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So I did the rundown on sprinklers kinda the way I did for plows. Although the initial cost of making and expanding a sprinkler system is quite steep, the operating costs are very low, just 0.0666 kero per run:

1÷24+0.025 = 0.0666

The bowl of water costs 0.025 kero to make in a diesel well, and the sprinkler takes 1/24th of a kero to run. To be worthwhile the minimum length a sprinkler system must be to pay off the operating cost is:

(1÷24+0.025)÷0.025=2.666

So for just 10 steel, an engine and a bit of work you can lay the foundation for a future sprinkler system, without worrying about it wasting water on the crops it works. Once it's built it'll never waste water compared to NOT using it. This would serve as a good learning tool for new players to figure out how to operate it, and shape the layout of the farm over time. It'll never pay off the cost of even the sprinkler pipes though:

3 steel = 0.6 kero
Piston blank = 0.04166 kero (water)
2 Rods = 0.08333 kero (water)
2 pipes = 0.0625 kero (water)
Precision piston = 0.03125 kero (water)
Steel valve = 0.03125 kero (water)
Nozzle body = 0.03125 kero (water)

Total: 0.85

This breakdown shows the cost of one sprinkler segment, assuming you get 6 operations out of each "hot" process, and 8 operations out of each "cold" process. The "hot" processes are the piston blanks and rods which require hot steel. These don't stack and are trickier to handle than "cold" processes that just take normal steel. I think 6-8 is a fair allotment, but it doesn't make up much of the cost, as steel takes a bunch of kero.

Each sprinkler segment makes 1 bowl of water per operation, so the break even point is as follows:

0.85÷0.025=34

That's a lot! Sprinklers take generations to pay themselves off, but unlike plows they work for gooseberries and milkweed, so it's a realistic number of runs. That's not counting the cost of operation:

(X*0.85)÷((X-2.666)*0.0025)

simplified:

34X÷(X-2.666)

Here we have arrived at the profit per run for a given length of X. The curve is fairly sharp, flattening out at around lengths of 15 to slowly approach the limit of 34. It's a promising curve until we take into account the cost of the engine:

((X*0.85)+5.17)÷((X-2.666)*0.025)

Now the curve has flattened quite a bit. The dropoff in cost is slow and we'll never get to that limit of 34. That's what we're left with though. There's nothing more to do really besides tweak the cost of the engine or maybe the cost of the pipes by adjusting how many operations you get out of each newcomen firing, or perhaps account for tool use. I think this is good enough though, so I've made a graph:

Some notes:

Basically don't purpose-build an engine for sprinklers unless you really, REALLY have nothing better to do. It might just kill your society. Instead go look for a spare engine from dead towns. If you can find one, hell yeah build it.

Never plant gooseberries on both sides of a sprinkler pipe, as you'll restrict your options for watering if the gooseberries are harvested unevenly, which is inevitable.

Pipe bends to redirect flow are inefficient and should be minimized. Each U-turn takes 4-5 steel, but the first U-turn compresses the length of the farm much more than a second or a third. If the sprinkler pump is on one end of the farm, the U-bend on the opposite and points of interest like the well, roads or buildings are at the midpoint of the sprinkler length then pathing can be minimized without excessive U-bends. Consider extending the opposite end of a sprinkler instead of bending it around, or move the first bend further out before adding a second bend.