Biggest misunderstandings with 3 phase power......

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The correct equation is e^(i*pi) = -1.
And this is something of a cheat, since I believe that any positive number raised to the power i*pi will equal -1.
 
GoldDigger said:
The correct equation is e^(i*pi) = -1.
And this is something of a cheat, since I believe that any positive number raised to the power i*pi will equal -1.
Click to expand...
Sorry, that doesn't compute. For example, e^2 to the i*pi will be the same as e^(i*pi) squared, i.e. 1.

Cheers, Wayne
 
GoldDigger said:
The correct equation is e^(i*pi) = -1.
And this is something of a cheat, since I believe that any positive number raised to the power i*pi will equal -1.
Click to expand...

Not true. For instance, 2^(i*pi) = -0.57 + 0.82*i.

The way to figure this out, is with Euler's formula. Euler is the namesake of why the special number is called e.
e^(i*x) = cos(x) + i*sin(x)

So negative exponents are a mix of sine and cosine functions. These form a circulating path around the complex plane, where the x in the argument indicates how far along this unit circle you travel from the point 1 + 0*i.

When the base of the exponent is not e, you re-arrange the exponent term so that you do have a base of e. Natural log, ln(), is the inverse of the base e exponential.
a^x = e^(ln(a) * x)

Therefore:
a^(i*x) = e^(ln(a)*i*x) = cos(ln(a)*x) + i*sin(ln(a)*x)

Now when x = pi, the arguments to the sine and cosine functions are no longer special cases (like cos(pi) = -1, and sin(pi) = 0), as they were when the exponent base is e.
 
Ingenieur said:
But water losses it thru your 'inductor'
electricity doesn't
what about phase
does mass flow or volume have a delay or phase difference with the pressure it exerts?

your model is too complicated for me to understand
on top of that I don't see the need or use of it? The thought experiment
so bear with me and simplify it
assume 1 ph AC

Please provide the hydraulic circuit equivilents
generator, pump I assume: centrifugal, positive displacement?
type piston reciprocating, rotary lobe, progressive cavity
???

resistor, orifice, rough pipe????

inductor

capacitor

pipe for conductor is a given
pressure = voltage
pressure drop = voltage drop
flow Q = current
power, both real and reactive???
phase relationship pressure to Q

then we'll build a simpler model/ckt that even I can undstand
yhanks for you patience and indulgence
Click to expand...

Hydraulic equivalents:
Voltage = pressure
Current = flow rate
Resistor = orifice / rough pipe / etc. Anything involving friction, that would convert the pressure energy/kinetic energy into heat.

Capacitor = a tank separated by a rubber partition, with a connection on both sides. This is called an accumulator.
Inductor = a free rotating paddlewheel. Its inertia makes it apply a counterpressure to the system, any time the water flow attempts to change its speed.

Generator = pump. This would happen if you connect that "inductor" to an external source of mechanical energy.
Motor = turbine. Which would happen if you connect that "inductor" to an external mechanical load.

Real power would be the rate at which any energy enters or leaves the hydraulic system. So this would occur in the pump, turbine, or friction energy loss components.

Reactive power would be the rate at which hydraulic energy is temporarily stored in the paddlewheel's rotation, or as strain energy in accumulator's rubber partition. Any time that the water is speeding up the paddlewheel, or increasing the stretch from the neutral position of the accumulator's rubber.

Negative reactive power would occur when the rubber partition in the accumulator returns to its neutral position, restoring energy to the hydraulic system. Or when the paddlewheel slows down, and does exactly the same.

Phase would only be an applicable concept, when the pump drives a back and forth oscillating flow of the water. But what it would be, is the time difference per period between the instant when the pump applies the peak pressure, and when the system has the peak flow rate. When there is a lag in the flow rate behind the pressure, it is because there is inertia in the system, probably due to a paddlewheel. When the flow rate leads the pressure, it is because there is a component such as the accumulator in the system. It takes a flow rate first to push the rubber partition to its high pressure position.
 
Carultch said:
Hydraulic equivalents:
Voltage = pressure
Current = flow rate
Resistor = orifice / rough pipe / etc. Anything involving friction, that would convert the pressure energy/kinetic energy into heat.

Capacitor = a tank separated by a rubber partition, with a connection on both sides. This is called an accumulator.
Inductor = a free rotating paddlewheel. Its inertia makes it apply a counterpressure to the system, any time the water flow attempts to change its speed.

Generator = pump. This would happen if you connect that "inductor" to an external source of mechanical energy.
Motor = turbine. Which would happen if you connect that "inductor" to an external mechanical load.

