Chapter 554: Lines of Fluid Force
The two undoubtedly both received feedback from the Dream Great Source. Although it was shared, it was enough to let Donna advance from a Senior Wizard Apprentice to a Level 1 Lifeform.
“Senior Sister, let’s sign our names together and publish this paper.”
Donna had advanced to Level 1, and her mood was extremely pleasant. She was now a genuine double Level 1: her strength and academic level were both Level 1, which made her very proud.
Blania shook her head and said: “This is your independent discovery. I only helped with the calculations. Even without me, if you spent a bit more time, you could still achieve this result. If I sign my name, isn’t that letting me steal the fruits of your labor? If you do this, we’ll break off our friendship!”
Donna persuaded her for a while, but Blania was still unwilling, so Donna had to give up.
She told this matter to her teacher Betty. Betty praised her and said: “You’ve made a friend with excellent character. This can be passed down as a beautiful tale.”
Blania’s mind was indeed not on this paper about “work.” While studying academic papers on heat with Donna, she discovered an extremely excellent paper: On Heat Conduction, a masterpiece by a Second Ring Wizard named Mayer.
“A temperature difference within an object or system is a necessary condition for heat conduction. In other words, as long as there is a temperature difference within or between mediums, heat transfer will inevitably occur. The rate of heat conduction is determined by the distribution of the temperature field within the object.”
Blania read softly while looking at a series of experiments and the final conclusion. This was the famous Mayer’s Law in the field of thermodynamics:
“In the phenomenon of heat conduction, the amount of heat passing through a given cross-section per unit time is directly proportional to the rate of temperature change in the direction perpendicular to that cross-section and the cross-sectional area, while the direction of heat transfer is opposite to the direction of temperature increase.”
Looking at that slightly complex formula, Blania’s eyes shone. She remembered His Excellency Thales’s viewpoint: “The way to solve perplexity is analogy. Two analogous physical objects or laws both possess mathematical similarity.”
This filled in certain parts of her previous analogy to fluid mechanics. The scattered thoughts in Blania’s mind were instantly strung together by a single thread, becoming a beautiful pearl necklace.
She unrolled a piece of magic paper, her heart surging with excitement. Her whole person seemed to form an invisible “field,” interacting with the surrounding Magic Net.
Blania’s pen flew as she wrote the title: On Thales’s Lines of Force.
She briefly reviewed the development history and current status of electromagnetism, pointed out some areas lacking mathematical support and perplexing fields, and indicated that the solution was the analogy Thales had mentioned.
Then, with bright eyes, she wrote forcefully:
“According to the method I will adopt, I hope to show that I am not trying to establish any physical theory from an academic field in which I have not yet produced any experimental results;
“The ultimate goal of my design is to show that, by rigorously applying Thales’s thinking and methods, the connection between the many different electromagnetic phenomena he discovered can be clearly displayed before mathematicians.
“Therefore, I will try to avoid proposing any direct examples that are not derived from Thales’s method, or any mathematical deductions that are not derived from Thales’s method.
“When exploring some of the simpler parts of the subject, I will use Thales’s mathematical methods and thinking. When the complex parts of the subject require it, I will use mathematical analysis, but still confine it to developing the original thinking of this great wizard.”
The Magic Net was vibrating slightly, seemingly having a premonition that something great was about to happen. Blania felt it too. Her mind was surging. She leaned over and wrote wholeheartedly:
“Fluid mechanics has already been perfectly established. The so-called fluid refers to objects that can flow, such as air, water, and so on.
“Thales’s lines of force can be extended into ‘tubes of force’ filled with an incompressible fluid.
“The direction of these tubes of force represents the direction of the force field (electric or magnetic field). The cross-sectional area of the tube of force is inversely proportional to the fluid velocity within the tube, and this fluid velocity can be analogous to the electric or magnetic field.
“Since an electric or magnetic field can be analogous to fluid velocity, of course, we can require the electric or magnetic field to obey part of the theories of fluid mechanics.
“Then, borrowing some mathematical frameworks from fluid mechanics, we can deduce a series of embryonic theories of electromagnetism in their initial forms.
“We know that Mayer’s Law of Heat Conduction, which describes heat conduction in uniform matter, and the relationship describing the electric field and electric potential in electrostatics, have equations of the same form.
“Obviously, if we set thermal conductivity equal to one, then electric potential can be analogous to temperature, and electric field can be analogous to heat flux.
