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I'm no engineer, but I was wondering how a steam-powered door would work. I want it to be difficult to open unless you know how (not a simple "twist the doorknob and open"). There is access to plenty of water and fire in this scenario as well.

Hero of Alexandria (c. 10 CE – c. 70 CE) was a Greek mathematician and engineer who was active in the 1st century CE in his native city of Alexandria, Roman Egypt.

He wrote several books describing very advanced machines, including a fully automated theater play performed by marionettes actuated "by a binary-like system of ropes, knots, and simple machines operated by a rotating cylindrical cogwheel" (Wikipedia).

More inline with the question, he described an engine which "used air from a closed chamber heated by an altar fire to displace water from a sealed vessel; the water was collected and its weight, pulling on a rope, opened temple doors". (Wikipedia)

The construction of the machine is described in his book, Pneumatica, section 37.

The construction of a small temple such that, on lighting a fire, the doors shall open spontaneously, and shut again when the fire is extinguished. Let the proposed temple stand on a pedestal, A B C D, on which lies a small altar, E D.

Through the altar insert a tube, F G, of which the mouth F is within the altar and the the mouth G is contained in a globe, H, reaching nearly to its centre: the tube must be soldered into the globe, in which a bent siphon, K L M, is placed. Let the hinges of the doors be extended downwards and turn freely on pivots in the base A B C D; and from the hinges let two chains, running into one, be attached, by means of a pulley, to a hollow vessel, N X, which is suspended; while other chains, wound upon the hinges in an opposite direction to the former, and running into one, are attached, by means of a pulley, to a leaden weight, on the descent of which the doors will be shut. Let the outer leg of the siphon K L M lead into the suspended vessel; and through a hole, P, which must be carefully closed afterwards, pour water into the globe enough to fill one half of it.

It will be found that, when the fire has grown hot, the air in the altar becoming heated expands into a larger space; and, passing through the tube F G into the globe, it will drive out the liquid contained there through the siphon K L M into the suspended vessel, which, descending with its weight, will tighten the chains and open the doors. Again, when the fire is extinguished, the rarefied air will escape through the pores in the side of the globe, and the bent siphon, (the extremity of which will be immersed in the water in the suspended vessel) will draw up the liquid in the vessel in order to fill up the void left by the particles removed.

When the vessel is lightened the weight suspended will preponderate and shut the doors.

Some in place of water use quicksilver, as it is heavier than water and is easily disunited by fire.

(Hero of Alexandria, Pneumatica, 37, translation by Bennet Woodcroft, London, 1851.)

Left, a 17th century German portrait of Hero of Alexandria. Right, a diagram illustrating Hero's pneumatic temple doors, as depicted in the 1851 English translation by Bennet Woodcroft.

Well, if you want a puzzle or lock of some kind, then do that yourself, but the basic action of opening a door is still "Push/Pull/Activate (Input Device).

Steam is pretty good at pressurizing, but as with all gases, it will want to expand before pressure starts to rise above normal. If you make it a bit longer than it needs to be to fill the doorway, you can fit a hollow space in the bottom. Place that over a chamber with valves to your boiler. When the steam is released into the chamber, it will push up the door with an action that might look similar to a trombone slide. When it's at the top, it can be locked and held in place. Lowering can be as simple as pulling a lever to release the lock.

Forget postulation; there's a real example of a steam-powered levering mechanism (in this case a bridge deck, but no reason why it couldn't be a door) within Tower Bridge in London.

London's Tower bridge is a Victorian steam-powered* bascule bridge; the bridge deck is moved (rocked/"basculed") using a cantilever and hydraulics system. The hydraulics system is powered using massive steam-operated driving engines, which drive the pumps which move the river water into accumulators (storage reservoirs). With the aid of the weight of the cantilever, the weight of the bridge deck is overcome and the deck is raised. The mechanism is so well balanced/engineered that it only takes a minute for the process to complete from the moment the operator engages the pump.

https://www.towerbridge.org.uk/Visit-Engine-Rooms/

https://www.towerbridge.org.uk/bridge-history/ (See How It Works)

Applying this to your original question, there's no reason why you couldn't do the same thing. In the case of Tower Bridge, the moving part is overcoming gravity. With a door, moving laterally of course, the force direction may be translated using a pulley. A steam pump puts some water into an accumulator, the accumulator drops, pulling the rope or chain on the pulley, the rope/chain on the other end is attached to the door which could, if you so wished, weigh tonnes.

In order for the door to return to its original position, an additional pump isn't required; a static weight (similar in operation to Tower Bridge's deck) may be chained taking the door in the opposite direction; the accumulator's contents are discharged in order to have the process reversed.

Note that the mechanism itself may be placed a distance away (owing to the pulleys), possibly underneath the door itself, hidden from view. The driving mechanism also has the potential to be armoured (such as behind a stone wall or floor) in the scenario that it's a defensive feature; much the same way that drawbridge/portcullis mechanisms were hidden in castles.

Regarding your "difficult to open" requirement: with this approach it's down to your imagination. Could be twist to open, could be a hidden lever; a book or statue that requires to be pulled. You could even have tap dancing on a sequence of floor tiles, operating effectively as a combination lock**. Anything that could be used effectively as a switch to fire up the steam engine hidden in the neighbouring room.

*strictly speaking the bridge has been electric-powered since 1976, however it was originally steam-powered.

**"In the Latin alphabet, Jehovah begins with an I!"

If you've ever seen the control panel of a steam locomotive, it certainly meets your criteria of 'difficult to {operate} unless you know how':

The ridiculous number of valves fundamentally does quite a simple job - regulates the flow of steam into a cylinder, where the pressure drives a piston. Many of the controls exist to prevent the boiler pressure exceeding safe limits.

Your simplest option, therefore, is to have an extremely heavy slider door, not unlike a blast door, which is opened and closed with a simple steam piston acting against the foundations of the building. The boiler must be fired up and brought up to pressure, then the steam can transfer energy to the piston to slide the door open. Difficulty to open can be achieved by not labelling any of the valves (which is evil in its own right!) and relying on some esoteric instructions, shapes, or mystic riddles to inform the protagonist(s) which are the correct valves to operate to cause the door to open (and should they get it wrong, a catastrophic boiler explosion is a good possibility). And because the door is incredibly heavy (just like the hundreds of tonnes of iron that form a locomotive), moving the door with anything less than its own power is impractical.

You could even store most of the moving parts on the other side of the door, leaving only the furnace and valves accessible (although do note that the moving parts have a huge appetite for oil, so in practical terms keeping these on the other side might mean the door seizes shut through lack of lubricant over time.