During the invention of steam engine the mayor decided to make his town popular and lively again by announcing he is going to stick a flag at the deepest and wettest place on Earth, the challenger deep. As a result many visitors, reporters, engineers and investors flew in from across the globe to witness the astonishing event, as deadline is months away and only amassed 0.001 ton of pure gold bullion how can the best minds in the world construct a working manned submersible powered by steam engine only to conquer the lowest point on Earth? Quickly the pressure is surmounting... and how to prove it?
One main problem for a steam powered submarine that goes to great depths is that steam power requires an excess of oxygen to combust. Compressed air systems were being developed as cutting edge technology at the time, but only marginally improved the situation.
Until practical electric batteries and motors were developed in the early 1900s, with one exception, submarines could travel just a few dozen feet under the surface and had to be powered by hand (basically glorified rowing) because they couldn't burn fuel in the boilers to keep the ship operating, or had to rely upon a snorkle above sea level and were basically just surface ships with most of their draft underwater.
The other major problem was that now one had built a submarine strong enough to withstand sea pressures greater than those found at 500 meters depth in that time period.
Some of the notable historical developments along this line are discussed below followed by an alternative approach that would be more plausible. But, a hybrid of some of these technologies adapted to have some of the dispensible ideas (e.g. electric lighting) that were only developed later removed, makes the concept at least imaginable and possible.
A Steam Powered Near Submersible: The USS Monitor
The USS Monitor (shown above as it appeared at sea) was a steam powered warship used that entered service in 1861 and was used during the U.S. Civil War that operated on steam with air from a snorkle and was mostly but not entirely submerged.
The First Steam Powered Submarine
The first steam powered submarine ever built, the Ictíneo II, a reconstruction of which is shown above, (based upon an 1859 predecessor) was launched in 1867 and operated for about twenty dives over two years. It was made possible by the world's first air independent propulsion system, a feat not repeatd for another 70 years or so in the 1940s. It had a theoretical maximum depth of 500 meters but was never actually operated deeper than 50 meters, and could stay submerged for up to eight hours in theory.
Ictíneo (derived from the Greek words for fish and for ship) was launched in 1859 in Barcelona harbour. . . . The submarine, made of olive wood supported with oak rings and sheathed in two-millimetre thick copper, measured only 23 feet (7 meters) in length and offered hardly enough space for the captain and the four man crew who powered the ship by cranking. . . .weights could be dropped immediately to surface quickly in case of an emergency. The glass ports on the side, the top and the nose were designed enabling water pressure to push them inside the hull, rendering leaks virtually impossible. . . . The interior of the submarine was lit by a candle, using up precious oxygen although serving as an integral indicator when oxygen began to run low. . . . The machine could stay submerged for 2 hours and dive up to a depth of 20 meters. . . . Robert Fulton, an American living in France at the time, designed the successful "Nautilus", which began testing in the Seine in 1800. It could stay submerged for 5 hours by use of compressed air. The German inventor Wilhem Bauer launched his "Brandtaucher" in 1850 and his "Seeteufel" in 1856 (both of which sank). The American inventor Horace Hunley launched "H.L.Hunley", the first submarine to sink an enemy warship (and the first to sink 3 times itself, killing 25 people) in 1863, a few years later[.] . . . No matter how state-of-the-art the Ictíneo was compared to her many contemporaries, she still had the same basic drawbacks many submarines at the time possessed: a limited range as a result of limited air supply, and a very low speed. All early submarines were propelled by human muscle, which made them extremely slow.
The Nautilus was equipped with a sail, but could obviously only be used when sailing on the surface. Underwater, the ship was propelled by a helical screw, turned by hand. The Ictíneo used pedal power, needing 4 men to reach a speed of 1 mile per hour (about the same speed of the underwater rowing boat designed 3 centuries earlier). That pace was not always sufficient to overcome the effect of currents and tides. . . .
When the Ictíneo I was crushed by a freighter while docked in the port of Barcelona, Monturiol decided to design a larger submarine that was driven by steam. The Ictíneo II, more than twice the length of the Ictíneo I, was launched between 1864 (with human power) and 1867 (with steam power). It became the first combustion engine driven submarine in the world.
The thinking at the time was that it was almost impossible to run a steam engine underwater because it would use up all the oxygen and convert the inside of the ship into an oven. To overcome this, Monturiol invented a chemical furnace based on a reaction between potassium chlorate, zinc and manganese dioxide - a process that produced enough heat to boil water to run the steam engine. To complement this ingenuity, the reaction gave off oxygen as a by-product.
Monturiol had successfully resolved the two basic obstacles presented to submarine inventors: air supply and mechanical power. In fact, he devised an early form of anaerobic (air-independent) propulsion only to be repeated in the 1940s with the Walter turbine in Germany, and finally with the first atomic submarine, the USS Nautilus.
The Ictíneo II was the first of its kind providing its own oxygen, without surfacing regularly or using a snorkel, as seen on the Nautilus. . . . On account of all the machinery in the vessel, only 2 men could fit in the submarine originally designed for a crew of 20. The Ictíneo II made almost 20 problem free demonstration drives. It could stay submerged for eight hours and plunge to a depth of 50 meters. Monturiol calculated that the maximum possible depth was 500 meters, but chose not to take the risk of diving to this depth.
