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Fluid Dynamics, Consistency, and the Question of Accuracy (Calc Group Only)

Mr. Bambu

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As the title says, comments should be restricted to staff and calc group with relevant things to say and relevant opinions to express.

Recently, I came across a calculation here with an interesting, albeit mildly heated, discussion in the comments. The gist of it boils down to whether we should take accurate fluid dynamics in relevant calcs over on-screen behavior of fluids in feats. The comparison used to argue the former (that is, go against on-screen behavior) struck me as being particularly in-line with our current philosophy regarding feats- the calculator, Flashlight, compared it to our standards on Kinetic Energy, which as all of you ought to know is that we will discard the KE of an object if it does not align with the apparent effects caused.

This is a very similar scenario, where the on-screen presentation of the feat renders the KE much, much higher than the actual effects it causes, to an immense degree (7-B KE vs 8-B+ for the original calc).

So, the question I pose to the other CGMs (who are more knowledgeable than I, surely) is whether we apply the same philosophy we apply to standard KE, to fluid dynamics, and then whether we ought to use the calculation method used by Flashlight in the linked blog. If there is an alternative, or even an established method, then that should be made known.

That's about it.
 
If there wasn't a visual to go off of and we only had values, I think the formula is fine to use. But if you have a visual of the feat itself, it can't just be ignored because that would be a dishonest move if it was ignored.

In the case as to why I found the calc wrong, the speed Flashlight got suggested that the water rose to max height in 6 seconds, but the actual animation shows that it happened in an eighth of a second, to which the water would then abruptly stop and fall at normal gravity speed. There is no damage the splash is causing with its KE when it's rising up because it's not even hitting anything (It only "hits" something by the time it loses a majority of its speed and falls back down at normal gravity speed to which the KE when falling down is much less then when it rose up), hence I found it to not violate KE rules. As for the inconsistent speed of the splash, this verse in context is a cartoon with mild-toon force, so it's not like the animators who made the scene were taking into account real life physics when they made that scene.
 
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Thank you. I felt a more proper discussion on the use of fluid dynamics would best work things out. I have only ever dealt with fluid dynamics one other time and it involves displacement: https://vsbattles.fandom.com/wiki/User_blog:Flashlight237/Splitting_the_Red_Sea_Calc

Aside from that, I have no memory of coming across any fluid dynamics feats. This is coming from a guy who has been around for over half a decade on this site.

Prior to having made the calc in question, I have sought out advice from SpaceBattles in regards to calculating splashes given they will readily help with any calculations needs possible. Admittedly neither party in the heated debate had a good grasp on the concepts of fluid dynamics prior to my decision to seek out guidance. I had made one other attempt to calc the same exact feat long before, but that just used simple conversion of momentum rather than any understanding of fluid dynamics, let alone a proper understanding of fluid dynamics.

In reading the Stack exchange article, the OP used conservation of momentum; however, a commenter noted that it wasn't the proper way to handle splashes, instead explaining the splash phenomenon (which is called the Worthington Jet) and provided some formulae for calculating the Froude Number, the Weber Number (which is more relevant to our handling of feats as the kinetic energy of the object impacting the water is used in another way of calculating the Weber Number of a splash), and the maximum velocity and height of the Worthington Jet itself (which oddly enough doesn't seem different from kinematics).

Admittedly this is my first time seeing a proper discussion on the matter of fluid dynamics due to the rarity of its involvement in calculations. I feel the formulae used would help users, staff, and Calc Groupers alike when it comes to fluid dynamics as a whole as opposed to just figuring out how to handle one silly island sinking calc.

My side of the debate concerns the nature of splashes and how, most accurately, they should be treated as what they are: water rebounding in response to a force hitting it. Things like friction and inertia (in this case, most likely inertia) serve as indicators as to how things resist motion. Friction is the force resisting the relative movement of moving objects. Inertia, on the other hand, is more relevant to splashes. Inertia involves the natural tendency for objects in motion to stay in motion and for objects at rest to stay at rest unless another force acts upon them. Think of a bouncy ball. A bouncy ball, when dropped, will bounce, but even the first bounce will be weaker because the ball loses energy. The same logic can be applied to water responding to an object impacting it. As the water takes in an object's kinetic energy, it will inevitably rebound and spout upwards in a Worthington Jet. Said jet will, inevitably, have lower energy than the object impacting the water thanks to inertia.

