Why is the flow rate constant in a circuit with two resistors?

[russ_watters]

Wait, do you agree the net drift velocity varies depending on the cross section of the conductor?
Would you agree that any such change in velocity involves some corresponding potential gradient?
Are saying an analogy with static pressure (as an extension of the analogy of external voltage with total pressure) is invalid, or just not necessary?

Well, I guess I should just say I've never heard of the analogy used in that way...and the electrical part is beyond my understanding anyway.

Just like a motor. (Or maybe analogous to a light bulb.) But a resistor just makes heat, which is why I think it is a close analog to any (simple or real) restriction (or obstruction) in the flow.

If we're using the analogy primarily as a teaching tool, I'd prefer using similar looking things together, so I'd prefer to use the losses through a pipe to be analagous to losses in a wire and something like an orifice plate to be analagous to a a resistor. After all - all an orifice really does is dissipate energy as heat too.

People don't tend to remember that in a closed circuit with no mechanical output, all input energy in a piping system ends up as heat. For my job, it sometimes matters. I recently designed a heat recovery loop where calculating the energy savings required subtracting the pump energy twice - once for the cost of the electricity itself and once for the heat energy put into the loop by the pump.

 

[cesiumfrog]

I think we're in agreement. I'm not sure I'd heard of the analogy used that way either, until MikeyW raised the issue.

Was that design for cooling recover or heat recovery? (For the latter I would have thought you would desire the heat from the pump, but not the spending of power for it, contributing opposing sign.)

 

[russ_watters]

Sorry, I only skimmed the thread and picked out a couple of major issues...

 

[sophiecentaur]

It's interesting to read that the more that a poster on this thread actually knows about fluid flow, the less likely he is to go along with the analogy with electron flow. Perhaps the less informed posters should take note of this.

 

[sameeralord]

In a pipe it's due to the walls coming closer so the water experiences more friction so it takes more force (pressure) to push the same amount of water through.

In electricity resistance means electrons are more tightly held to the atoms and so it takes more force (voltage) to push the same amount of current through

I think I have almost understood voltage but if I can understand this I'll post my new understanding of what voltage is.

+----------A---resistor-B----------C--_

I'm confused with the fact that you said not all electrons move through the whole circuit. Ok so in this case if the electrons from the resistor move from B to C. Wouldn't electrons accumulate in the A area. Also what happens if the resistor loses all the electrons it is holding. I'm getting confused here. I'm thinking that resistor is also supplying electrons apart from the battery, I'm thinking of a resistor as metal that has delocalised electrons,I don't know if this is wrong, but I want to know why you said not all electrons are moving from positive end to negative end.

 

[mgb_phys]

Electrical current isn't really electron flow in the same way water flows down a pipe.
The first electron pushes the next electron which pushes the next electron and so on - they are all negatively charged so repel each other. That's how 'electricity' travels down a wire at near the speed of light while electrons themselves move through a conductor at walking pace.

It's more like fluid flow in a hydraulic system, the brake fluid under the brake pedal pushes the next molecule of fluid, which pushes the next and so on until the last molecule pushes the brake caliper piston.

 

[sameeralord]

Electrical current isn't really electron flow in the same way water flows down a pipe.
The first electron pushes the next electron which pushes the next electron and so on - they are all negatively charged so repel each other. That's how 'electricity' travels down a wire at near the speed of light while electrons themselves move through a conductor at walking pace.

It's more like fluid flow in a hydraulic system, the brake fluid under the brake pedal pushes the next molecule of fluid, which pushes the next and so on until the last molecule pushes the brake caliper piston.

Thanks I'm close to posting my new understanding of voltage but I have one more clarification before that. Do electrons move through the resistor? What I mean is you said that resistors hold on to their electrons move tightly, so when these electrons leave do other electron come and enter the resistor to fill the gap? Otherwise electrons would accumulate in the circuit.

 

[sameeralord]

Ok I think the answer for my previous question is yes, or else it won't work. Ok this is my final understanding of voltage. I'm sure there are many faults in this.

Ok there is a circuit and there is a battery. The positive and negative end of the battery creates an electric force field. If I put a coulomb of charge and let it move along the electric field right to the end, it would gain some energy due to its movement, this energy is generated by the electric force W=fx. Now voltage is equal to this "W" energy. It is the energy before the electric field is acting upon the charge. Once the electric field acts upon the charge the voltage is converted to energy of movement of charge (may be kinetic energy I don't know). When the charge finally travels along the whole circuit, the charge has energy (kinetic energy equal to W and voltage would be zero)

Also since individual electrons take time to move from + to -. My explanation is bit lacking but I think if find the number of electrons traveling in the whole circuit(meaning from A to B) at one point in time and add all their kinetic energies up that should equal to voltage. Is that right?

For resistors what I think is they weaken the electric force field, so molecules have to go slower (low current) to reach the other end.

 

[sophiecentaur]

Electrons move VERRRRY slowly (a few mm per second) and the conduction electrons constitute a very tiny fraction of the mass of the bulk metal (1/100000 ish). I don't think you need count the KE of the electrons in the energy transferring process. Contrast this with the whole mass of water flowing in a pipe.

Would you say the Kinetic Energy of the links in a bicycle chain was a major factor in what gets you up a hill? It's the same with electrons only much much more so.

 

[sameeralord]

Electrons move VERRRRY slowly (a few mm per second) and the conduction electrons constitute a very tiny fraction of the mass of the bulk metal (1/100000 ish). I don't think you need count the KE of the electrons in the energy transferring process. Contrast this with the whole mass of water flowing in a pipe.

