either zero or positive pressure.
Memristor
: 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.
) : 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
) : Particle speed of water. The moving charges themselves move rather slowly.
DC
: Constant flow of water in a circuit of pipe
Low frequency
AC
: Water oscillating back and forth in a pipe
Higher-frequency
AC and transmission line
s : Sound
being transmitted through the water pipes
Inductive spark : Used in induction coil
s, similar to water hammer
, caused by the inertia of water
See also Bond graph
.
If the differential equations have the same form , the response will be similar .
Fields
: 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 positive ions or single protons
(H+ ions).
Leaking pipes: If a hole is made in an open hydraulic system, the water can pour out. But the movable charges present within electrical conductors are always attracted to unmoving opposite charges in the material. The "electric fluid" can be forcibly removed from metals, but enormous voltages arise if even a tiny amount is removed. For this reason, the surfaces of conductors act as if they always have a high energy-barrier preventing leaks. Also 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. 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.
Quantum Mechanics
: Conductors and insulators contain charges at more than one quantized 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 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.
Oliver Heaviside
Oliver Heaviside was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations , reformulated Maxwell's field equations in terms of electric and...
) is the most widely used analogy for "electron fluid" in a metal conductor. Since electric current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
is invisible and the processes at play in electronics
Electronics
Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...
are often difficult to demonstrate, the various electronic component
Electronic component
An electronic component is a basic electronic element and may be available in a discrete form having two or more electrical terminals . These are intended to be connected together, usually by soldering to a printed circuit board, in order to create an electronic circuit with a particular function...
s are represented by hydraulic equivalents. Electricity (as well as heat) was originally understood to be a kind of fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
, and the names of certain electric quantities (such as current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
) are derived from hydraulic equivalents. Like all analogies, it demands an intuitive and competent understanding of the baseline paradigm
Paradigm
The word paradigm has been used in science to describe distinct concepts. It comes from Greek "παράδειγμα" , "pattern, example, sample" from the verb "παραδείκνυμι" , "exhibit, represent, expose" and that from "παρά" , "beside, beyond" + "δείκνυμι" , "to show, to point out".The original Greek...
s (electronics and hydraulics).
Basic ideas
There are two basic paradigms:- 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.
- Completely enclosed version with pumps providing pressure only; no gravity. This is reminiscent of a circuit diagram with a voltage source shown and the wires actually completing a circuit.
Applications:
Flow and pressure variables can be calculated in fluid flow network with the use of the hydraulic ohm analogy.
The method can be applied to both steady and transient flow situations.
Component equivalents
Wire
A wire is a single, usually cylindrical, flexible strand or rod of metal. Wires are used to bear mechanical loads and to carry electricity and telecommunications signals. Wire is commonly formed by drawing the metal through a hole in a die or draw plate. Standard sizes are determined by various...
s : A relatively wide pipe completely filled with water is equivalent to a piece of 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 forcibly 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.
Electric potential
Electric potential
In classical electromagnetism, the electric potential at a point within a defined space is equal to the electric potential energy at that location divided by the charge there...
: Equivalent to pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
.
Voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...
: Also called potential difference. A difference in pressure between two points. Or in open hydraulic troughs and tanks, a difference in water height or "head". Usually measured in volts.
Electric charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
: Equivalent to a quantity of water.
Current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
: Equivalent to a hydraulic volume flow rate; that is, the volumetric quantity of flowing water over time. Usually measured in amperes.
Ideal voltage source
Voltage source
In electric circuit theory, an ideal voltage source is a circuit element where the voltage across it is independent of the current through it. A voltage source is the dual of a current source. In analysis, a voltage source supplies a constant DC or AC potential between its terminals for any current...
: A dynamic pump
Gas compressor
A gas compressor is a mechanical device that increases the pressure of a gas by reducing its volume.Compressors are similar to pumps: both increase the pressure on a fluid and both can transport the fluid through a pipe. As gases are compressible, the compressor also reduces the volume of a gas...
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.
Ideal current source
Current source
A current source is an electrical or electronic device that delivers or absorbs electric current. A current source is the dual of a voltage source. The term constant-current sink is sometimes used for sources fed from a negative voltage supply...
: A positive displacement pump. A current meter (little paddle wheel
Paddle wheel
A paddle wheel is a waterwheel in which a number of scoops are set around the periphery of the wheel. It has several usages.* Very low lift water pumping, such as flooding paddy fields at no more than about height above the water source....
) shows that when this kind of pump is driven at a constant speed, it maintains a constant speed of the little paddle wheel.
Resistor
A linear resistor is a linear, passive two-terminal electrical component that implements electrical resistance as a circuit element.The current through a resistor is in direct proportion to the voltage across the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's...
: 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 like all wires have some resistance to current.
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...
: Equivalent to a one-way check valve
Check valve
A check valve, clack valve, non-return valve or one-way valve is a mechanical device, a valve, which normally allows fluid to flow through it in only one direction....
with a slightly leaky valve seat. Like 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.