Real power would be the rate at which any energy enters or leaves the hydraulic system. So this would occur in the pump, turbine, or friction energy loss components.

Reactive power would be the rate at which hydraulic energy is temporarily stored in the paddlewheel's rotation, or as strain energy in accumulator's rubber partition. Any time that the water is speeding up the paddlewheel, or increasing the stretch from the neutral position of the accumulator's rubber.

Negative reactive power would occur when the rubber partition in the accumulator returns to its neutral position, restoring energy to the hydraulic system. Or when the paddlewheel slows down, and does exactly the same.

Phase would only be an applicable concept, when the pump drives a back and forth oscillating flow of the water. But what it would be, is the time difference per period between the instant when the pump applies the peak pressure, and when the system has the peak flow rate. When there is a lag in the flow rate behind the pressure, it is because there is inertia in the system, probably due to a paddlewheel. When the flow rate leads the pressure, it is because there is a component such as the accumulator in the system. It takes a flow rate first to push the rubber partition to its high pressure position.
Click to expand...


Vdrop is linear with current
pressure drop thru an orifice is not linear with flow

your L and C have no phase shift
describe what a phase shift would look like between pressure and flow
you store power in the wheel? Spring? Flywheel?
so when flow decreases it increases and augments flow?
nutty

it takes real power to charge an accumulator
and is only released when the pump is shutdown
not so with a capacitor, no real power, continuous exchange with generator

Neglecting phase is absurd since it is a key variable in electric power
the model is invalid
that is why it is not used

trust me
if it was a good idea it would have been thought up long before you lol
it is a bad idea, pointless

is it easier to mentally visualize hydraulics than electricity?
you can't see either
can't see pressure
 
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Carultch said:
Hydraulic equivalents:
Voltage = pressure
Current = flow rate
Resistor = orifice / rough pipe / etc. Anything involving friction, that would convert the pressure energy/kinetic energy into heat.

Capacitor = a tank separated by a rubber partition, with a connection on both sides. This is called an accumulator.
Inductor = a free rotating paddlewheel. Its inertia makes it apply a counterpressure to the system, any time the water flow attempts to change its speed.

Generator = pump. This would happen if you connect that "inductor" to an external source of mechanical energy.
Motor = turbine. Which would happen if you connect that "inductor" to an external mechanical load.

Real power would be the rate at which any energy enters or leaves the hydraulic system. So this would occur in the pump, turbine, or friction energy loss components.

Reactive power would be the rate at which hydraulic energy is temporarily stored in the paddlewheel's rotation, or as strain energy in accumulator's rubber partition. Any time that the water is speeding up the paddlewheel, or increasing the stretch from the neutral position of the accumulator's rubber.

Negative reactive power would occur when the rubber partition in the accumulator returns to its neutral position, restoring energy to the hydraulic system. Or when the paddlewheel slows down, and does exactly the same.

Phase would only be an applicable concept, when the pump drives a back and forth oscillating flow of the water. But what it would be, is the time difference per period between the instant when the pump applies the peak pressure, and when the system has the peak flow rate. When there is a lag in the flow rate behind the pressure, it is because there is inertia in the system, probably due to a paddlewheel. When the flow rate leads the pressure, it is because there is a component such as the accumulator in the system. It takes a flow rate first to push the rubber partition to its high pressure position.
Click to expand...

This is a wonderful description of the components for the design. Thank you so much. It describes exceedingly well and extends on what Ingenieur and Smart $ (by the way I am enthralled with his avatar!!!!) had proposed.

May I suggest that the pump be a reciprocating double sided piston with perfect seal or a peristaltic design where the cams rotate cw for one half cycle and ccw for the second half. We will need three such identical pumps with their phases offset by one third of a cycle from each other.

Maybe someone has a better idea here.:?
 
Ingenieur said:
Vdrop is linear with current
pressure drop thru an orifice is not linear with flow
Click to expand...

I'm aware of that inherent problem with constructing the analogy. Which is why there is not a hydraulic concept called resistance. There is a linear relationship between pressure difference and flow rate with a straight section of pipe for the special case of laminar flow that you get with a thick viscous substance like oil. However, most practical cases of water flow are turbulent, which introduces a lot of non-linear relations among the quantities.

it takes real power to charge an accumulator
and is only released when the pump is shutdown
not so with a capacitor, no real power, continuous exchange with generator
Click to expand...

There is a power exchange in the functionality of an inductor and a capacitor. It just isn't immediately obvious, since the energy remains within the circuit. There still is an instantaneous value of I*V that indicates this exchange of energy from within the current & voltage of the circuit to these components.

