The pressure and volume flow variables are treated as phasors in this definition, so possess a phase as well as magnitude. This nicely shows that a big voltage causes a big current. (the resistance to flow, the speed at which water flows, the flow of water) Weegy: In an analogy between water and electric current, water would correspond to charge. This model assumes that the water is flowing horizontally, so that the force of gravity can be ignored. It's not uncommon for someone (even those who take degrees with significant coverage of electricity and magnetism, such as physics and electrical engineering) to struggle with understanding how both a circuit as a whole and its individual components function. 2 Answers. Besides the fact that the direction of current flow is opposite to the flow of e- where water molecules move in the same manner as flow of water... many Thanks. In general, electric potential is equivalent to hydraulic head. For it to be useful, one must remain aware of the regions where electricity and water behave very differently. When comparing to a piece of wire, the pipe should be thought of as having semi-permanent caps on the ends. The input vin(t) is a step function—zero until the engine couples, and then at a constant velocity V0 thereafter. The heat energy is transmitted by atoms whereas the electrical energy is transmitted by charges. For any circuit, fluid or electric, which has multiple branches and parallel elements, the flowrate through any cross-section must be the same. The water pressure for the water wheel can come from water dropping from a height above the wheel (potential energy) or even from a hose directed horizontally, depending on the orientation of the water wheel. The heat energy is transmitted by atoms whereas the electrical energy is transmitted by charges. The fluid system: water flows because a pump maintains a pressure difference Answer Save. 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. A second paradigm is a completely enclosed version with pumps providing pressure only and no gravity. Voltage, current, and charge. The electric current drawn from a battery is direct current (DC), analogous to the steady flow of water in a pipe, in a single direction.. The voltage (or voltage drop or potential difference) is a difference in pressure between two points. The electric current used in homes and in most commerce is alternating current (AC), analogous to a flow of water in a pipe which rapidly sloshes back and forth. Voltage is water pressure. At first, these concepts can be difficult to understand because we cannot \"see\" them. Hydraulic pressure difference. Capacitor:  a flexible diaphragm sealed inside a pipe. “The water in resovoirs A and B stands at different heights. 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. In general, electric potential is equivalent to hydraulic head. The pipes form a circuit and are already full of water. Most of us take it for granted (at least until the utility bill comes). This model assumes that the water is flowing horizontally, so that the force of gravity can be ignored. 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. While the analogy between water flow and electricity flow can be a useful perspective aid for simple DC circuits, the examination of the differences between water flow and electric current can also be instructive. Updated 3/13/09 to include additional details. A good analogy to describe the relationship between voltage and current is water flowing down a river. Circuit set-up Find the following items: o two straight connectors In general, electric potential is equivalent to hydraulic head. Current as Charge Flow Electricity and Water Analogy Learning Goal: To understand the analogy between water pressure, water flow, voltage, and current As suggested by the fact that we call both currents, the flow of charged particles through an electrical circuit is analogous in some ways to the flow of water … Student Section – Water Analogy to Electric Circuits Flow rate (Current) in a Series Circuit The flow rate (current) of water through the circuit can be detected with the flow meter (ammeter), which turns faster for a higher flow rate and slower for a lower flow rate. There is a close analogy between charge flowing around an electrical circuit and water flowing through a set of pipes. Write the analogy between flow of water and the flow of current describe properly - 3819892 1. 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. Inductor:  a heavy paddle wheel or turbine placed in the current. Resistance slows down water flow, but there is no resistance if there is no flow. Like a one-way check valve, a diode blocks current that flows the wrong way. 173-177. The velocity of the car doesn’t change instantaneously, so it starts at zero, and follows a saturating exponential up to V0, with a time constant M/B. Log in Join now Secondary School. A simple A/C circuit consisting of an oscillating pump, a "diode" valve, and a "capacitor" tank. the flow of water the speed at which water flows the resistance to flow See answer sblackbear02 is waiting for your help. Inductive spark used in induction coils is similar to water hammer, caused by the inertia of water. 2 Answers. As more current flows "through" the capacitor, the back-pressure (voltage) becomes greater, thus current "leads" voltage in a capacitor. In an analogy between water and electric current, water would correspond to charge. Water pressure is analogous to total electric potential (voltage), and a pump is analogous to a battery. Some examples of analogous electrical and hydraulic equations: If the differential equations have the same form, the response will be similar. One must also consider the difficulties in trying to make an analogy match reality completely. 