Vol 5 Chapter 46: Fluid line of force

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Both of them have undoubtedly received the feedback from Dream Dayuan, although, it is enough to promote Donna from a senior wizard apprentice to a first-level life.
"Senior sister, let's sign together and send out this paper."
Donna was promoted to the first level, and she was extremely happy. She is now a genuine double-level one, both in strength and academic level, which made her very proud.
Blenia shook her head and said: "This is your independent discovery. I am just helping calculus. Even if you don't have me, you can get this result if you spend more time. If I sign it, wouldn't it mean that I will steal your fruits? In this way, we will break our friendship!"
Donna persuaded for a while, Blenia was still unwilling, and Donna had to give up.
She told her teacher Betty about the incident, and Betty admired and said: "You have made a friend of good character. This can be a good story."
Blenia's mind is indeed not in this paper on "gong". She was studying the academic paper on the direction of heat with Donna, and found an extremely excellent paper "On Heat Conduction" by a person named Meier. The masterpiece of the second ring wizard.
"The temperature difference in an object or system is a necessary condition for heat conduction. In other words, as long as there is a temperature difference in or between the media, heat transfer must occur. The rate of heat transfer depends on the distribution of the temperature field in the object."
Blenia read softly while watching a series of experiments and the final conclusion. This is the famous Meyer's law in the field of heat:
"In the heat conduction phenomenon, the amount of heat passing through a given cross-section per unit time is proportional to the temperature change rate and cross-sectional area in the direction perpendicular to the cross-section, while the direction of heat transfer is opposite to the direction of temperature rise."
Looking at the slightly complicated formula, Blenia's eyes sparkled, and she remembered Her Excellency Thales’s point of view:
The way to solve the confusion is analogy. Two analogous physical objects or laws are similar in mathematical form.

This supplemented some parts of the fluid mechanics of her previous analogy, and the scattered thoughts in Blenia's mind were strung together by a string in an instant, forming a beautiful pearl necklace.
She unrolled a roll of magic paper, feeling agitated, and the whole person seemed to form an invisible "field" that interacted with the surrounding magic net.
Blenia flew his pen and wrote the title "On Thales' Lines of Force."
She briefly reviewed the development process and status quo of electromagnetics, pointed out some areas lacking mathematical support and confusing areas, and pointed out that the solution was the analogy mentioned by Thales.
Then she had piercing eyes and wrote vigorously:
"According to the method I will adopt, I hope to show that I am not trying to establish any physical theory from an academic that I have not made any experimental results;
The ultimate goal of my design is to show that by rigorously applying Thales’ thinking and methods, many of the connections between different electromagnetic phenomena he discovered can be clearly displayed in front of mathematicians.
Therefore, I will try to avoid putting forward any direct examples that are not derived from the Thales method, or any mathematical inferences that are not derived from the Thales method.
When discussing some of the simpler parts of the subject, I will use Thales’ mathematical methods and thinking. When the complex part of the subject needs it, I will use mathematical analysis, but I am still limited to developing the original thinking of this great wizard. "
The magic net was shaking slightly, as if foreseeing something great would happen, Blenia also felt that her mind was agitated, and she bent down and wrote wholeheartedly:
"The mechanics of fluids has been perfectly established. The so-called fluids are objects that can flow, such as air and water.
Thales’ line of force can be extended as a
force tube
filled with incompressible fluid.
The direction of the force tube represents the direction of the force field (electric field or magnetic field). The cross-sectional area of ​​the force tube is inversely proportional to the fluid velocity in the force tube, and the fluid velocity can be compared to an electric field or a magnetic field.
Since the electric or magnetic field can be compared to the velocity of a fluid, of course, the electric or magnetic field can be required to comply with part of the theory of fluid mechanics.
Then, by borrowing some mathematical frameworks of fluid mechanics, a series of preliminary electromagnetic theories can be derived.
We know that Meyer's law of heat conduction, which describes the conduction of heat to a uniform substance, is in the same form as the equation describing the relationship between electric field and electric potential in electrostatics.