In the case of an inductor, it is the energy being stored in the magnetic field within the coils and ferrous core.
In the case of the capacitor, it is energy being stored in the electric field within the dielectric between the plates.

is it easier to mentally visualize hydraulics than electricity?
you can't see either
can't see pressure
Click to expand...

It is not only about what you can see. You can feel pressure, and you can see flow rate. You can directly relate hydraulic quantities to your senses, a lot easier than you can relate the quantities of electricity.
 
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iwire said:
it is that they have the knowledge to understand water does not behave like electricity and trying to say it does only confuses the person trying to learn the facts.
Click to expand...

I do fully respect the point you make, iwire. Howsoever, what this thought experiment is about is to see how much like a fluid electricity does behave. It is an open question as to whether we will succeed or not and even more so whether the abstraction will serve as a learning tool. The point is that I cannot find anything that has carried the analogy to the full level of three phase as we are all trying to do here. As you so expertly know the analogy holds up very well in DC (no not the hot air DC!!!!!:D) but the reactive components in AC present some challenge and, as you can see, the contribution from Carultch above is the best I have come across.
 
Carultch said:
Hydraulic equivalents:
Voltage = pressure
Current = flow rate
Resistor = orifice / rough pipe / etc. Anything involving friction, that would convert the pressure energy/kinetic energy into heat.

Capacitor = a tank separated by a rubber partition, with a connection on both sides. This is called an accumulator.
Inductor = a free rotating paddlewheel. Its inertia makes it apply a counterpressure to the system, any time the water flow attempts to change its speed.

Generator = pump. This would happen if you connect that "inductor" to an external source of mechanical energy.
Motor = turbine. Which would happen if you connect that "inductor" to an external mechanical load.

Real power would be the rate at which any energy enters or leaves the hydraulic system. So this would occur in the pump, turbine, or friction energy loss components.

Reactive power would be the rate at which hydraulic energy is temporarily stored in the paddlewheel's rotation, or as strain energy in accumulator's rubber partition. Any time that the water is speeding up the paddlewheel, or increasing the stretch from the neutral position of the accumulator's rubber.

Negative reactive power would occur when the rubber partition in the accumulator returns to its neutral position, restoring energy to the hydraulic system. Or when the paddlewheel slows down, and does exactly the same.

Phase would only be an applicable concept, when the pump drives a back and forth oscillating flow of the water. But what it would be, is the time difference per period between the instant when the pump applies the peak pressure, and when the system has the peak flow rate. When there is a lag in the flow rate behind the pressure, it is because there is inertia in the system, probably due to a paddlewheel. When the flow rate leads the pressure, it is because there is a component such as the accumulator in the system. It takes a flow rate first to push the rubber partition to its high pressure position.
Click to expand...
I wouldn't say equivalents. Analogy is a better term. You will still find situations where the hydraulic analogy doesn't quite fit the electrical application. And if trying to explain to someone that is not schooled on the topic they must be made aware that not all aspects of the analogy will necessarily apply, it is just a simplification to possibly help understand something a little easier.

How many basic electricity concepts books used as textbook for higher learning institutions use hydraulic analogies to explain the theory. I won't say there isn't any, but most higher respected institutions probably don't use them if they are out there. All I remember reading in my textbooks was explanations that described the physics and maybe had some graphics to demonstrate things as well. Like describing current as a particular amount of coulombs per second passing through a conductor - after explaining what a coulomb and a conductor was.

Teach the laymen the technical terminology, if they get lost then it is obvious they are not going to be electricians in the near future. Tell them that current is like water flow in a hose and some just might try to use a garden hose as a conductor:blink:
 
Carultch said:
It is not only about what you can see. You can feel pressure, and you can see flow rate. You can directly relate hydraulic quantities to your senses, a lot easier than you can relate the quantities of electricity.
Click to expand...

As children we learn about our world using our known proverbial five senses and much more. It might be easier for me to explain a waterworks toy to a child than to try to explain the "thing" referred to above. The reason for that is that the child is using his sensory inputs like you state.
 
dionysius said:
This is a wonderful description of the components for the design. Thank you so much. It describes exceedingly well and extends on what Ingenieur and Smart $ (by the way I am enthralled with his avatar!!!!) had proposed.

May I suggest that the pump be a reciprocating double sided piston with perfect seal or a peristaltic design where the cams rotate cw for one half cycle and ccw for the second half. We will need three such identical pumps with their phases offset by one third of a cycle from each other.

Maybe someone has a better idea here.:?
Click to expand...

