Q:

How large could my sea serpents be?

EDIT: (Important) M. A. Golding commented that the regalecid method of locomotion would be unfit for a constricting predator, so I have completely redone the taxonomy of the sea serpent. They are now eels, closely related to moray eels. The sea serpent taxon has been upgraded to family Serpentimaridae, as opposed to the old subfamily Serpentimaria. I don't have time to draw up a dendogram right now, but they're in the suborder Muraenoidei, in a clade with moray eels.
I think that the current lack of answers is because I have not alluded much information as to the physiology of these animals. Here is a rough sketch I made in Paint (Originally a preparatory draft for a real illustration of sea serpent anatomy):

Note: the reproductive and excretory systems are not shown here, but do not affect their potential size anyway so it shouldn't matter.
So, if the heart needs enlarging, or I should have a bundle of ganglia towards the back as an extension of the CNS, or any other amendment, please let me know. Hopefully, I'll get some answers now that I have clarified a bit more. 

This is currently the sixth question about my ongoing worldbuilding project on viable fantasy creatures. I'm too lazy to link all of them here, but the last two were: What kind of animals are my trolls? and How can I explain the evolution of my giants?. You can find links for the rest at the latter.
Now, from giants and trolls we progress to the largest creature in my project, the sea serpent (Subfamily Serpentimaridae). These beasts are not serpents but fish, in the suborder Muraenoidei. 
I want these serpents to be massive, at least the length of a blue whale - and upwards from there. Seriously, if the answer is "600 metres", then I'll take that. But, I rather doubt that a fish could grow to a length of 600 metres (Feel free to prove me wrong), so I'll have to find out what's rational and what's not.
Sea serpents are constricting predators, like boas, and use their musculature to crush whales - and, on occasion - ships. They also have pharyngeal jaws, like their close relatives the muraenids, which allow them to swallow a rowboat whole.
I haven't figured out what oceanic zone they'll inhabit, but any is fine for me really. Deeper zones would be convenient as an explanation for why they've remained undiscovered, except for reports by sailors throughout history. They need to be large enough to be able to create waves with lashes of their tail, as well.
To summarise: How big could Muraenoideian sea serpents be?

A:

To answer your question, consider how thick would be the body of the largest animal you intend your sea serpent to prey on by constriction.  
If, for example, the prey has a thickness of 1 foot and is perfectly cylindrical, it will have a circumference of 3.14 feet.  If the sea serpent wraps around the victim three times and has length left over, it must more than 9.4 feet long.  And the giant snakes known to science would usually be 10 to 20 feet long if they attacked prey a foot thick.
If, for example, the prey has a thickness of 10 feet and is perfectly cylindrical, it will have a circumference of 31.4 feet.  If the sea serpent wraps around the victim three times and has length left over, it must more than 94 feet long. It could easily be 150 to 200 feet long accounting for the extra neck and tail lengths.
I point out that the longest prehistoric or contemporary animals known to science had or have lengths in the region of 100 to 200 feet.  And some scientists find such lengths amazing because of various factors including the time it takes for signals to travel the length of the body along nerves which sometimes are single immensely long cells.  Some scientists would claim the longest animal proven to have existed must have been the longest animal possible, while others would say that longer animals might be possible.
https://biology.stackexchange.com/questions/44788/has-the-human-body-the-greatest-total-length-of-nerves-of-all-animals1
How thick can the body of the constrictor be if it is capable of bending enough to constrict around the body of the prey?  Depending on the flexibility of the constrictor, what is the maximum possible relative thickness of the constrictor's body compared to the prey's body?
If a sea serpent is flexible enough to constrict a victim with a diameter of 10 feet, will the sea serpent be flexible enough to constrict prey with diameters of 5 feet or 1 foot, or will those smaller animals simply escape out of the oversized loops of the constrictor because it can't constrict tightly enough?
It seems to me that a growing sea constrictor will only be able to constrict animals within a certain range of body thicknesses.  It will be unable to constrict thinner or thicker animals.
Once you have decided upon the body thickness necessary for your constrictor to constrict prey within the desired thickness range, you must then decide how your constrictor is proportioned.  The length of your constrictor would range from X  times its thickness to X plus Y times its thickness.
And what would be plausible relative proportions for your sea constrictor?  You can study the proportions of various snakes that constrict.  You could make your sea constrictor proportioned between the stubbiest snake that constricts and the most elongated snake that constricts.  Or you can make a more generalized study of the relative proportions of all the long, narrow creatures in the world.
Or, if you decide that your sea constrictor should have a certain width, you can calculate what its body mass would be at various lengths.  If it is carnivorous it shouldn't be much more massive than the largest known present day or prehistoric sea carnivores or it probably won't be able to feed itself.
Or, you can decide what is the largest mass sea creature it can swallow whole.  Since it will probably usually eat several smaller sea creatures for a meal instead of only one of the largest it can eat, you might decide that the largest creature it can swallow whole is as large as the largest meal it needs, and then decide what body mass a creature would need for that amount of flesh to make a meal.
I think that a combination of those methods should enable you to decide what size your sea constrictors usually are, though of course there could be freak exceptionally small (boring) or large (terrifying) specimens.
I can't help thinking that even the smallest monster you might decide upon would be horrifyingly large. 