While cartoons may bend certain rules (even though from what I've seen from the show as a Total Drama veteran, the characters usually aren't willing to do so), quite frankly so would any other fictional media like movies, tv shows, comic books and video games. Calculations, at their core, intend to mathematically explain how powerful certain feats, no matter how wack they are, would be using real world scientific and mathematical concepts. The thing about math is math tends to be objective rather than subjective like our interpretations of feats. Antvasima makes it very clear to each Calc Grouper (myself included) that we should uphold standards of accuracy. While I can understand how using basic methods like kinetic energy can be convenient to many people, ultimately formulae that fits the topic in question (in this case, the use of fluid dynamics formulae for splashes) will provide the most accurate results for the feats we intend to calculate. Likewise if we use the methods that are convenient to us (which is how we got a 4000 m/s splash that car-crashed 650 meters in the air after a tenth of a second and lingered for whole seconds), it may lead to some very skeptical results that, like I said, people more mindful of how our rules work would find suspicious. That's something we silly math men must understand as the Calc Group, I guarantee it.

Long story short, I hope my methods of calculating a silly splash and my decision to stand firm with those methods will help people understand and work with fluid dynamics better in the long run.
 
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If there wasn't a visual to go off of and we only had values, I think the formula is fine to use. But if you have a visual of the feat itself, it can't just be ignored because that would be a dishonest move if it was ignored.

In the case as to why I found the calc wrong, the speed Flashlight got suggested that the water rose to max height in 6 seconds, but the actual animation shows that it happened in an eighth of a second, to which the water would then abruptly stop and fall at normal gravity speed. There is no damage the splash is causing with its KE when it's rising up because it's not even hitting anything (It only "hits" something by the time it loses a majority of its speed and falls back down at normal gravity speed to which the KE when falling down is much less then when it rose up), hence I found it to not violate KE rules. As for the inconsistent speed of the splash, this verse in context is a cartoon with mild-toon force, so it's not like the animators who made the scene were taking into account real life physics when they made that scene.
To give credit, while I agree with the logic applied by Flashlight (in that this is similar enough to our KE standards as to render it an identical scenario, thus deserving of an identical response, i.e., that the effects of the feat should be taken over the KE), this is a relatively unique scenario (I couldn't name another one) and I don't think you're strictly wrong to evaluate the feat in the way that you did.

I'm not particularly knowledgeable on fluid dynamics, or much of anything really, but I felt it ought to be said. Your evaluation is strictly correct for the standards as they are currently. With that acknowledged, is it your opinion that the standards ought to remain in this way, that Flashlight's contentions ought not be introduced into the standards? I won't question that further, I just want a bit of clarification.
 
Is it in this case that the result is less than when using on-screen speed? 'cause there are lots of reasons for the splash to end up less high than the formula would predict, so that the calc may undershoot the value.
On the other hand, maybe the holes in the island could increase the splash...

Anyway, in general, I wouldn't use fluid dynamics in too extreme instances. Things quickly become ridiculous and enters areas where the regular formulas should not apply. IIRC shooting something a hundred meters in some fraction of a second underwater yields relativistic projectiles or something...
On more reasonable scales it should be fine, though, especially if there are no alternative methods.
 
Is it in this case that the result is less than when using on-screen speed? 'cause there are lots of reasons for the splash to end up less high than the formula would predict, so that the calc may undershoot the value.
On the other hand, maybe the holes in the island could increase the splash...

Anyway, in general, I wouldn't use fluid dynamics in too extreme instances. Things quickly become ridiculous and enters areas where the regular formulas should not apply. IIRC shooting something a hundred meters in some fraction of a second underwater yields relativistic projectiles or something...
On more reasonable scales it should be fine, though, especially if there are no alternative methods.
No, the opposite; using fluid dynamics yields a much lower result than using the on-screen displayed speed. Theoretically, this clause would have the same function as the Kinetic Energy clause, wherein if the fluid dynamic calculation returned a lower result than the KE, then the KE would be invalidated, but the inverse would not be true- if the KE were the lower result, then it would not invalidate the fluid dynamic calc.
 