Would you say the Kinetic Energy of the links in a bicycle chain was a major factor in what gets you up a hill? It's the same with electrons only much much more so.

Hey thanks for the response. I think your last analogy was excellent Tell me if this is right. Ok due to electron movements,very small speed(the charge is pushed along, so it is like the chain meaning it itself doesn't travel the whole distance in quick time, but like spins along, or as you said pushes the charge along), the charge(the bicycle moves). If there is a movement of something there must be energy expended. So that is voltage. Did I get this? If I did you analogy did it for me.

 

[sophiecentaur]

Pretty ok. I should think.
As you say, when something is moved (I would say changed, perhaps) then energy is transferred.
In the case of Electrical energy, the energy per Coulomb of charge is, indeed, the voltage drop.

1Volt = 1Joule/Coulomb is what we learn.

You can rewrite this as Energy = QV
or, more familiarly, by dividing both sides by time,
Power = V I
(Power being Energy per second and Current being Coulombs per second)

Energy per coulomb is really nothing like Newtons per square metre is it?

 

[rcgldr]

Energy per coulomb is really nothing like Newtons per square metre is it?

Multiply Newtons per square meter by meter/meter and you get energy per meter^3, energy per unit volume as opposed to energy per unit mass or energy per unit charge. However, I would consider static pressure as actual energy per unit volume, while voltage as potential energy per unit charge.

 

[sophiecentaur]

I see where you're coming from.

 

[russ_watters]

It's interesting to read that the more that a poster on this thread actually knows about fluid flow, the less likely he is to go along with the analogy with electron flow. Perhaps the less informed posters should take note of this.

I see it the opposite way - most people who object to the analogy seem to object based on misunderstandings of the fluids part.

 

[sophiecentaur]

Dunno about misunderstandings (or perhaps I've actually 'misunderstood' your wording).
'Fluid' people are often dealing with masses of stuff, on the move, carrying energy. With the exception of Hydraulic rams ('high impedance' systems), possibly, they are mainly considering Kinetic Energy. Once you have fast circulating water, you get further and further away from a valid analogy with the situation with charge flow in metals and I seriously believe that is the picture in most people's heads when they think of the water analogy. That's why I don't like it, despite rcgldr's last post.

 

[rcgldr]

believe that is the picture in most people's heads when they think of the water analogy. That's why I don't like it, despite rcgldr's last post.

My last post was to explain pressure as energy per unit volume, as well as the fact that it's not a potential energy. Unlike static pressure, voltage is position sensitive, the position in a field, or the "position" in a circuit (at least where resistance exists in the circuit). In a static field, such as the field between two plates, the force per unit charge is constant within the field, but voltage varies with position within the field. Static pressure doesn't have this position aspect of potentials like voltage or gravitational potential.

 

[Antiphon]

The water analog is no good but the water analogy is almost perfect. The analog cannot be used to solve problems the way you can use conductivity potentials as an analog to solve electric field problems using carbon paper.

The analogy is excellent. You can use the intertia of water to make inductors where there is an induced pressure across a pipe section due to the time derivative of the flow. In fact you can build a real water-and-pipe transformer! It works by eletrogravitational induction (too weak to measure except by gravity probe B but real nonetheless).

 

[sophiecentaur]

I agree again. (Edit: with last post but one!)The work done by shifting a column of water against a piston is pressure times volume - that's all. The dimensions are correct and you can't say much more than that. It's not a 'source of energy' whereas, an emf (owch, the force word) implies as much energy as you want.
As all the last posts have been more or less in agreement, why don't we all go to another thread where, perhaps, we can not agree and verbally tear each other's throats out?

 

[sophiecentaur]

Oh.
I spoke too soon

 

[Studiot]

The two systems (water flow in pipes and electrical circuits) are not identical. Each has characteristics unrepresented in the other.
A good teacher will understand both systems, their differences and similarities, and know when to offer the analogy and when to draw the line.

 

[Antiphon]

There needs to be a permanent sticky article that adresses this. It comes up over and over.

 

[sophiecentaur]

The analogy is excellent. You can use the intertia of water to make inductors where there is an induced pressure across a pipe section due to the time derivative of the flow. In fact you can build a real water-and-pipe transformer! It works by eletrogravitational induction (too weak to measure except by gravity probe B but real nonetheless).

I can't say that recommends itself to the would-be elementary student of electrical theory then. Correct as it may be, it sounds like a great way of distracting from a simple appreciation of Ohm's laws and others we learn in college!
I'm not sure that "analog" and "analogy" are universally or strictly the way round that you claim.

I wonder whether we should have a grading system which we could apply to our posts, corresponding to the level they come from and where they're aimed. (Where they're aimed, in particular)

 

[mikeph]

As is often the case, the main problem with the water analogy is that people don't understand the fluid dynamics part and thus apply it wrong:
There isn't one type of pressure, there are three in the most common form of Bernoulli's equation. The relevant pressure here is total pressure and Bernoulli's principle, simply stated, is that total pressure is constant along a streamline. It is often the case that people drop the one-word qualifier stating which pressure they are talking about. In the case of a venturi tube, it is static pressure that drops, but velocity pressure rises, keeping total pressure constant.

Even more important, none of this has any relevance to the water/electricity analogy, since the most common form of Bernoulli's equation is a conservation of energy statement, so it isn't saying anything about energy dissipation. It's not a restriction that is needed for the description, but a device to dissipate flow energy. This dissipation of flow energy shows up as a decrease in total pressure (ie, voltage) for a certain constant flow rate (ie, amperage).

I try to explain my thoughts on the subject but they are often not fully developed, I guess the issue requires more thought than I gave!

Thanks for the help.