The Shadow of Great Britain

Chapter 881: Revised: Chapter 12 The Issue of Beyond and Within the Scope of the College Entrance Examination_3

Navier walked as he spoke: ”Speaking of Mr. Poisson, I heard that the Royal Society of Britain seems to plan to award him this year’s Copley Medal. Yesterday, the delegation sent to present the award even sent someone to the Academy of Sciences to contact him, asking when Mr. Poisson would be available to receive the medal.”

Coriolis, somewhat envious, said: ”With such an honor, I suppose the Academy of Sciences will hold a special award ceremony for Mr. Poisson?”

Navier slightly curled his lips: ”Who cares, I don’t like getting involved in such things anyway. I just hope the ceremony ends quickly and doesn’t delay our real work. Besides, compared to the award ceremony, I’m obviously more interested in the award guest coming from London.”

Coriolis asked: ”Who is the award guest?”

”Sir Arthur Hastings, a young electromagnetism researcher from Britain. I’ve heard that he has a very good relationship with Mr. Faraday and often participates in the work at the Faraday Laboratory. Among the current young researchers in electromagnetism in Britain, he is definitely one of the best. Unfortunately, I don’t research electromagnetism much, otherwise, I would definitely ask him to tell me about the current advancements and breakthroughs in British electromagnetism research.”

Coriolis also smiled and said: ”I feel the same. I find mechanics to be a bit more interesting than electromagnetism. Electromagnetic induction is fascinating, but I am obviously more interested in that fluid dynamics equation you just mentioned.”

”Is that so?” Navier looked in a good mood: ”Then let me take you to see it. Most people in the Mechanics Department think it’s a niche direction. If you can be interested in it, that’s quite rare. The manuscript of the fluid dynamics equations I’ve been working on is in the library. If you’re interested, we can go there now. Plus, we can have a good chat about the new force you’ve mentioned in a rotating system.”

Coriolis asked: ”Do you mean the library in the eastmost corner?”

”Yes, that library is very secluded, so few people go there. But people like me, Ampere, and Cauchy, we all like quiet places, so we all gather there. How do you feel about it?”

”It’s better to accept deferentially than to decline courteously.”

The two of them chatted and laughed along the tree-lined path and soon arrived at the library door.

Navier was about to pull open the library door when he found it being pushed open from the inside.

Ville was leading a gentleman they didn’t recognize out of the library, and they bumped right into them.

When Ville saw the two academic giants, he was taken aback at first, then took off his hat and greeted: ”Ah! Good morning, gentlemen!”

Arthur followed suit and greeted: ”Good morning, gentlemen.”

”Good morning.”

Coriolis knew Ville, but the tall young man before him was a stranger. However, he wasn’t interested in asking about the other person’s identity.

After all, in the French Academy of Sciences, assistants came and went every day, newcomers joining and the old ones leaving, there was nothing strange about it.

He stepped aside to clear the way, watching Ville leave with Arthur, and just as he was about to enter, he heard Navier say: ”Is that young man a new assistant?”

Coriolis shrugged: ”Most likely, right? Could there be anyone else in the Academy? Even if there were, they’d be officials, but everyone knows officials wouldn’t come to the library.”

Navier said in surprise: ”If he’s an assistant, how come I don’t know him? I’ve taught at the École Polytechnique in Paris for so many years, I know every student in the Mathematics and Natural Philosophy departments, but I have no impression of him at all.”

Coriolis joked: ”Are you suggesting the Academy hired an assistant who didn’t graduate from the École Polytechnique? You must be joking, Mr. Navier. Even the most ordinary assistant at the Paris Academy of Sciences is among the best of their peers, and almost all top scholars of every age group are graduates of the École Polytechnique. It’s the same for Mr. Cauchy, Mr. Poisson, you and I, and even Ville who just left. Are you implying that among all of us École Polytechnique graduates, there’s a graduate from a lesser-known school? I think the Academy hasn’t become that incompetent yet.”

Navier did not delve into this further, but instead stepped inside, saying: ”Forget it, why care about this? Let’s talk about something more interesting. You sit down, and I’ll look for the manuscript I’m missing.”

As soon as he entered, Navier headed straight for the bookshelf, remembering he had tucked that sheet of calculation paper into a book.

Coriolis, in the meantime, walked towards the still-warm chair and found the calculation paper filled with formulas and derivations on the oak table.

Coriolis picked up the calculation paper and glanced over it, quickly exclaiming: ”Mr. Navier, this must be what you’re looking for. This derivation is indeed exquisite. However, it seems you didn’t mention to me earlier that you recently introduced three new hypotheses based on the original derivation?”

”Three hypotheses?”

Navier, hearing this, put down the book in his hand and walked towards Coriolis, taking the calculation paper from him.

The calculation paper, which should only have contained Navier’s personal derivation process, unexpectedly had three additional sets of derived equations. Each set of equations was thoughtfully noted with its range of applicability.

The first set, Navier recognized, as it was derived by Cauchy.

The second set, Navier also recognized, as it was derived by Poisson.

But the third set...

Hypotheses:

1. The fluid is isotropic.

2. The normal stress equals the static pressure when the fluid is at rest.

3. The stress is linearly related to the strain rate.

Based on these hypotheses, one can derive the constitutive relationship of fluid stress, and by substituting into the aforementioned fluid motion differential equations, carrying out the following derivation, one can obtain the equations of motion applicable to compressible viscous fluids with variable viscosity...