Capacitor
A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...
: A tank with one connection at each end and a rubber sheet dividing the tank in two lengthwise (a hydraulic accumulator
Hydraulic accumulator
A 'hydraulic accumulator' is an energy storage device. It is a pressure storage reservoir in which a non-compressible hydraulic fluid is held under pressure by an external source. That external source can be a spring, a raised weight, or a compressed gas...
). When water is forced into one pipe, equal water is simultaneously forced out 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.
Inductor
Inductor
An inductor is a passive two-terminal electrical component used to store energy in a magnetic field. An inductor's ability to store magnetic energy is measured by its inductance, in units of henries...
: A heavy paddle wheel placed in the current. The mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
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
Inertia
Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion. It is proportional to an object's mass. The principle of inertia is one of the fundamental principles of classical physics which are used to...
, 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
Hydraulic ram
A hydraulic ram, or hydram, is a cyclic water pump powered by hydropower. It functions as a hydraulic transformer that takes in water at one "hydraulic head" and flow-rate, and outputs water at a higher hydraulic-head and lower flow-rate...
. The inertia
Inertia
Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion. It is proportional to an object's mass. The principle of inertia is one of the fundamental principles of classical physics which are used to...
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.
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...
: A valve in which a diaphragm, controlled by a low-current signal (either constant current for a BJT
Bipolar junction transistor
|- align = "center"| || PNP|- align = "center"| || NPNA bipolar transistor is a three-terminal electronic device constructed of doped semiconductor material and may be used in amplifying or switching applications. Bipolar transistors are so named because their operation involves both electrons...
or constant pressure for a FET), moves a plunger which affects the current through another section of pipe.
CMOS
CMOS
Complementary metal–oxide–semiconductor is a technology for constructing integrated circuits. CMOS technology is used in microprocessors, microcontrollers, static RAM, and other digital logic circuits...
: A combination of two MOSFET
MOSFET
The metal–oxide–semiconductor field-effect transistor is a transistor used for amplifying or switching electronic signals. The basic principle of this kind of transistor was first patented by Julius Edgar Lilienfeld in 1925...
transistors. As the input pressure changes, the pistons allow the output to connect to either zero or positive pressure.
Memristor
Memristor
Memristor is a passive two-terminal electrical component envisioned by Leon Chua as a fundamental non-linear circuit element relating charge and magnetic flux linkage...
: A needle valve
Needle valve
A needle valve is a type of valve having a small port and a threaded, needle-shaped plunger. It allows precise regulation of flow, although it is generally only capable of relatively low flow rates.- Construction and operation :...
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.
Principle equivalents
EM wave speed (velocity of propagationVelocity of propagation
The velocity factor , also called wave propagation speed or velocity of propagation , of a transmission medium is the speed at which a wavefront passes through the medium, relative to the...
) : Speed of sound
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
in water. When a light switch is flipped, the electric wave travels very quickly through the wires.
Charge flow speed (drift velocity
Drift velocity
The drift velocity is the average velocity that a particle, such as an electron, attains due to an electric field. It can also be referred to as Axial Drift Velocity since particles defined are assumed to be moving along a plane. In general, an electron will 'rattle around' in a conductor at the...
) : Particle speed of water. The moving charges themselves move rather slowly.
DC
Direct current
Direct current is the unidirectional flow of electric charge. Direct current is produced by such sources as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Direct current may flow in a conductor such as a wire, but can also flow through...
: Constant flow of water in a circuit of pipe
Low frequency
Low frequency
Low frequency or low freq or LF refers to radio frequencies in the range of 30 kHz–300 kHz. In Europe, and parts of Northern Africa and of Asia, part of the LF spectrum is used for AM broadcasting as the longwave band. In the western hemisphere, its main use is for aircraft beacon,...
AC
Alternating current
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....
: Water oscillating back and forth in a pipe
Higher-frequency
High frequency
High frequency radio frequencies are between 3 and 30 MHz. Also known as the decameter band or decameter wave as the wavelengths range from one to ten decameters . Frequencies immediately below HF are denoted Medium-frequency , and the next higher frequencies are known as Very high frequency...
AC and transmission line
Transmission line
In communications and electronic engineering, a transmission line is a specialized cable designed to carry alternating current of radio frequency, that is, currents with a frequency high enough that its wave nature must be taken into account...
s : Sound
Sound
Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...
being transmitted through the water pipes
Inductive spark : Used in induction coil
Induction coil
An induction coil or "spark coil" is a type of disruptive discharge coil. It is a type of electrical transformer used to produce high-voltage pulses from a low-voltage direct current supply...
s, similar to water hammer
Water hammer
Water hammer is a pressure surge or wave resulting when a fluid in motion is forced to stop or change direction suddenly . Water hammer commonly occurs when a valve is closed suddenly at an end of a pipeline system, and a pressure wave propagates in the pipe...
