But what if... Wailord *wasn't* impossible?
Mia Smith Density is a relative concept when it comes to sealife - if it's less dense than water, it floats. If it's more dense, it sinks. The same logic applies to all fluids, like oil and air (yes, air is a fluid). Wailord's density, which we can get by dividing its mass of 398 kg by its volume of 188.6 meters cubed, is then 2.11 kg/m3. But why does this matter? Well, here's some comparative densities you might find interesting:
Air: 1.225 kg/m3*
Pure water: 1,000 kg/m3
Seawater: 1,024 kg/m3
Blue whale: 827.1207 kg/m3
(*At atmospheric pressure and standard temperature.)
This means that Wailord is just under twice as dense as air, but several hundred times less dense than water. And, well... Wailord's a whale. They kind of need to dive, or at least partially submerge, in order to eat food. But with this density, Wailord is far too buoyant to even submerge itself a little bit, much less...
"dive close to 10,000 feet beneath the waves." (Emerald Pokedex entry)
The blue whale, Wailord's IRL basis, provides a great example of why this matters. The average fully-grown blue whale weighs about 290,000 - 330,000 pounds, or 131,500 - 150,000 kg, and has a volume of about 157 to 183 meters cubed, giving an average density as listed above. When such a blue whale wants to submerge and hunt for food, it must fight against its own buoyant force to do so. The buoyant force F(b) of an object in a fluid is given by:
F(b) = pgV
Where p is the density of the fluid the object is submerged in, g is the gravitational acceleration at the surface, and V is the volume of the object doing the displacing. Plugging in the values above for the density of seawater and the larger volume of the blue whale, as well as a gravitational acceleration of 9.81 meters per second squared, we get a buoyancy force for the larger blue whales of about 1,840,000 Newtons. That seems like a lot! However, anyone who's taken a physics class will quickly realize that this upward force is counteracted by the object's weight, which exerts a force of its own pointing in the exact opposite direction. For the larger blue whale, this is about 1,471,500 Newtons, meaning the overall force on the whale is about 368,500 Newtons in the upward direction - much more tolerable! (A note - while 368,500 Newtons may seem large to us, being enough force to snap most anything that isn't a high-strength ceramic, it's being distributed over such a wide area that the blue whale wouldn't be feeling much.)
Now let's compare the same setup when we substitute in a Wailord for our blue whale. The buoyant force is roughly the same, at 1,894,570 Newtons, but the counteracting force of Wailord's weight is only 3,904.38 Newtons, meaning the net force is now about 1,890,662 Newtons in the upward direction. This means that Wailord has to work more than 5 times as hard as the average blue whale to make any progress when diving. In other words,
According to all known laws of hydrodynamics, there is no way a Wailord should be able to dive. Its fins are too small to get its fat, balloonish body below the waves. The Wailord, of course, dives anyway, because Wailord don’t care what humans think is impossible.
That doesn't sound like a lot, but it adds up pretty quickly when it comes to muscle expenditure - keep in mind that oxygen is vital to the action of muscles, even those of a whale, and diving necessarily means a limited supply of the stuff. Thus, it's best to use as little muscle power as possible to move around in the water, which is why many aquatic creatures have developed gas bladders to achieve neutral buoyancy and thus not have to expend any calories just on diving. While we could just handwave and say that Wailord having four fins instead of two offsets this, I'd much rather explore alternatives.
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The first alternative is that Wailord's weight refers mostly to its actual, physical body, and discounts any air inside. We can actually find out what Wailord's 'true' weight would be by using the rule of mixtures and assuming that its physical body has the same average density as that of a blue whale:
398 kg / 827.1207 kg/m3 = 0.4812 m3 (volume of Wailord that isn't air)
188.6 m3 - 0.4812 m3 = 188.1 m3 (volume of Wailord that is air)
X kg = (0.4812 m3 * 827.1207 kg/m3) + (188.1 m3 * 1.225 kg/m3) = 398 kg + 230.46 kg = 628.46 kg
As you can see, this hardly makes things any better, being less than double what we started with. So that's not it.
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The second alternative is that Wailord simply exhales most of its air in order to dive. Assuming that Wailord’s ‘average’ animal substance is once again the same density as a blue whale, it would lose 99.9% of its volume and 58% of its mass, obtaining a new buoyancy force of just over 1,983 Newtons – much, much better! It turns out reducing the volume by three orders of magnitude really helps when trying to become dense enough to almost sink. Compare this to Wailord’s 3,904.38 Newtons of weight, and it turns out Wailord is actually capable of achieving neutral buoyancy – when weighed, for some reason, it chose not to. From this, we can actually estimate what percentage of total air capacity Wailord must be at to achieve neutral buoyancy. At 3,904.38 Newtons of weight to be displaced by buoyant force, Wailord would then need to have 0.398 m3 of volume to achieve neutral buoyancy, or about 0.104% of its total air capacity. Well, that's... not great, considering Wailord needs that air in order to, you know, breathe, assuming its air bladder is the same as its lungs as is typical for most whales. Plus, it'd look kind of deflated and sad every time it needed to dive.