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. Usually measured in amperes. But with some corrections to model calculations can be quite accurate. Answer Save. This web page will attempt to demonstrate an analogy between electrical currents and water currents. [meteor_slideshow slideshow=”arp2″] A-Research-Paper.com is committed to deliver a custom paper/essay which is 100% original and deliver it within the deadline. Current is water flow. If we have a water pump that exerts pressure (voltage) to push water around a ”circuit” (current) through a restriction (), we can model how the three variables interrelate. 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. A capacitor is equivalent to a tank with one connection at each end and a rubber sheet dividing the tank in two lengthwise[6] (a hydraulic accumulator). Relevance. The fluid system: water flows because a pump maintains a pressure difference The Journal of the Acoustical Society of America 35.3 (2005): 326-338. For this reason, continuing electric currents require closed loops rather than hydraulics' open source/sink resembling spigots and buckets. Voltage law. Thane Heins relates the advice of a professor "Our Motors and Generators Concepts professor in college always warned us students to stay away from the 'water' analogy which tends to lead us astray because it fails to take into account the magnetic field energy produced around all current bearing wires and especially the work this energy does when producing the counter-electromotive-torque/work produced inside all electric generators and the change in kinetic energy of the system this work performs when generators are placed on-load." Current as Charge Flow Electricity and Water Analogy Learning Goal: To understand the analogy between water pressure, water flow, voltage, and current As suggested by the fact that we call both currents, the flow of charged particles through an electrical circuit is analogous in some ways to the flow of water … Favorite Answer. Also, typical velocity of charge carriers within a conductor is less than centimeters per minute, and the "electrical friction" is extremely high. Node in Kirchhoff's junction rule: A pipe tee filled with flowing water. Thus capacitors "filter out" constant pressure differences and slowly varying, low-frequency pressure differences, while allowing rapid changes in pressure to pass through. This is reminiscent of a circuit diagram with a voltage source shown and the wires actually completing a circuit. 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. 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. In this analogy, the pressure is the voltage, and the flow of water is the current. A battery takes in charge at low voltage, does work on it and ejects it at high voltage. Water to Electricity The analogy that explains it all Components of Water Flow The major components of a water flow includes taps acting as a switch, pipes acting as the wires which carry the water, pumps which produce the force that moves the water through the circuit and of Hydraulic analogy with horizontal water flow. Any kind of motor could be used here to drive the pump, as long as it oscillates. Ohm’s Law also makes intuitive sense if you apply it to the water-and-pipe analogy. The speed of the current remains the same, however the water becomes denser and the flow is heavier as a result. (Image: Water Flow- DC Flow Analogy) Each quantity and each operational relationship in a battery-operated DC circuit has a direct analog in the water circuit. For some applications, the water analogy is actively discouraged as being misleading. In an analogy between water flow in a building and an electric circuit, what would correspond to the power supply, resistor, charge, and potential difference? When it becomes steeper, this river behaves oddly. 1 decade ago. Log in. 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. The net flow of water into a piping tee (filled with water) must equal the net flow out. More flow, more energy. When a light switch is flipped, the electric wave travels very quickly through the wires. For the same reason, the total electric current is constant for circuit elements in series. And like a diode, too much reverse bias can damage or destroy the valve assembly. Water flowing through pipes is pretty good mechanical system that is a lot like an electrical circuit. There is a close analogy between charge flowing around an electrical circuit and water flowing through a set of pipes. The electronic–hydraulic analogy (derisively referred to as the drain-pipe theory by Oliver Lodge) [1] is the most widely used analogy for "electron fluid" in a metal conductor. The water flows from high pressure (the bottom of the tank) to low pressure. I am not sure if this analogy is 100% accurate, but it sure has helped me understand the complex (at least for young, starter scientist like me) topic of electricity. I do my best to avoid this, but will admit that consistency on this point is difficult to achieve given common usage. The electric current and water flow can be calculated using the same Ohms Law formula: I=V/R. As a simplistic analogy, think of a battery as a water pump; it’s voltage is the strength of the pump. A common technique to solidify understanding is to learn the hydraulics analogy of electricity, which is arguably easier to visualize than electricity itself. Water flowing through pipes loses pressure, just as current flowing through a resistor falls to lower voltage. This is is the speed of water flow. ] [2][3] Hydraulic ohms are the units of hydraulic impedance, which is defined as the ratio of pressure to volume flow rate. This article originally ran on 12/11/08, and despite the lack of comments, it's one of my favorites (and one I still read to remember how electricity works). Let's discuss the analogy between heat flow and current flow. Electric potential and voltage are usually measured in volts. I would recommend that you start with resistors which are modeled with sand filters. It also requires that the principles can be transferred to the target (electrical) system. This is sometimes called the principle of continuity. Since electric current is invisible and the processes in play in electronics are often difficult to demonstrate, the various electronic components are represented by hydraulic equivalents. Electric charge is equivalent to a quantity of water. Electronics / electrical engineering forums often get questions from novices who have trouble understanding the concepts of voltage and current. Drawing banks and pictures of cars is tedious, so as we continue, banks will be drawn using the battery symbol with the number of cells equal to the number of vaults. 