Yep, that would be how it would work, to make a three phase hydraulic analogy. Three pumps, with staggered timing. Two of the pumps would pull exactly half the flow back to them, while the third pump is pushing out its peak flow. The inlets would all be connected at the neutral for a WYE system, or the inlet of one connected to the outlet of another for a delta system. It would work as three single phase pump circuits, except they now would be permitted to share a common return piping path (neutral). In fact, when all sources and sinks of energy are balanced, the neutral pipe would be filled with "dead water".

It is uncommon to see this either built in practice. Single phase or three phase AC in a hydraulic system isn't practical, as no water would make it from the pump to the load. All that would pass is its energy, and electricity is a more efficient way of doing the same thing.
 
Carultch said:
I'm aware of that inherent problem with constructing the analogy. Which is why there is not a hydraulic concept called resistance. There is a linear relationship between pressure difference and flow rate with a straight section of pipe for the special case of laminar flow that you get with a thick viscous substance like oil. However, most practical cases of water flow are turbulent, which introduces a lot of non-linear relations among the quantities.



There is a power exchange in the functionality of an inductor and a capacitor. It just isn't immediately obvious, since the energy remains within the circuit. There still is an instantaneous value of I*V that indicates this exchange of energy from within the current & voltage of the circuit to these components.

In the case of an inductor, it is the energy being stored in the magnetic field within the coils and ferrous core.
In the case of the capacitor, it is energy being stored in the electric field within the dielectric between the plates.



It is not only about what you can see. You can feel pressure, and you can see flow rate. You can directly relate hydraulic quantities to your senses, a lot easier than you can relate the quantities of electricity.
Click to expand...

you can feel current and voltage
you can see it
an arc, a glowing wire

the power exchange is all real power in a hydraulic ckt
it is not in an electric
this important distinction can't be swept under the table to fit an arguement
trying to use hydraulics to describe ac electricity only confuses the issue
that is why it is not done
 
Carultch said:
Yep, that would be how it would work, to make a three phase hydraulic analogy. Three pumps, with staggered timing. Two of the pumps would pull exactly half the flow back to them, while the third pump is pushing out its peak flow. The inlets would all be connected at the neutral for a WYE system, or the inlet of one connected to the outlet of another for a delta system. It would work as three single phase pump circuits, except they now would be permitted to share a common return piping path (neutral). In fact, when all sources and sinks of energy are balanced, the neutral pipe would be filled with "dead water".

It is uncommon to see this either built in practice. Single phase or three phase AC in a hydraulic system isn't practical, as no water would make it from the pump to the load. All that would pass is its energy, and electricity is a more efficient way of doing the same thing.
Click to expand...

Re the last statement refer to this from the "Wicked Pedia" : "This process is called peristalsis and is used in many biological systems such as the gastrointestinal tract. Typically, there will be two or more rollers, or wipers, occluding the tube, trapping between them a body of fluid. The body of fluid is then transported, at ambient pressure, toward the pump outlet. Peristaltic pumps may run continuously, or they may be indexed through partial revolutions to deliver smaller amounts of fluid."
 
dionysius said:
I do fully respect the point you make, iwire. Howsoever, what this thought experiment is about is to see how much like a fluid electricity does behave. It is an open question as to whether we will succeed or not and even more so whether the abstraction will serve as a learning tool. The point is that I cannot find anything that has carried the analogy to the full level of three phase as we are all trying to do here.
Click to expand...
Not all of us are trying to do that. I'm not. Water behaves like water and electricity behaves like electricity. They have some attributes in common but if you dive deep they are not alike. What we must be careful of, in my opinion, is extrapolating erroneous predictions of the behavior of electricity because of the way water behaves.
 
ggunn said:
Not all of us are trying to do that. I'm not. Water behaves like water and electricity behaves like electricity. They have some attributes in common but if you dive deep they are not alike. What we must be careful of, in my opinion, is extrapolating erroneous predictions of the behavior of electricity because of the way water behaves.
Click to expand...


This
 
dionysius said:
As children we learn about our world using our known proverbial five senses and much more. It might be easier for me to explain a waterworks toy to a child than to try to explain the "thing" referred to above. The reason for that is that the child is using his sensory inputs like you state.
Click to expand...

What are the senses beyond 5?
much more?
like logic
intuition?
learning?
are those senses?
I thought senses were tactile interface mechanisms with the physical world?

children aren't schooled in math/physics so do not have the tools to understand ac power
so a simplified analogy may be required
but if you think your analogy will help, not confuse a child, think again
water? Electricity? What???
lol
 
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