, caused by the inertia of water
See also Bond graph
Bond graph
A bond graph is a graphical representation of a physical dynamic system. It is similar to the better known block diagram and signal-flow graph, with the major difference that the arcs in bond graphs represent bi-directional exchange of physical energy, while those in block diagrams and signal-flow...
.
Equation examples
Some examples of equivalent electrical and hydraulic equations:| type | hydraulic | electric | thermal Thermal A thermal column is a column of rising air in the lower altitudes of the Earth's atmosphere. Thermals are created by the uneven heating of the Earth's surface from solar radiation, and are an example of convection. The sun warms the ground, which in turn warms the air directly above it... |
|---|---|---|---|
| quantity Quantity Quantity is a property that can exist as a magnitude or multitude. Quantities can be compared in terms of "more" or "less" or "equal", or by assigning a numerical value in terms of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation... |
volume Volume Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....  [m3] |
charge Electric charge Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...  [C] |
heat Heat In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...  [J] |
| potential Potential *In linguistics, the potential mood*The mathematical study of potentials is known as potential theory; it is the study of harmonic functions on manifolds... |
pressure Pressure Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...  [Pa=J/m3] |
potential Electric potential In classical electromagnetism, the electric potential at a point within a defined space is equal to the electric potential energy at that location divided by the charge there...  [V=J/C] |
temperature Temperature Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...  [K=J/ ] |
| flux | Volumetric flow rate  [m3/s] |
current  [A=C/s] |
heat transfer rate  [J/s] |
| flux density | velocity Velocity In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...  [m/s] |
current density Current density Current density is a measure of the density of flow of a conserved charge. Usually the charge is the electric charge, in which case the associated current density is the electric current per unit area of cross section, but the term current density can also be applied to other conserved...  [C/(m2·s) = A/m²] |
heat flux Heat flux Heat flux or thermal flux is the rate of heat energy transfer through a given surface. The SI derived unit of heat rate is joule per second, or watt. Heat flux is the heat rate per unit area. In SI units, heat flux is measured in W/m2]. Heat rate is a scalar quantity, while heat flux is a vectorial...  [W/m2] |
| linear model | Poiseuille's law  |
Ohm's law Ohm's law Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points...  |
Fourier's law  |
If the differential equations have the same form , the response will be similar .
Limits to the analogy
If taken too far, the water analogy can create misconceptions. For it to be useful, we must remain aware of the regions where electricity and water behave very differently.Fields
Field (physics)
In physics, a field is a physical quantity associated with each point of spacetime. A field can be classified as a scalar field, a vector field, a spinor field, or a tensor field according to whether the value of the field at each point is a scalar, a vector, a spinor or, more generally, a tensor,...
: 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 positive ions or single protons
Proton conductor
A proton conductor is an electrolyte, typically a solid electrolyte, in which H+ are the primary charge carriers.-Composition:For practical applications, proton conductors are usually solid materials. Typical materials are polymers or ceramic. Typically the pores in practical materials are small...
(H+ ions).
Leaking pipes: If a hole is made in an open hydraulic system, the water can pour out. But the movable charges present within electrical conductors are always attracted to unmoving opposite charges in the material. The "electric fluid" can be forcibly removed from metals, but enormous voltages arise if even a tiny amount is removed. For this reason, the surfaces of conductors act as if they always have a high energy-barrier preventing leaks. Also 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. 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.
Quantum Mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
: Conductors and insulators contain charges at more than one quantized level of atomic orbit energy
Energy level
A quantum mechanical system or particle that is bound -- that is, confined spatially—can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy. These discrete values are called energy levels...
, 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
Battery (electricity)
An electrical battery is one or more electrochemical cells that convert stored chemical energy into electrical energy. Since the invention of the first battery in 1800 by Alessandro Volta and especially since the technically improved Daniell cell in 1836, batteries have become a common power...
's charge pumping ability, a diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...
's voltage drop, solar cell
Solar cell
A solar cell is a solid state electrical device that converts the energy of light directly into electricity by the photovoltaic effect....
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.
Good analogy
- Hyperphysics
- Hyperphysics 2 — Doesn't have the reservoir.
- With animations! — The paddle behaves like a resistor if the paddle itself is massless and has friction, and like an inductor if it is frictionless and has mass. Also has equivalent equations.
- Ohm's law
- Capacitor analogy
- Newsgroup thread with lots of good analogies and a few bad ones
Acceptable analogy
- Understanding Electricity — an analogy with water
- Water analogy to transistors Slightly better version would be something like an exhaust gas recirculationExhaust gas recirculationIn internal combustion engines, exhaust gas recirculation is a nitrogen oxide emissions reduction technique used in petrol/gasoline and diesel engines. EGR works by recirculating a portion of an engine's exhaust gas back to the engine cylinders. In a gasoline engine, this inert exhaust...
(EGR) valve - Basic circuit theory
- Measuring electricity
- Plumbing analogy
- Animation