Thing is, moving water would be something that is used to remove waste. Waste would'nt become a liquid in and of itself. Waste would just be a substance layer, like vomit or blood, which would contaminate/ propagate in water, which ultimately removes it. The alternative is waste just getting piled up to be removed with the cleaning labor or removed by rain/ weather after a bit. The stuff decomposes, after all.
Or turns to soil; or critters eat it; or whatever. What I'm getting out of this discussion is that if it is simplified too much, it's unrealistic and therefore shouldn't be added, but if it's too realistic, it's too complicated worth doing. There's a lot that needs to be added to make Dwarf Fortress more "realistic."
Making an even more elaborate system for modelling waste is an even worse idea. I think this is probably one of those things that can be abstracted a bit, if represented at all.
This is an abstraction. If you want it to be more realistic, Dwarves can have their moods affected by their bowel movements, which is dependent on the quality and type of food they eat, and the quality of the butcher and cook. We could be discussing implementing diseases based on lack of waste management, etc.
When dealing with suggestions such as these, I always ask myself a few things (in no particular order): 1). Can the suggestion operate uniquely? Is there another element within the game that can be used for this suggestion? 2). Will this be forced to change other properties in the game? 3). Can this suggestion make old ideas or new ideas work easier? 4). Does this suggestion enhance gameplay?
Well, let's review the facts: This is an abstraction of life's waste management system, in that it only focuses on that waste is produced and must be managed on a fortress-level. This means that cat's burial practice is ignored, and that texture and consistency and gastro-efficiency of a creature is ignored. Waste is waste, it can be composted and turned into fertilizer.
So, 1). This suggest does operate uniquely, with the exception of crossing into water, which has everyone up in a snag (and in other threads about this, as well). 2). Some people want to argue that better flow properties are demanded for this to work properly. I'd say it's not, but we'll go into that later. Nothing needs to be changed otherwise, other than implementing new labors (composting and prioritization of waste cleaning); dwarves who deal with compost probably won't have to wash their hands with soap, because we aren't interested (yet) with the health risks of handling waste (I'd talk about wounds getting infected, but wounds get infected without soap nearly all the time, so I don't think there's much a reason to discuss it any further); the reason why a player should handle waste is because of miasma, which already has its own mechanics. 3). This suggested mechanic, if done properly, can also deal with other semi-solids: By introducing semi-solid waste, you can also introduce semi-solid soil which can cause people to get stuck. Quicksand and mud, for instance. This also introduces a new fertilizer mechanic, which is great because it adds new elements into the farming system. 4). This suggestion allows for a few things in gameplay that wasn't there before: Specifically, fortress design is going to have to account for waste storage and disposal; it allows for idiotically immature things to happen in Adventure mode (The spinning XXXX hits the Goblin in the head and bruises the muscle!"). So why not?
For the water-problem, here is what I have:
1). Flowing water. A pile in flowing water moves one or two units to the next adjacent tile, to the direction of flow; if the square already has waste in it, it stacks or pushes it down one, until there's only 1/1 per available tile, or until it can no longer flow. It cannot block water, so it just moves aside. Such a mechanic can also be applied to causing light objects to be pushed around by water flow. Contaminate is not cumulative, and it dissipates slowly over time at a rate of the amount per square. Therefore, more waste in a body of water means it takes longer to purify itself with flow. This isn't entirely realistic, as quantity of waste actually impacts duration and severity; for the purposes of gameplay, however, that's not necessary. Once water is contaminated, dwarves won't use it for cleaning wounds or drinking, so there's no reason to track it anymore than that. It should all dissipate evenly so the game doesn't have to track a population of waste and try to figure out which one is the most upstream or downstream. A river filled with 1/5 waste all around cleans out faster than a river with one square at 5/5 caught at the edge of a bend. Flowing water over waste does not produce miasma, but dwarves working near it might have unhappy thoughts.
2). Standing water. Waste dissipates evenly outward from where it stands until it can either move no longer, or each square has 1/5 waste. All water is instantly contaminated until all waste dissipates as above. Waste-saturated water does not produce miasma, but dwarves working near it might have unhappy thoughts.
3). Waste on the ground in rain paths to the next adjacent square; this could be accomplished by just tracking the direction of the next z-level drop, and just moving it to the next square there. Why this? Because it can also be used for mudflows. Be !!FUN!! to have a whole hill with trees and all move that way over your fort, forcing you to clean everything out or build around it. This might produce miasma, but outside, miasma doesn't do anything.
This sort, though, shouldn't have more mechanics that what I've just described: Waste produces miasma, therefore it's important to deal with miasma. Standing water diffuses waste, flowing water pushes it downstream. It goes away on a set period of time (at the end of the season if it's in the first half of the season, or if it's in the second half of the season, to the end of the next season? Something like that). Flow mechanics of semi-solids, which is just simple one-square at a time pathing, could be used for sand or mud. The raws that define semi-solid waste can also be used for semi-solid substances, which are too granular or too moist to be considered true solids.
By handling waste as an "activity" that a dwarf has to perform, like period cleaning or trimming of hairs, eating, sleeping, whatever, you add in another layer of daily dwarven life. You can leave it in the halls and have your peasants clean it up, or you can build elaborate dwarvenly sewer systems to wash it away and keep miasma from forming. The flow of semi-solids might not be a hindrance on FPS, as it the calculation cycles don't have be done every frame (instead one could calculate the flow of semisolids piecemeal and draw it piecemeal).
Either way, this level of abstraction is perfect for such a system and it doesn't get into too much of the ridiculous or the vulgar.