“Thales’s electric lines of force become heat flow lines, and equipotential lines become isothermal lines.
“Therefore, methods for analyzing heat conduction problems can be used to analyze electrostatics problems.”
The violent fluctuations of the Magic Net had already attracted Thales’s attention. With a flash, he appeared behind Blania, hovering in mid-air. Without interrupting, he quietly looked at Blania’s paper, his eyes flashing with extraordinary brilliance.
Thales had never thought that his consistently serious, meticulous, and gentle secretary Blania could be so outstanding academically. Her genius analogy of lines of force to incompressible fluid made even Thales himself feel enlightened.
Blania was still discussing the similarity between heat conduction and electrostatics, her eyes shining with extraordinary brilliance.
“Heat conduction relies on the contiguous action produced by the mutual contact of two adjacent particles of matter; consider two electric charges far apart, exerting a force directly on each other without any medium. If the electric field force is this kind of force, then the electric field force is an action at a distance. Two completely different physical phenomena can actually be described using the same mathematical form. This gives people a lot of room for imagination.”
She didn’t over-discuss this and continued to bring the tip of her pen back to incompressible fluids.
Thales also watched carefully, a trace of a smile appearing at the corner of his mouth. Blania truly understood his theory too well.
“The heat conduction mechanism can only limitedly draw analogies to the physical phenomena of electromagnetic fields. The fluid flow mechanism has greater power and more functions to draw analogies to electrostatics and magnetostatics.
“The volume of any part of an incompressible fluid will not change as time evolves.
“This is a hypothetical ideal fluid, a very simple fluid.
“We might as well go a step further and assume that the fluid flow is steady.
“At any position, the direction and speed of the flow do not contain time.
“In this way, the time factor need not be considered.
“Any element within the fluid, as it flows, will trace out a curve, called a ‘flow line’ (streamline).
“The lines of force conceived by Thales can be analogous to flow lines.”
Words flowed out continuously like mercury pouring onto the ground, so naturally, everything fitting so perfectly together. Blania was indeed a math genius. Following this were large paragraphs of mathematical proofs. To those who didn’t understand, it was dizzying; to those who did, it was like the key to truth.
Tears almost welled up in Thales’s eyes. He felt as if he were getting to know Blania anew. His eyes shone with extraordinary brilliance. Only top scholars truly admire other top scholars.
Blania’s proof was nearing its end. She wrote heavily:
“An incompressible fluid system obeys the principle of superposition, which is a linear mapping.
“Given three fluid flow systems, suppose the flow velocity of the third system at every position is the vector sum of the flow velocities of the other two systems at the same position.
“Then the fluid volume per unit time passing through a surface of the third system is equal to the sum of the fluid volumes per unit time passing through the same surface of the other two systems.”
The nearby Magic Net had already boiled over. A large swath of Source Power was already waiting here, quietly waiting for Blania to pluck it. However, Blania paid it no mind. She continued writing about this hypothetical fluid, launching into a new large section of discussion, focusing on the uniform motion of a massless fluid flowing through a resistive medium.
“An ideal fluid has no mass, no inertia, and has nothing to do with Ace’s Laws of Motion. This model is a geometric model, not a physical model.
…
“Given the isobaric surfaces of a fluid system, the flow velocity at all positions in space can be calculated, and all unit tubes of force can be arranged, including their sources and sinks. Conversely, given all the sources and sinks of tubes of force in a system, the flow velocity at all positions in space can be calculated, and the isobaric surfaces can also be calculated.
“Given a fluid system, knowing its pressure at every position, the distribution of sources of tubes of force, and the distribution of sinks of tubes of force, suppose the resistance coefficient of its medium is k. This system is equivalent to a system where the resistance coefficient of the medium is one, and the flow rates of the sources and sinks of tubes of force are both k times as much. The pressure of the two systems at every position is equal, and the flow velocity is also equal.
“This fluid system still obeys the principle of superposition. Given three fluid flow systems, suppose the pressure of the third system at every 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 every position in three-dimensional space is the vector sum of the flow velocities of the other two systems at the same position.”
Like a bolt from the blue, the mathematical model perfectly explained Thales’s lines of force, giving lines of force solid mathematical support. From this day forward, no one would dare say Thales’s lines of force lacked mathematical proof.
