How many water pumps can fill a single pipe channel without losing efficiency?
I believe the answer is technically just one. My reasoning is based off this Wiki page that states that one pump can fuel 10 Steam engines and 14 boilers. After that, you will start to run low on water (plus, in my time playing this game, I've never seen my water pipes drop below 10 units). But if we are talking about just pipes with nothing drawing on them, then one pump will satisfy filling up the pipes to maximum.
However, I think another thing needs to be considered, and that is the speed of fluids. A pipeline that leads to nothing (no matter it's length) will eventually reach 10 units of water in each segment. But, when you begin to construct long pipe systems, the speed of the fluid decreases, meaning it will take longer for all the pipes to reach 10 units. According to this Factorio forum page, the following speeds occur at:
- 0 pipes - 240 fluid/sec
- 4 pipes - 150 fluid/sec
- 14 pipes - 120 fluid/sec
- 224 pipes - 90 fluid/sec
- 357 pipes - 60 fluid/sec
- 759 pipes - 30 fluid/sec
To counter this, you can use underground pipes, as they count as only one pipe but stretch up to 9 spaces between each end. However, even this will eventually be impacted. The more efficient method would be using a small pump. Smalls pumps, as the Wiki words it, are like the inserters of pipes. They can be used to boost the speed of long pipelines. From the same forum page linked above, the following amount of pumps can be used to boost the speed of the fluids:
- 30 fluid/sec - 1 pump - 759 pipes
- 60 fluid/sec - 2 pumps - 357 pipes
- 90 fluid/sec - 3 pumps - 224 pipes
- 120 fluid/sec - 4 pumps - 14 pipes
- 150 fluid/sec - 5 pumps - 4 pipes
They also have a screenshot showing some efficient ways to set up these pumps:
Um... that answer doesn't exactly apply to this specific question? :)
The Offshore Pump produces... 60 units of water per second." Source: Offshore Pump
As we know, pipes can handle up to 150 units of water per second. Therefore it will take more than just 1 pump to achieve full capacity.
150/60 = 2.5, or 3 minimum pumps to achieve 150 "pressure".
In fact using the "pumping stations" from the other answer literally won't even work if your input isn't as high as your desired output. If you're putting in a single pipe from a single pump into any of those stations, the maximum output will still be 60. Those stations can't "increase" more water than they get in the first place through the single input pipe.
That being said, because the first 30 "pressure" drops off so quickly, it's probably best to just stick to 120 pressure. This will start you off with only 2 offshore pumps and pumping stations far less, if you're needing to transport water so far.
If power is your concern, consider the following:
My reasoning is based off this Wiki page that states that one pump can fuel 10 Steam engines and 14 boilers
1 pump on 1 pipe handles 10 engines, because it pumps 60 units per minute, and the engines consume 6 units a minute. 10 engines consume... 60 units per minute.
You can also use 2 pumps, 28 boilers, and 20 engines, etc. Basically if input/output = 1 then you're good.
(1 pump * 60 pressure = 60) / (10 engines * 6 consumption = 60) = 1
(2 pumps * 60 pressure = 120) / (20 engines * 6 consumption = 120) = 1
If you're going for the 150 it gets a little wonky and not a perfect 1, but oh well.
If you're pumping other liquids you'll likely need storage tanks as your output (since you can't "offshore pump" those liquids), as these "single" sources can actually have up to 3 small pumps draining them, and since smalls only add or "push" 30 "pressure" you'll need 5 in a small distance to achieve 150 pressure, or just 4 if you're fine with the 120 pressure.
Oh, and as a final note to the small pumps, be warned, they have a maximum pumping capacity of 30 pressure. MAX. That means if you put just a single pump anywhere in the length of your pipe you have created a maximum throughput of 30 for the entire length of pipe after that single pump. If you feed that pump 150 pressure it still only puts out 30 pressure. (As depicted in the first "pumping station" in the other answer's image.)