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The third alternative is that Wailord replaces that air with water in order to dive. This makes Wailord a ternary system of animal components, air, and water, and we can calculate how much of each is required to achieve neutral buoyancy using a modified form of the same equation. (Note - I've simplified Wailord's buoyant force back to a mass of 193126.402 kilograms to fit the equation - because gravitational acceleration is a constant in this equation, this ends up not mattering.)
193126.402 kg = (0.4812 m3 * 827.1207 kg/m3) + ((188.1-X) m3 * 1.225 kg/m3) + (X m3 * 1024 kg/m3)
Solving for X, we find that it's equal to 188.2 m3. Wait a second, wouldn't that mean that there's negative air present? Yes, it would!
(398 kg + (-0.099419775 kg) + 192728.064 kg) = 193125.965 kg (I'm assuming there's a rounded number in there somewhere, so it comes out slightly different.)
Okay, so maybe it replaces all of its air with water? This would first require that the 398 kg once again be split up into air and animal components, since otherwise Wailord would have been weighed with nothing in there and nature abhors a vacuum (even if the Pokemon franchise usually doesn't):
398 kg = (X m3 * 827.1207 kg/m3) + ((188.6-X) m3 * 1.225)
Solving for X, we find that it's 0.202146 m3. This means that out of Wailord's 398-kilogram weight, about 167.2 kg of it is animal stuff (fat, bones, organs, etc.), while the remaining 230.8 kg is air. This air comprises about 99.89% of Wailord's volume, at 188.408882 m3. We can then plug these values into a modified version of the previous equation to find how much water Wailord would need to be neutrally buoyant:
(0.202146 m3 * 827.1207 kg/m3) + (188.408882 m3 * 1024 kg/m3) = 193097.894 kg
This makes sense, as even if Wailord does replace all of its air with water, it's still not quite enough to achieve neutral buoyancy - it is, however, enough to make it comparable to a blue whale in terms of overall buoyant force. And before you go about saying it's ridiculous for Wailord to fill itself with water instead of air when it needs to breathe, its pre-evolution Wailmer has this to say:
"Wailmer's nostrils are located above its eyes. This playful Pokémon loves to startle people by forcefully snorting out seawater it stores inside its body out of its nostrils." (Ruby Pokedex entry)
"Wailmer can store water inside its body to transform itself into a ball for bouncing on the ground. By filling itself up with more water, this Pokémon can elevate the height of its bounces." (Sapphire Pokedex entry)
So this third alternative is clearly the best - it mathematically works, fits with Pokedex lore for Wailord's pre-evolution, and even allows Wailord to control its own buoyancy while on the surface. This is sort of the inverse of most fish, which are heavier than water and thus have a gas bladder to get back up to neutral buoyancy, but it's a functional alternative for something with a pair of lungs.
Speaking of lungs, Wailord's would have to be relegated to elsewhere in the body. Assuming they're part of its 'animal' component (really the only place to put them, when you think about it), they could store up to 0.202146 m3 and probably realistically somewhere around 0.1 m3 at a maximum. For comparison, the average blue whale has a lung capacity of about 5 m3 and can hold its breath for up to 10-20 minutes. However, a Wailord that's filled with water would exert about 0.0759% of the force a blue whale occupying the same volume would need to in order to dive, meaning that proportionally Wailord would need far less oxygen to achieve the same dive time - just 0.00379 m3 would do, assuming proportional metabolic efficiencies. Given the in-game size of Wailord's mouth, they're probably on the larger side, allowing it to dive even deeper... according to the Pokedex, far deeper.
The average blue whale takes about 5 minutes to dive down or return to the surface from a depth of 100 meters (their typical feeding depth). This gives an average diving speed of about 0.333 meters per second. To get to 10,000 feet (3,000 meters) at this same speed, Wailord would then spend 9,000 seconds (or about 2.5 hours) for a total dive time of about 5 hours. Note that they could probably go much faster due to their greatly reduced workload when diving, but we'll use this speed for calculation purposes. We can find the minimum required lung capacity for a blue whale to do this from the following equation:
5 m3/(15 minutes * 60 seconds/minute) = X m3/(5 hours * 60 minutes/hour * 60 seconds/minute)
For a IRL blue whale, a lung capacity of 100 m3 would be required for this trip - 20 times as much as their typical set of lungs. However, we can then plug in Wailord's buoyant efficiency ratio of 0.222% from above to find out how much lung capacity it would need instead. This is found to be 0.0759 m3 - my guess of 0.1 was almost right on the money! Note that some other animals can also dive to 3,000 meters or close, most notably the Cuvier's beaked whale (2,992 m) and the sperm whale (2,250 m).
TL;DR:
-Wailord's listed weight is actually somewhat misleading, as it was measured at the surface and not while Wailord is diving. When diving, Wailord weighs even more than a typical blue whale!
-Wailord, unlike most fish or whales, intakes water to achieve neutral buoyancy - its sheer size allows it to easily swim around upon doing so.
-Wailord diving 10,000 feet is actually realistic, both in comparison to other whales and in how much oxygen it would metabolically need to accomplish this compared to a 'normal' blue whale.
-Wailord can use Hydro Pump without violating the laws of physics? At least once, that is...
