# Electricity/Water Analogy Fails?

Hi All,

I'm familiar with this analogy:

"The voltage is equivalent to the water pressure, the current is equivalent to the flow rate, and the resistance is like the pipe size." -HowStuffWorks.com

Power comes to our house on high-voltage, low current lines. Through a transformer, it gets converted to lower voltage, higher current. Neglecting losses, power is conserved.

If current is the rate of flow of electrons and my high-voltage lines are therefore carrying few electrons/sec (low current) ... how can I possibly get more electrons/sec (high current) after the transformer stage?

I know that the analogy is not perfect but am I thinking of it incorrectly? Please help ... it's bugging me so much ...

## Answers and Replies

LeonhardEuler
Gold Member
Power is the rate of energy delivered, not charge. Voltage is the energy per unit charge. So even though you get a higher current (more electrons/sec), since they come at a lower voltage (less energy/electron), the power (energy/sec) is the same (neglecting losses).

I think what confuses you is that ordinarily when you flow water into your house, what you care about is the amount of water you get (analogous to amount of charge or number of electrons). When you bring electricity what you care about is power, which is not only determined by amount of charge, but also voltage. If you were using water to power a turbine, instead of drink or do dishes, the analogy would be clearer.

russ_watters
Mentor
If you were using water to power a turbine, instead of drink or do dishes, the analogy would be clearer.
In other words, you can indeed, convert the incoming water stream in your house to a lower flow, higher pressure stream (or vice versa) while maintaining constant power, just like with a transformer. (losses excluded)

Thanks guys! It makes more sense when thinking of the power.

I think the thinking that was confusing me was that I was thinking the NUMBER of electrons going into the transformer has to be the same as the number coming out. But I can't think of it like that since the two ends of the transformer are electrically isolated. So it must be the action of the changing magnetic fields that allows electrons to flow at a higher rate on the other side of the transformer.

russ_watters
Mentor
Correct, there is no conservation of charge in that case and what tripped you up on the water example was the assumption that water mass flow was conserved. But if you use a turbine to power a pump, you end up discarding some of the water, so mass flow isn't conserved in that case either.

"The voltage is equivalent to the water pressure, the current is equivalent to the flow rate, and the resistance is like the pipe size." -HowStuffWorks.com

The units don't come out right if people say voltage is analogous to water "pressure". When a unit of water has potential energy mgh, then it has potential energy (gh) per unit mass. The voltage is electrical potential energy per unit charge. Therefore, voltage is analogous to the water's (gh) term, that is, gravitational potential. The units aren't "pressure." It does cause a pressure to be produced.

LeonhardEuler
Gold Member
The units don't come out right if people say voltage is analogous to water "pressure". When a unit of water has potential energy mgh, then it has potential energy (gh) per unit mass. The voltage is electrical potential energy per unit charge. Therefore, voltage is analogous to the water's (gh) term, that is, gravitational potential. The units aren't "pressure." It does cause a pressure to be produced.

The units do not have to be the same: it's an analogy. The point is that certain variables for fluid flow have a similar role to variables in circuits. In pipe flow, volumetric flow results from a pressure difference and is resisted by friction in the pipes. In circuits, electric current results from a voltage difference and is resisted by electric resistance.

In spite of the fact that the units of pressure and voltage don't necessarily need to work out to being analogous, they do. Voltage has units of energy/charge, where charge is what flows in a circuit. Pressure has units of energy/volume, where volumes of fluid are what flow in a pipe.

rcgldr
Homework Helper
pressure and voltage ... analogy
This is not a good analogy. A better analogy was already given, voltage is a potential. The gravitational equivalent doesn't have a special name, it's just called gravitational potential. For a constant gravitational field with "intensity" g, gravitational_potential = g h, where h is the distance from the source of the gravitational field.

Pressure is an undirected force per unit area, when what is needed for an analogy is intensity, a directional force per unit mass (or per unit volume x density). In the simplied case where the intensity is constant (regardless of position), then potential = intensity x position, where position is relative to some reference point.

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LeonhardEuler
Gold Member
This is not a good analogy. A better analogy was already given, voltage is a potential. The gravitational equivalent doesn't have a special name, it's just called gravitational potential. For a constant gravitational field with "intensity" g, gravitational_potential = g h, where h is the distance from the source of the gravitational field.

Pressure is an undirected force per unit area, when what is needed for an analogy is intensity, a directional force per unit mass (or per unit volume x density). In the simplied case where the intensity is constant (regardless of position), then potential = intensity x position, where position is relative to some reference point.

Pressure is a fine analogy to voltage. In fact, it plays exactly the same role mathematically as gravitational potential (times density) in incompressible flow. For this reason, the $$\frac{\partial P}{\partial x}$$ and $$\rho g_x$$ terms are often combined (and analogously for other directions) into a single effective pressure term.

rcgldr
Homework Helper
Pressure is a fine analogy to voltage. In fact, it plays exactly the same role mathematically as gravitational potential (times density) in incompressible flow. For this reason, the $$\frac{\partial P}{\partial x}$$ and $$\rho g_x$$ terms are often combined (and analogously for other directions) into a single effective pressure term.
In my opinion it's not a good analogy.

Pressure is energy per unit volume. It is independent of position, and doesn't need a reference point.

Potential and potential energy are position dependent. Potential energy is normally expressed as the negative of the work done by some source of force when an object is moved from one point to the other. One of those points can be a reference point. Potential is the potential energy per unit charge or per unit mass.