The Source Power surged like waves, driving the mana around the entire Wizard Tower to oscillate. Quite a few wizards had already gathered here. People were discussing enthusiastically, all thinking Thales had made another decisive theoretical achievement.
“Lord Thales is really too amazing. Words fail me to describe it. He is to electromagnetism what Lord Ace is to magic. In the field of electromagnetism, Lord Thales is the torch in the long night!”
A hardcore supporter said loudly.
The other opponents felt deeply touched and stopped speaking.
People waited quietly. The nearby Legendary Wizards also approached the Wizard Tower. Bayen rubbed the space between his eyebrows forcefully. He was completely convinced. This Thales was simply too much of a genius. Anyway, making a lot of huge commotions. Fortunately, he had done a lot of reinforcement and insurance for his mental imagery world recently; it shouldn’t be a big problem.
Blania hadn’t finished writing her decisive paper on lines of force yet. Stroke by stroke, she applied this hypothetical ideal fluid to many electromagnetic phenomena.
Electrostatic action, magnetostatic action, induced magnetic field action, electric current, etc., could all be perfectly explained using this ideal fluid. Blania quietly finished writing the last stroke. Surging Source Power instantly swallowed her like tempestuous waves.
She bathed in the ocean of Source Power. That Source Power actually gradually condensed into a cocoon, dissolving her clothes. The naked Blania was like returning to the mother’s womb. Her aptitude was constantly improving. Originally possessing only excellent magical aptitude, under the cleansing of the Great Source, her magical aptitude was close to top-tier, similar to a natural overdrive.
Her strength also climbed rapidly, easily piercing the barrier separating Level 1 from advancing to Level 2. Her Soul Sanctuary space evolved into an empty shell mental imagery world. A phantom of an ideal state compressed fluid quietly lingered in the center, seeming to wait for her.
Blania touched her mind to that phantom, instantly obtaining a large amount of runes and rune structures fed back by the Great Source. Countless Third Ring and Fourth Ring magics flowed in her mind. In just an instant, she achieved becoming an extremely powerful Third Ring Wizard.
If it weren’t for a large amount of Source Power being used to improve her aptitude, advancing to a Fourth Ring Golden Wizard would probably have been no problem at all.
But being slow now was for being faster later. With top-tier aptitude, advancing from the Third Ring to the Fourth Ring was only a matter of time. As a Level 2 Lifeform, her lifespan in this world was nearly ten thousand years; she had plenty of time.
Even in the Kaya World, Blania’s condition was enough to live for several hundred years.
She slowly opened her eyes. The cocoon of Source Power instantly shattered, turning into void powder and disappearing.
The naked Blania opened her eyes ignorantly and stared blankly at Thales in front of her. Thales also stared wide-eyed at her. The two just stared blankly like this for a long time. Thales felt his mind go completely blank and his mouth go dry.
He swallowed his saliva, his face bright red. Unconsciously chanting a spell, a moon-white cloak draped over Blania.
Only then did Blania realize it belatedly and scream. She then abruptly covered her mouth, her heart pounding wildly. A thought hovered in her mind: Oh no, oh no. Lord Thales wouldn’t think I’m that kind of superficial witch, would he? He must be thoroughly disappointed in me.
Thales also snapped out of it. He felt his heartbeat faster than ever before. Just now, watching Blania write her paper, his impression of her had vastly improved, like discovering a treasure. The impact just now caused ripples in his heart even more.
He thought to himself: This is bad. I usually don’t pay attention to my appearance and don’t know how to perform and care for a lady. Suddenly staring at her naked body for so long like that, she definitely hates me now. Might as well smash a cracked pot.
Thales’s face remained cold, and he said in a deep voice: “Blania, your research triggered the Magic Net and Great Source feedback, so I came to take a look. Your paper is very good, but in the future, you must also pay attention to, ahem, pay attention to the way you absorb the power of the Great Source. That’s all. Everyone is waiting for you outside. Change into proper clothes, and we’ll go out together.”
Blania was instantly dejected, muttering constantly in her heart: He definitely hates me now. My lady image… Why am I so unlucky? Originally, this paper should have made Lord Thales greatly surprised and appreciate me very much. Now it’s ruined.
She walked back to her room despondently to change clothes.
Thales, on the other hand, kept slapping his own mouth in his heart. What was I saying? Pay attention to the way of absorption? How do you pay attention to this? My mouth simply ran away to the sky. I should have explained that I didn’t mean to stare for so long just now.
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