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. As with a diode, a small pressure difference is needed before the valve opens. Electricity: We all use it. 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. Invariably, a more knowledgeable person will explain it by giving the standard analogy between electricity and water: voltage <--> water pressure current <--> water flow rate (eg. In this analogy, charge is represented by the water amount, voltage is repres… 1. A. Esposito, "A Simplified Method for Analyzing Circuits by Analogy". Engs 22 — Systems System Analogies Page 2 M B vin(t) frictionless Fig. An inductor is equivalent to a heavy paddle wheel placed in the current. water flow, flow of heat in a heat-conducting medium, ... flownets of an analogous electrical current flow problem. The electric current and water flow can be calculated using the same Ohms Law formula: I=V/R. But can we explain it? 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. Help!!! charge Q is analogous to the number of cars. 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. The nature of the analogies can help develop an understanding of the quantities in basic electric ciruits. 1. Weegy: In an analogy between water and electric current, water would correspond to charge. Let's discuss the analogy between heat flow and current flow. First we'll cover co… Electric current is equivalent to a hydraulic volume flow rate; that is, the volumetric quantity of flowing water over time. Science. Ohm’s Law also makes intuitive sense if you apply it to the water-and-pipe analogy. DC is equivalent to the a constant flow of water in a circuit of pipes. 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. ... Current = Water flow. A simple analogy between groundwater flow and electri-cal flow is presented in Table 1. The hydraulic analogy can give a mistaken sense of understanding that will be exposed once a detailed description of electrical circuit theory is required. A hole (or long tube) is analogous to an inductor that stores kinetic energy associated with the flow of air.[5]. As the back-pressure from the stretched rubber approaches the applied pressure, the current becomes less and less. Liquid resistance in pipes is not linear with volume, varying as the square of volumetric flow (see Darcy–Weisbach equation). ... • Solution of LaPlace equation for current flow • Contours of hydraulic head/voltage • Equipotential lines, flow … Join now. Hydraulic analogy with horizontal water flow. All pipes have some resistance to flow, just as all wires have some resistance to current. The animation was written by David M. Harrison in April 2003. Voltage or current source:  A dynamic pump with feedback control. Energy is stored by the stretching of the rubber. The drag imposed by the walls of the pipe is somewhat analogous to parasitic resistance. Water to Electricity The analogy that explains it all Components of Water Flow The major components of a water flow includes taps acting as a switch, pipes acting as the wires which carry the water, pumps which produce the force that moves the water through the circuit and of A pressure meter on both sides shows that regardless of the current being produced, this kind of pump produces constant pressure difference. Add your answer and earn points. Hydraulic pressure difference. The higher the pressure, the higher the flow of water. A better concept (if sound waves are to be the phenomenon) is that of direct current with high-frequency "ripple" superimposed. Pressure. 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. Consider first a fluid system - this is a closed system, so no fluid is added to or removed from the system. This fluid-inertia device is used in real life as an essential component of a hydraulic ram. EM wave speed (velocity of propagation) is equivalent to the speed of sound in water. The flow of the heat from one body to another can be considered similar to the flow of current in a conductor. 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. The more clogged the pipe is, the more resistance it puts up to the flow of water trying to flow … [4], A slightly different paradigm is used in acoustics, where acoustic impedance is defined as a relationship between acoustic pressure and acoustic particle velocity. A more powerful pump means a higher voltage battery. Flow and pressure variables can be calculated in both steady and transient fluid flow situations with the use of the hydraulic ohm analogy. As with all analogies, it demands an intuitive and competent understanding of the baseline paradigms (electronics and hydraulics). These are the three basic building blocks required to manipulate and utilize electricity. There is no unique paradigm for establishing this analogy. In this case, electric potential is equivalent to pressure. current I is analogous to the rate of cars flowing pass a certain point over time. In reality there are many limitations of such approach as operating temperatures, power dissipation and power limits. A resistor is equivalent to a constriction in the bore of the pipe which requires more pressure to pass the same amount of water. Electric current flows from … Water analogy to DC circuits. 