P/x refers to a rate of change in pressure versus position. A pressure differential between two points, times the cross sectional area will result in the directional force I alluded to before. Once you have a function for this directional force versus position, you can then calculate the work done by the force when an object moves from one point to the other, which in turn allows you to calculate potential energy and potential. This requires that pressure changes with position. If there's a zone where the pressure remains constant, then there is no directional force and the potential will be identical at all points within a constant pressure zone if there are no other forces present.

g h is gravitational potential, ρ g h is is gravitational potential energy / unit volume which is different than potential, but results in the same units as pressure. Voltage is the electrical equivalent of g h, not pressure.

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In the loose manner of speaking that a well-driller or plumber might use, where the word "pressure" just indicates "how strongly the water is pushed", the term could apply to a circuit. But in physics we are always reminding the student that pressure is a specific thing, the distribution of a force over an area, newtons per square meter, which is not used in an electrical problem. It's bad educational practice to ask the student to use the word "pressure" is the technical sense all year long but just for today's lesson use the same word colloquially.

To compare voltage to the gravitational product (gh) requires us to be more wordy. You have to tell the student something like "it's a combination of two effects, first, gravity is strong on this planet, and secondly, the water reservoir is on top of a high mountain." Now it will take on the correct "energy per unit" form. Now you have a complete analogy between gravitational PE per kilogram of water and electrical PE per coulomb of charge.

rcgldr
Homework Helper
To compare voltage to the gravitational product (gh) requires us to be more wordy. You have to tell the student something like "it's a combination of two effects, first, gravity is strong on this planet, and secondly, the water reservoir is on top of a high mountain." Now it will take on the correct "energy per unit" form. Now you have a complete analogy between gravitational PE per kilogram of water and electrical PE per coulomb of charge.
It may also help to explain that the gravitational potential is the same for a reservior of water and a reservior of mecury at the same altitude, even though the mercury is much denser, and the gravitational force and gravitational potential energy is much larger for the mercury than is it for the water. This is because potential is the potential energy per unit mass. Similarly for voltage, if a very large charged plate is the source of an electrical field, then voltage is a function of the distance from that charged plate, independent of any charge on the object at that distance from the plate. This is because voltage is also a potential, the potential energy / unit charge.

LeonhardEuler
Gold Member
In my opinion it's not a good analogy.

Pressure is energy per unit volume. It is independent of position, and doesn't need a reference point.
Pressure does depend on position when it is not constant. You can give it a reference point by using gauge pressure.

This requires that pressure changes with position. If there's a zone where the pressure remains constant, then there is no directional force and the potential will be identical at all points within a constant pressure zone if there are no other forces present.
This applies almost verbatim to gravtiational potential as well.

g h is gravitational potential, ρ g h is is gravitational potential energy / unit volume which is different than potential, but results in the same units as pressure. Voltage is the electrical equivalent of g h, not pressure.
If you are hung up on the units, take the analogy to be between voltage and $$\frac{P}{\rho}$$, but it is an analogy, there is no need for the units to be the same.

LeonhardEuler
Gold Member
In the loose manner of speaking that a well-driller or plumber might use, where the word "pressure" just indicates "how strongly the water is pushed", the term could apply to a circuit. But in physics we are always reminding the student that pressure is a specific thing, the distribution of a force over an area, newtons per square meter, which is not used in an electrical problem. It's bad educational practice to ask the student to use the word "pressure" is the technical sense all year long but just for today's lesson use the same word colloquially.

All you have to do to correct the plumber is say that the pressure gradient indicates how strongly and in what direction the water is pushed.

rcgldr
Homework Helper
Pressure does depend on position when it is not constant.
A point at the middle of an expanding or collapsing volume doesn't move, but the pressure is changing. The main issue is that pressure isn't directional. Dynamic pressure and gravitational potential energy/unit volume, which have the same units are directional. Gravitational potential is very similar to voltage, and I feel it's a much better example of voltage.

This requires that pressure changes with position.
This applies almost verbatim to gravtiational potential as well.
In all of my examples, I used constant gravitational and electrical fields, such as a field generated from an infinitely large plate with some amount of mass or charge per unit area. The intensity of such a field is constant at all points within the field. Stating gravitational potentail = g h is an approximation based on this constant field analogy.

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All you have to do to correct the plumber is say that the pressure gradient indicates how strongly and in what direction the water is pushed.

I think I see your point. If I were trying to explain why a current density vector is perpendicular to the equipotential lines, I might compare it to a fluid velocity being perpendicular to the lines of equal pressure. I would also compare it to heat conduction across a temperature gradient, and gas diffusion across a concentration gradient. These are all comparable situations to explain a point about nature's pattern of cause-and-effect: the way nature works is that a "through" variable is often caused by an "across" variable.

But I'm talking about a different lesson. The topic I'm choosing to focusing on is work and energy calculations.

The meaning of a conservative field
The work done by the battery equals the resulting electrical PE given to a charge.
Work W=Fd where F=qE, therefore W=qEd
Potential difference V=Ed, therefore W=qV
Later when covering power P=VI we can refer back to this.

For the topic I'm talking about, I need to preserve units of work and energy. I'm not saying that it's the only important point that needs to be communicated.

A.T.
Science Advisor
This is not a good analogy. A better analogy was already given, voltage is a potential. The gravitational equivalent doesn't have a special name, it's just called gravitational potential. For a constant gravitational field with "intensity" g, gravitational_potential = g h, where h is the distance from the source of the gravitational field.
I agree, but you can go even simpler than that. Since it is just analogy and g is constant in it, you can drop it and say:

The voltage measured between two points of a circuit is analogous to the height difference between two points of a pipe.

It's basically the same what you said, yet for laymen height difference is much easier to understand than potential. But the key point why this is a better analogy than pressure is that both are measured between two different points of the water/electric circuit. Pressure is something you measure locally and doesn't translate well to voltage.