Obviously, if the thermal conductivity is set equal to one, the electric potential can be compared to the temperature, and the electric field can be compared to the heat flux.
Thales’ power lines have become heat flow lines, and the equipotential lines have become isotherms.
Therefore, the method of analyzing heat conduction problems can be used to analyze electrostatic problems. "
The dramatic changes in the magic net have attracted Thales's attention. He appeared behind Blenia in a flash, floating in the air, without interruption, quietly looking at Blenia's paper, his eyes shining brightly.
Thales had never thought that Blenia, the secretary who was always serious, meticulous and gentle, was so outstanding academically. Her genius analogy to the line of force and the incompressible fluid made Thales himself feel that suddenly see the light.
Blenia was still discussing the similarities between heat conduction and electrostatics, and her eyes were shining brightly.
"The heat conduction relies on the adjacency effect between two closely spaced particles of matter contacting each other; think about the forces that are directly applied to each other without passing through any medium, if the electric field force is this If there is a kind of force, the electric force is a kind of over-distance action. Two completely different physical phenomena can be described by the same form of mathematics, which gives people a lot of room for imagination.
She did not discuss too much, and continued to return the pen front to the incompressible fluid.
Thales also watched carefully, with a smile on the corner of her mouth, Blenia really understood her theory too much.
"The heat conduction mechanism can only be compared to the physical phenomena of the electromagnetic field to a limited extent. The fluid flow mechanism has more power and more functions to compare electrostatics and magnetostatics.
The volume of any part of the incompressible fluid will not change over time.
This is a hypothetical ideal fluid, a very simple fluid.
Let us further assume that the fluid flow is stable.
At any location, the direction and rate of flow does not contain time.
In this way, there is no need to consider the time factor.
Any element inside the fluid, along with the flow, will draw a curve, called the ‘flow line’.
The lines of force that Thales came up with can be compared to the lines of flow. "
The text gurgled out like mercury, it was so natural, everything was so fit, Blenia deserves to be a mathematics genius, and then there are a lot of mathematical proofs, which are dizzying to those who don’t understand. Those who understand seem to be the keys to truth.
Thales almost burst into tears in his eyes, as if he had met Blania again, his eyes shone with brilliance, and Xueba admired only Xueba.
Blenia’s proof is nearing completion, she wrote heavily:
"Incompressible fluid systems follow the principle of superposition, that is, linear mapping.
Given three fluid flow systems, it is assumed that the velocity of the third system at each location is the vector sum of the velocity of the other two systems at the same location.
Then the volume of fluid per unit time passing through a curved surface of the third system is equal to the sum of the volume of fluid per unit time passing through the same curved surface of the other two systems. "
The magic net nearby is already boiling, and the source of the blockbuster is already waiting here, waiting for Blenia to pick it up, but Blenia does not pay attention to it. She continues to write this imaginary fluid and expand new large paragraphs. The emphasis is on the uniform motion of massless fluid flowing through the impedance medium.
"The ideal fluid has no mass, no inertia, and has nothing to do with Ace's law of motion. This model is a geometric model, not a physical model.
...
Given the equal pressure surface of a fluid system, the flow velocity at all positions in the space can be calculated, and all unit force tubes, including the force tube source and the force tube gully, can be arranged. Conversely, given all the force pipe sources and force pipe gully in a system, the flow velocity at all positions in the space can be calculated, and the isobaric surface can also be calculated.
Given a fluid system, know its pressure, force tube source distribution and force tube gully distribution at each position, assuming that the impedance coefficient of its medium is k. This system is equivalent to a system where the impedance coefficient of the medium is one and the flow rates of the force tube source and the force tube gully are k times respectively. The two systems have the same pressure at each location and the same flow rate.
This fluid system still follows the principle of superposition. Given three fluid flow systems, it is assumed that the pressure of the third system at each position is the sum of the pressures of the other two systems at the same position. Then the flow velocity of the third system at each position in the three-dimensional space is the vector sum of the flow velocity of the other two systems at the same position. "
Just as shocking, the mathematical model perfectly explained Thales’ lines of force and gave them powerful mathematical support. From now on, no one would dare to say that Thales’ lines of force lacked mathematical proofs.