No, the opposite; using fluid dynamics yields a much lower result than using the on-screen displayed speed.
Yeah, that's what I meant in my first sentence.
Theoretically, this clause would have the same function as the Kinetic Energy clause, wherein if the fluid dynamic calculation returned a lower result than the KE, then the KE would be invalidated, but the inverse would not be true- if the KE were the lower result, then it would not invalidate the fluid dynamic calc.
The thing is, a splash like this kinda depends on the waves hitting together in a particular way. With a sinking island there probably is a lot more chaotic current going on than for a ball, not "concentrating" forces quite as well.
In reality, if we did it as an experiment, it wouldn't surprise me at all if the splash is smaller than the formula would predict for the sinking speed.
 
Well, no. The result is higher using on-screen speed, in this instance. If you meant that, I guess that's fine, but you did type the opposite.
 
Is it in this case that the result is less than when using on-screen speed? 'cause there are lots of reasons for the splash to end up less high than the formula would predict, so that the calc may undershoot the value.
On the other hand, maybe the holes in the island could increase the splash...

Anyway, in general, I wouldn't use fluid dynamics in too extreme instances. Things quickly become ridiculous and enters areas where the regular formulas should not apply. IIRC shooting something a hundred meters in some fraction of a second underwater yields relativistic projectiles or something...
On more reasonable scales it should be fine, though, especially if there are no alternative methods.
Okay, so I think I may explain things better.

A splash isn't exactly as one-and-done as you're making it out to be. Ideally with any splash, the resulting KE should be lower than the KE of the thing going into the water regardless of its size, shape, or coat of paint (apparently even that would cause different splashes). This is because some of the energy will get lost in the water itself when something is going into it (again, bouncy balls, inertia and stuff). In this case, the island's KE, based on it's own on-screen speed and theoretical mass, is 159 megatons of TNT (it would be lower because of the holes, but the holes are so small compared to the island that I don't think accounting for them really changes anything).

When you compare it to the calculated results of the splashes, the calculations I've done using fluid dynamics, you can see that the results line up with the island's KE, with the high end being 83 megatons, slightly more than half of the island's own KE. This lines up with both fluid dynamics and our own KE rules. (Before you point the Owen thing out, that's a whole mess of inconsistencies I don't want to get to just because the characters appear to be drawn 50 feet tall relative to the cliff's size)

When you look on the other end of the spectrum, things get really messy. Like, most egregiously, how do you get 1 teraton off a 159-megaton sinking island? That doesn't line up with our KE rules where basically, the KE needs to line up with what you expect to happen. At that point, we may as well expect even the largest lake in the Muskoka Region to be wiped off the map. We rejected a Tier 7 Lazytown calc (bear in mind that it's more liberal with the toonforce even though it's live action) because the apple didn't so much as even produce a Tier 10 result, never mind Tier 7. I feel the same scrutiny should apply to things entire SI prefixes higher than what you expect as they already do with things entire SI prefixes lower than what you expect.

And also, let's be real, I don't think the Worthington Jet's on-screen speed should really be considered a reliable metric when that speed only existed for the initial four frames before becoming effectively zero on the fifth frame (unlike the island whose on-screen speed is maintained the entire time it sank into the water). Note that the splash lasts three seconds from the initial burst until the last bits of water fall back into Earth and was even preceded by a smaller water spout.

Lastly, in response to the waves thing...
9gmg2h.jpg


I mean the diagram provided by the guy explaining the concepts of fluid dynamics in the StackExchange thread pointed that out as part of his logic (where the formulae came in).

In other words, the most accurate results to come from a splash would be reasonably lower than the impactor's KE. I think I reflected that fairly decently.
 
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I've only had time so far to skim through things, but the argument of:
  • P1: Splashes have less energy than the object creating the splash, in most situations.
  • P2: The object creating the splash had a KE of 159 megatons.
  • C: Therefore, a calculation of the splash should be less than 159 megatons.
Seems pretty solid to me. A more in-depth calc lining up with that makes me more willing to take it seriously.

That plus the claim of the water's high-speed being derived from a few frames, before it slowed down substantially, makes me a lot more sympathetic to dismissing this.
 
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