Does steam follow path of least pressure?

depends.

i've made a video about how enlarging one main vent dramatically changes steam distribution in early stages of steam production. basically, all things equal, steam takes the path of least resistance. BUT as the boiler keeps on producing steam, the steam starts going anywhere there is an opening.

It's really a lot more complicated, but basically vent size controls how FAST air will be able to leave at a given pressure difference from inside to outside, but not how MUCH air will leave. Then steam inside the pipes leading to the radiator will move at a velocity determined by the pressure difference between one end of the pipe and the other and the condition and other characteristics of the pipe. Then the volume is determined by the velocity and the size of the pipe.

So it won't follow the path of least resistance entirely. What will happen is that the steam will move faster with a greater pressure difference or, to look at it sort of in reverse, the pressure difference will be determined by how fast the steam is moving.

Now the pressure difference between the boiler and the outlet of every vent will be the same (neglecting pressure variations in the house, for simplicity) and so in a sense you could say that the steam will move in the path of least resistance — but as more steam moves in that path, the resistance will build and the steam will also move in any other paths available to it — until the mount of steam moving in each path is just the right amount so that all the pressure differences are equal.

So for your example, @CoachBoilermaker , the radiator with the bigger vent will get more steam, all else being equal, but they will both be getting steam at once.

Now there is a complicating factor here — nothing is ever simple! — which is that once the steam gets t o the radiator it starts to condense. This is not related to the vent size directly — but is related to whether the vent is open or closed. That reduces the pressure in the radiator — and hence increases the flow to that radiator. Once the vent closes, however, the pressure will rise slightly and the flow of steam is governed by how fast the radiator can condense the steam rather than how fast the air can escape.

This (and a few other factors) is why balancing the heat in a one pipe steam system is difficult. The output of the radiator, taken over time, is related to the radiator size (naturally) and the vent size (a given radiator with a larger vent will fill with steam faster than if the vent were slower) but also, and usually quite neglected in the thinking, by how long a given boiler steaming cycle is. As a result, a system which is beautifully balanced at one outside temperature and heat demand may be quite far off at another one.

Which is a nuisance…

Another interesting story about how steam "chooses" which path to take, at the end of this chart.

https://heatinghelp.com/assets/documents/Balancing-Steam-Systems-Using-a-Vent-Capacity-Chart-1.pdf

Steam and air can not mix. they can not take up the same place. Just like oii and water can not mix. Of course you can have oil and water in the same bottle and shake the bottle and make the oil and water gets mixed together. BUT the oil and the water don't actually take up the same space. they coexist near each other, and when you stop shaking the bottle the oil and the water separate and the oil goes to the top and the water goes to the bottom.

Keep that image in your mind's eye while I give you a comparison.

if you have a tank full of oil in the basement (water in the boiler in the basement) and you heat up that oil so it gets about 1700 times larger than the oil used to be. ( and the steam is 1700 times bigger by volume than it was as water) do you thing you might boild up a little pressure? That oil that is lighter than the water is in all the radiators. Now picture that the water leaves the pipes by a valve that is open when water is there but closes when oil gets there. (air leaves the pipes thru the steam vents). That oil will keep pushing the water out of the main vent valve until oil gets there and closes the valve at the end of the main.

Now you have some radiators in the rooms that are still full of water. (NO HEAT YET). So the valve vent on each radiator is open to different amounts and the valve vent that is completely open lets the oil in faster because the water is leaving faster. The oil floats to the top because it is lighter that the water and the water ends up at the bottom of the radiator. Can you see that in your minds eye? The vent valve is still open on all the radiators and the oil pressure is pushing water out of those open vent valves. the fully open valve gets oil first and closes first.

As that oil heats up the radiator it shrinks back to being 1700 times smaller. What happens to the water and oil pressure in the radiator? It just lost 1700 times the volume it used to be. Do you think the pressure might drop a little? (as the steam in the radiator condenses the pressure drops) When the pressure drops, inside that radiator what will fill the void? Maybe the oil pressure from the basement tank and that will send more oil into that radiator. (if the boiler is still steaming then the steam pressure will fill the void.)

High pressure goes to low pressure. That is a basic principle of physics. What happens to the water that is still in the bottom of the radiator? (What happens to the air that is still inside the bottom of the radiator? it just gets stuck there, that is why steam vents on radiators are not at the top you want to get as much air at the bottom out as you can before the vent closes)

Now you have heated oil going into the radiator to replace the cooled off oil and all that oil is lighter that the water so it just goes in and in and in as the oil shrinks from giving off the heat. But the vent valve is close since there is oil at the vent valve. Now that radiator keeps heating as long at the pressure is pushing the oil into the radiator. But there is another radiator with the water valve still open so as the pressure in the radiator filled with hot oil and very little water is heating the room, the other radiator with the water is still letting water out from the pressure entering that radiator.

Can you see the flow in your mind's eye? As long as the steam is making any pressure in all those pipes and radiators, the pressure will still go from higher pressure to lower pressure. The higher pressure is always at the boiler because that is where the water grows 1700 times bigger when it turns to steam. The only time that the steam pressure goes the other way is when the burner stops making steam and all the steam in the system turns into condensate and gets 1700 times smaller and collapses. That will suck air from outside the radiator thru the vent in the radiator to fill that void because the air pressure outside the radiator is higher than the vacuum inside the radiator caused by the collapsing steam getting 1700 times smaller as it cools off and turns into water again.

When the boiler is making steam pressure, even just a few ounces of steam pressure, the steam is always moving from the boiler (higher pressure ) to the radiators (lower pressure from air leaving or steam condensing cause the lower pressure) and as long as the steam in the boiler is making more pressure than the radiators can use up, the steam will always move into the radiators, it will not turn around and move to the supply pipe and go to another radiator.

The steam may move faster and slower as it goes into each radiator but it will always go in the same direction, never the other way.