The source force is like waves, driving the magical shock around the entire wizard tower. Many wizards have gathered here, and people are talking about it, and they all believe that Thales has achieved decisive theoretical results.
"Master Thales is really amazing. I can hardly describe it. He is like Master Ace to magic. In the field of electromagnetics, Master Thales is the torch of the long night!"
A supporter said loudly.
Other opponents felt grief and stopped talking.
People were waiting quietly. The legendary wizard nearby also approached the Wizard Tower. Bayern rubbed his brow vigorously. He was completely convinced. This Thales was simply too genius. In short, he made a lot of big things. Recently, a lot of reinforcement insurance has been done for the mental world, which should not be a big problem.
Blenia hasn't finished her thesis on the decisiveness of force lines. She applied this hypothetical ideal fluid to many electromagnetic phenomena stroke by stroke.
Electrostatic effect, magnetostatic effect, induced magnetic field effect, electric current, etc. can all be perfectly explained by this ideal fluid. Blenia quietly finished the last stroke, and the turbulent source force instantly swallowed her like a stormy sea.
She was bathed in Yuanli’s ocean, and that Yuanli gradually condensed into a cocoon, dissolving her clothes, and the naked Blenia seemed to return to her mother. Her aptitude was constantly improving, but she was only with excellent magic aptitude, in Dayuan. After refining, the magic aptitude is close to the top, similar to a natural overclocker.
Her strength also rose rapidly, easily breaking through the barrier between level one and level two, and the soul secret space evolved into a hollow mind-like world, with an ideal state of compressed fluid phantom quietly hovering in the center, seemingly waiting she was.
Blenia touched the phantom with her mind, and instantly received a large amount of runes and rune structures from the great source of feedback. Numerous three-ring and four-ring magic flowed in her heart. In just a moment, she became an extremely A powerful three-ring wizard.
If it weren't for a large amount of source power to improve her aptitude, I am afraid it would be no problem to be promoted to the Fourth Ring Golden Wizard.
However, the current slowness is for the future faster, top-level qualifications, it is only a matter of time to promote from the third ring to the fourth ring, as a second-level life, life in this world has nearly ten thousand years, she has time.
Even in the world of Kaya, Blenia's situation is enough to live for hundreds of years.
She slowly opened her eyes, and Yuanli's cocoon instantly shattered, turning into void powder and disappearing.
The naked Blenia opened her eyes ignorantly and stared at Thales in front of her in a daze. Thales also stared at her wide, and the two of them stared blankly for a long time, Thales felt his head Blank, dry mouth.
He swallowed his saliva, his face flushed, and he unconsciously chanted a curse, and put a moon-white robe on Blenia.
Blenia screamed in hindsight, and then she slammed her mouth, her heart beating, and her mind wandered: Oh, oh, Lord Thales didn’t think I was that kind of superficial witch. , He must be disappointed in me.
Thales also recovered~EbookFREE.me~ He felt that his heartbeat was faster than ever before. When he was just reading Blenia’s paper, he changed his view of Blenia, as if he had discovered a treasure. The impact made ripples in his heart even more.
He thought in his heart: It's broken, I usually don't squeeze, I don't understand and care about the lady. Suddenly, I watched other people's body for so long. She must hate me, and the jar broke.
Thales’ face was still cold, and he said in a deep voice,
Blenia, your research has inspired feedback from Mowang and Dayuan, so I’ll take a look. Your paper is very good, but you should pay attention to it in the future. , Pay attention to the way to draw the great source of power, so be it, everyone is waiting for you outside, change into decent clothes, and we go out together."
Blenia was frustrated for an instant, and she kept talking in her heart. She must have hated me. My image of a lady is so unlucky. Originally, this paper should surprise Master Thales to me and become very appreciative of it. Up.
She walked back to her room in despair, and changed her clothes.
Thales kept beating his own mouth in his heart, saying what he was talking about, and paying attention to the way of drawing. How to pay attention to this thing, it was like a mouthful. At this time, he should explain that he did not deliberately watch it for so long.