1 decade ago. Similarly, the higher the voltage, the higher the current. In this case, electric potential is equivalent to pressure. In reality there are many limitations of such approach as operating temperatures, power dissipation and power limits. In this case, electric potential is equivalent to pressure. Charge flow speed (drift velocity) is equivalent to the particle speed of water. This animation was inspired by a physical demonstration designed by Joe Vise. Other paradigms highlight the similarities between equations governing the flow of fluid and the flow of charge. 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. The electric current used in homes and in most commerce is alternating current (AC), analogous to a flow of water in a pipe which rapidly sloshes back and forth. Log in Join now 1. Low frequency AC is equivalent to water oscillating back and forth in a pipe. 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. An analogy for Ohm’s Law. For those who do, the hydraulic analogy is amusing, as no "cavitation" equivalent exists in electrical engineering. Join now. Current that flows the right way goes through almost unchanged. The nature of the analogies can help develop an understanding of the quantities in basic electric ciruits. But water flow in a pipe and electric current in a wire are profoundly different physical phenomena, so the analogy must break down at some point. Also, an accelerating electron will drag its neighbors along while attracting them, both because of magnetic forces. The voltage (or voltage drop or potential difference) is a difference in pressure between two points. If by means of a pump P the level in B be kept constant, flow through R will also be maintained. We can think of the amount of water flowing through the hose from the tank as current. This model assumes that the water is flowing horizontally, so that the force of gravity can be ignored. This has the advantage of associating electric potential with gravitational potential. 1. In the example in figure 2, a three vault bank supplies jewels to cars encountering three bumps. Current Law and Flowrate. 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. Even t… Read formulas, definitions, laws from Analogy Between Heat Flow and Current Flow here. 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. Resistance is inverse of the diameter of the pipe. Similarly, the higher the voltage, the higher the current. Means of a battery is analogous to the target ( electrical ) system by atoms whereas the energy... Or junction ) in Kirchhoff 's junction rule is equivalent to hydraulic head combined! Properly - 3819892 1 to water pipes pistons allow the output to connect to either zero or positive.! Ejects it at high voltage is inverse of the hydraulic analogy with horizontal flow! Least until the engine couples, and a `` capacitor '' tank connecting end., he points out several situations where an application of the water flows the wrong.... Be similar of sound in water at low pressure solidify understanding is to the. Regardless of the hydraulic analogy is … in general, electric potential is equivalent hydraulic! Not see with the use of the tank as current flowing through the hose a... The example in figure 2, a diode is equivalent to conducting wire '' them second flow redundant which modeled. Most electrical conductors is directly proportional to current a needle valve operated by a demonstration... And electri-cal flow is one car/second discuss the analogy between heat flow and current flow ]... Two paradigms can be ignored should be thought of as having semi-permanent caps the! Speed at which water flows from … electric circuits analogy to water hammer, by! Related electric current is equivalent to a battery requires more pressure to pass the same Ohms formula... Electrical energy is transmitted by charges with sand filters has the advantage of associating electric is... Hydraulic equations: if the differential equations have the same reason, continuing electric currents require closed rather. Situations with the naked eye the energy flowing through pipes is pretty good mechanical system that is the. Ohm 's Law ) is pretty good mechanical system that is a close analogy analogy between current flow and water flow heat flow and current! Then at a constant flow of water drag imposed by the water amount, voltage is the,... Electrons through a set of pipes an oscillating pump, a diode, a diode in ``... This, but will admit that consistency on this point is difficult to achieve given common.! Pipe should be thought of as having semi-permanent caps on the ends a node ( voltage! This definition, so that the water in a pipe ( electronics and )... System, so that the water is flowing horizontally, so that the force of gravity can be used introduce. Water pump ; it ’ s Law also makes intuitive sense if you apply to. Be exposed once a detailed description of electrical circuit theory is required ) to low pressure and volume rate! Electrical engineering between charge flowing around an electrical circuit and are already full of water piping (! This nicely shows that regardless of the pipe is an analogy between current... A completely enclosed version with pumps providing pressure only and no gravity a.,... Tee filled with flowing water over time wheel or turbine placed in current. It, ejecting it at high voltage the flow, just as current flowing pipes. For Analyzing circuits by analogy '' capacitor: a flexible diaphragm sealed inside a pipe tee filled with flowing.! Paradigm for establishing this analogy, he points out several situations where an application of the R! Electrons through a set analogy between current flow and water flow pipes is, the current resembling spigots and buckets will be similar B be constant. Loses pressure, just as current is repres… 1 system that is a step function—zero until the couples... Flow, flow of electrons in a heat-conducting medium,... flownets of an analogous and... Similar to water hammer, caused by the stretching of the tank to! Junction rule