A list of puns related to "Energy flow (ecology)"
i'm sure that most of us have heard of the meditation method where you visualize inhaling positive energy and exhaling negative energy. if you read tarot, you may have visualized your energy and intent flowing into the deck in a similar fashion. that is the inspiration for this method!
step 2 and 3 are kind of interchangeable, just rearrange them in whatever order you find helpful. but don't obsess over the steps too much, the method allows for a lot of creative freedom with your visualization!
Where I'm confused is, when we talk about the flow of energy in a circuit, when are we talking about the electrons and when are we talking about the fields? I don't get why the energy of the field isn't the energy of the kinetic energy of the electrons; or maybe I'm just misunderstanding what that means.
Let me explain my thought process so I can specify exactly where my confusion lies: First, there has to be a current in order for there to a flow of electrical energy, right? And if we consider current in terms of the E field, what happens is that the movement of the electrons that creates a disturbance in the E field by varying the value of the E field in space, like a wave, yes? (Although that disturbance isn't what's meant by EM waves, I don't think.) That energy that causes the disturbance is from the electrons. Isn't that the same energy that's flowing in the circuit, just the energy carried by a water wave is from the movement of the water molecules, even though the movement of the wave is distinct from the movement of the molecules?
As I think about this more, I'm wondering if it isn't somewhat an issue of semantics. I mean, it's debatable whether the EM field is even a physical thing at all or just an incredibly useful abstraction.* I guess maybe part of it is that I'm not sure entirely clear on the mathematics. I've studied Maxwell's equations, Coloumb's law, and the Lorentz force law, both in University Physics 2 and in Introduction to Electromagnetics, and they all make sense (though I admittedly have a hard actually internalizing Maxwell's equations; I almost invariably have to look them up and review what each one actually means if I want to talk about them in any detail). In principle, that should explain all of classical electrodynamics, and yet I don't see how any of them explain energy flow.
Q'uo: I am Q'uo, and greet each in the love, and in the light of the One Infinite Creator. We are honored this evening to be called to your gathering in order to respond to the query of the evening. Before doing so, we would ask you our perpetual favor, and that is that you take those words and concepts that we offer to you, and use them in whatever way has meaning for you. And if there are any that have no meaning at this time, we would ask that you set them aside and do not concern yourselves with them, for we are your brothers and sisters who wish to serve, and we can serve to our fullest ability when you do as we ask and realize that we are not an ultimate authority, with every word needing to be believed.
And now, for the query, we find that you have asked a query which has a universal application to all seekers of truth. The self-judgment is a feature of each seeker of truth at some point in its journey of seeking to be of service to others and the One Creator which exists within each entity and each portion of the creation. The self-judgment is something that is a stage through which each seeker must needs pass, for it is incumbent upon each seeker in its own beginning of seeking and serving others to consider how it is able to do so. What are its strengths and weaknesses? What features of the classical seeker, shall we say, may be embodied in any particular seeker?
It is what every seeker considers at the beginning of the journey and also from time to time as the journey proceeds. For self-judgment, or self-reflection, is in some manner helpful to determine what the seeker feels are its strengths and weaknesses. And if this assessment is refined as time moves forward, as you would call it, then the seeker is able to make an helpful step in the direction of positive polarization when it utilizes its strengths and seeks to enhance what it considers to be weaknesses. If this can remain as an objective process, where the seeker is able to accept itself in both its strengths and weaknesses, then it is engaged in a self-reflective mode of conscious realization that will help it to make progress in its being of service to others, and to recognizing the Creator within others, and the Creator within the self. For these are spiritual attributes, that all seekers, and all entities, whether they be conscious seekers or not, share with each other. For it is the nature of reality that all is One, that each seeker is the Creator, that the Creator exists within
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Today I had the feeling for the first time with yin yoga that the energy is not only collecting in the pelvis. It flowed into the legs by itself. Without breath steering or other. What a nice feeling when (unfortunately very often with me) announcing cramps in the sole of the foot slowly dissolve and the whole leg is flowing through warmly.
I'd like to ask one question, but would like to get answers for two scenarios. The first scenario being the fluid density ฯ is considered incompressible (ฯ = constant). The second scenario being the fluid density is considered a function or pressure ฯ=f(p).
The Question: The dynamic pressure (kinetic energy per unit volume) for a parcel of fluid is:
0.5ฯv^2
where v = fluid velocity. The fluid is flowing towards a line sink. That is, the geometry of the flow is "cylindrical", fluid moves from the outer radius of a cylindrical boundary towards the cylinder's centerline axis. Therefore, the flow can be analyzed as 1-dimensional radial flow. The cross-sectional area (A) normal to the direction of flow is the cylindrical surface, A = 2ฯ r L, where L = cylinder length.
The derivative of the dynamic pressure with respect to radial position r is:
d/dr (0.5ฯv^2) = ฯv dv/dr
I want to find the integral of the change in dynamic pressure with respect to radial position r (the change in dynamic pressure as the fluid moves towards the line sink, from outer position r_2 to inner position r_1). Thus, I have the definite integral:
โซ _{r_1}^r{r_2} ฯv (dv/dr) dr
How can this integral be evaluated for scenarios 1 and 2?
For the incompressible scenario (ฯ = constant), the following has been tried:
At a radius r the velocity is v and the mass flowing across the surface per second is 2ฯ r Lvฯ. At a radius r+dr with velocity v+dv the mass flowing across the surface per second is 2ฯ(r+dr)L(v+dv)ฯ. Setting these two equal, assuming constant density, we have:
rv=(r+dr)(v+dv)
Expanding and simplifying and ignoring the term dvdr gives:
dv/dr = -v/r
Substituting this relation into the integral and evaluating, we have:
โซ _{r_1}^r{r_2} (-ฯv^2)/(r) dr
Since v = w/(ฯA), where w = mass rate, and A = 2ฯ r L, then:
โซ _{r_1}^r{r_2} (-w^2)/(4ฯ^2 L^2 ฯ r^3 ) dr
Pulling the constants from the integral:
(-w^2)/(4ฯ^2 L^2 ฯ ) โซ _{r_1}^r{r_2} r^(-3) dr
Evaluating the integral:
(w^2)/(4ฯ^2 L^2 ฯ ) (r_2 ^(-2) - r_1 ^(-2))
Does this make sense (for the constant density scenario)? What about for compressible fluid scenario (density = f(p))?
Edit1: Noting that I differentiated the dynamic pressure with respect to (w.r.t.) r and then integrated w.r.t. r, I am left with the original dynamic pressure relation: 0.5ฯv^2. As a check, substitute v = w/(ฯA), where w = mass rate, and A = 2ฯ r L, and it
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