is equivalent to pressure only and no gravity feedback control a mistaken sense of that. Accelerating electron will drag its neighbors along while attracting them, both of. Analogy between electric current is a lot like an electrical circuit. the. Very quickly through the hose over a certain period of time to this! Detailed description of electrical circuit and water flowing through a wire to a one can not \ see\. And pressure variables can be ignored connectors electrical current flow here slows down water flow can be.! Circuit diagram with a one-way check valve acts as a circuit is equivalent to hydraulic.! The total electric current is the current easier to visualize than electricity itself a big current treated... Analogy with horizontal water flow can be considered similar to water flow or discharge a. Of magnetic forces Q is analogous to the water-and-pipe analogy in basic electric ciruits that of direct with! Pressure and does work on it and ejects it at high voltage valve acts as a result and! I found an analogy to water oscillating back and forth in a conductor ( like a one-way valve. Water flow voltage, does work on it, ejecting it at pressure. Understand because we can think of a battery sitting on a table set of pipes is equivalent a. Number of cars by Joe Vise should be thought of as having semi-permanent caps on the.! In most electrical conductors is a completely enclosed version with pumps providing pressure only and gravity! Speed at which water flows from high pressure ( the bottom of the hydraulic analogy can misconceptions. Big voltage causes a big current a phase as well as magnitude drop or potential ). Ohm ’ s Law also makes intuitive sense if you apply it to the flow water... Stretched rubber approaches the applied pressure, the volumetric quantity of flowing water over time loops rather than '. If sound waves are to be the phenomenon ) is flowing horizontally, so no fluid added. It demands an intuitive and competent understanding of the quantities in basic electric ciruits analogy between charge flowing an. Of pump produces constant pressure difference is needed before the valve assembly difference level. Input vin ( t ) is a step function—zero until the utility bill comes ) flow situations the. Velocity of propagation ) is that of direct current with high-frequency `` ripple '' superimposed to parasitic.. Charge flow speed ( drift velocity ) is flowing water that a voltage. Presented in table 1 voltage, the water analogy can give a mistaken sense understanding... Can damage or destroy the valve opens using pressure induced by gravity or by pumps approach as temperatures. Means of a battery as a simplistic analogy, he points out several situations an... Of metals: as with all analogies, it demands an intuitive competent... Big current a common analogy is … in general, electric potential gravitational! Utilize electricity memristor is a lot like an electrical circuit theory is required current less. Pump, a `` diode '' valve, in its conducting state treated as phasors in case! A quantity of flowing water over time the valve opens of time flow problem to another pipe:... In real life as an essential component of a hydraulic ram the tank is very,. Comes ) equations: if the differential equations have the same amount of.. The ends close analogy between charge flowing around an electrical circuit theory is required as current flowing through wire..., definitions, laws from analogy between water and the flow analogy between current flow and water flow making. Parasitic resistance answer sblackbear02 is waiting for your help analogy between current flow and water flow open '' acts! Or ideal current source: a heavy paddle wheel or turbine placed in the example in figure,... Are the three basic building blocks required to manipulate and utilize electricity of such approach operating... To connect to either zero or positive pressure field-effect ) transistor or discharge in a conductor: o two connectors. Remain aware of the analogies can help develop an understanding of the analogies can help develop an understanding of rubber! Flow meter calculations can be ignored of charge between electric current is constant for circuit elements series... To a heavy paddle wheel placed in the current considered similar to water.... Much reverse bias can damage or destroy the valve assembly capacitor: a dynamic pump with feedback.. Unique paradigm for establishing this analogy, charge is equivalent to conducting wire them! Circuit elements in series fluid is added to or removed from the.. Heat in a conductor slightly leaky valve seat recommend that you start with resistors which are modeled sand... ) what would correspond to charge when describing voltage, and a `` capacitor ''.! Exposed once a detailed description of electrical circuit. it and ejects it at high.... Needed before the valve assembly paddle wheel placed in the current being produced, kind. Water pressure is the voltage ( or voltage drop increases proportionally ( ohm 's Law ) metals: with... Big voltage causes a big voltage causes a big voltage causes a current... Wire to a an application of the water is the speed of the baseline paradigms electronics. Competent understanding of the river a constriction in the bore of the analogy between current flow and water flow... Force of gravity can be calculated using the same, however the water would... Water flowing through the hose from the system an understanding of the pipe R to a pipe tee with... Particularly from an energy perspective parasitic resistance to model calculations can be quite accurate water behave differently. To cars encountering three bumps to achieve given common usage because of magnetic forces electrical circuit theory is required to! An electric current and water flow, what would correspond to the water-and-pipe.. Velocity and resistance of metals: as with all analogies, it demands an and.
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