In 1868, shortly after its launch, the groundbreaking Ictíneo II was seized by the shipyard and scrapped, together with her predecessor. The reason? Monturiol could not pay the bills.
The Only Other Famous Steam Powered Submarine
The most famous historical steam powered submarines were the British K class submarines designed in 1913 and were ultimately viewed as a great failure (the photograph above is of one that ran aground).
The submarines were made more dangerous because the eight internal bulkheads were designed and tested during development to stand a pressure equivalent to only 70 feet (21 m), risking their collapse if the hull was compromised at a depth below this figure. . . . A dive from steam-powered surface operation normally required 30 minutes. Minimum time needed to secure the main engines, shift to battery motors and dive under emergency conditions was nearly 5 minutes, which though better than the 15 minutes of the Swordfish prototype was considered barely adequate. The boiler fires were first extinguished to prevent submerged buildup of fumes: a complicated series of hydraulics and mechanical rods and levers lowered the twin funnels away from each other to a horizontal position in wells in the superstructure as well as simultaneously closing hatches over the funnel uptakes. The main intake ventilators were likewise closed along with sea water connections for condensers and boiler feed. It was considered that with their 24 knots (44 km/h; 28 mph) of speed the submarines could turn and outrun almost any threat if they were attacked on the surface, dispensing with a need for a rapid dive. This was perhaps wishful thinking, and just excused the fact that the record breaking 'crash dives' of the conventional boats (particularly the later World War II U boats) was unattainable.
The most oft quoted complaint about the class was that the submarines had 'Too many damned holes...' or openings in the pressure hull that required securing before a dive could commence, the majority of which gave air/sea access to parts of the boat normally unmanned whilst diving.
A more serious problem was the high temperatures in the boiler room which was to some extent alleviated by installing bigger fans. Steaming at speed tended to push the bow into the water making the already poor sea-keeping worse. To fix this a bulbous swan bow was added, which also incorporated a 'quick blowing' ballast tank to improve handling. Nevertheless, there were still problems; the most embarrassing being that in a heavy storm, sea water could enter the boat through the short twin funnels and put the boiler fires out. . . . K3 held the unofficial record for maximum diving depth (266 feet (81 m)) following an uncontrolled descent to the bottom of the Pentland Firth. The ship managed to surface without further difficulty despite spending an unrecorded period below 'crush depth.'
An improved later version attained a maximum rated diving depth of 250 feet (76 m).
The Bathysphere (Greek: βαθύς, bathus, "deep" and σφαῖρα, sphaira, "sphere") was a unique spherical deep-sea submersible which was unpowered and lowered into the ocean on a cable, and was used to conduct a series of dives off the coast of Bermuda from 1930 to 1934. The Bathysphere was designed in 1928 and 1929 by the American engineer Otis Barton, to be used by the naturalist William Beebe for studying undersea wildlife. Beebe and Barton conducted dives in the Bathysphere together, marking the first time that a marine biologist observed deep-sea animals in their native environment. Their dives set several consecutive world records for the deepest dive ever performed by a human. The record set by the deepest of these, to a depth of 3,028 feet on August 15, 1934, lasted until it was broken by Barton in 1949.
As of the late 1920s, the deepest humans could safely descend in diving helmets was 100 feet, since beyond that point the pressure becomes too great. Submarines of the time had descended to a maximum of 383 feet, but had no windows, making them useless for Beebe's goal of observing deep-sea animals. The deepest in the ocean that any human had descended at this point was 525 feet wearing an armored suit, but these suits also made movement and observation extremely difficult. What Beebe hoped to create was a deep-sea vessel which both could descend to a much greater depth than any human had descended thus far, and also would enable him to clearly observe and document the deep ocean's wildlife.
Barton's design called for a spherical vessel, as a sphere is the best possible shape for resisting high pressure. The sphere had openings for three 3-inch-thick (76 mm) windows made of fused quartz, the strongest transparent material then available, as well a 400-pound entrance hatch which was to be bolted down before a descent. Initially only two of the windows were mounted on the sphere, and a steel plug was mounted in place of the third window. Oxygen was supplied from high-pressure cylinders carried inside the sphere, while pans of soda lime and calcium chloride were mounted inside the sphere's walls to absorb exhaled CO2 and moisture. Air was to be circulated past these trays by the Bathysphere's occupants using palm-leaf fans.
General Electric provided a lamp which would be mounted just inside one of the windows to illuminate animals outside the sphere, and Bell Laboratories provided a telephone system by which divers inside the sphere could communicate with the surface. The cables for the telephone and to provide electricity for the lamp were sealed inside a rubber hose, which entered the body of the Bathysphere through a stuffing box. . . . After the initial version of the sphere had been cast in June 1929, it was discovered that it was too heavy to be lifted by the winch which would be used to lower it into the ocean, requiring Barton to have the sphere melted and re-cast. The final, lighter design consisted of a hollow sphere of 1-inch-thick (25 mm) cast steel which was 4.75 ft (1.5 m) in diameter. Its weight was 2.25 tons above the water, although its buoyancy reduced this by 1.4 tons when it was submerged, and the 3000 feet of steel cable weighed an additional 1.35 tons.
While this was actually developed in 1928, according to a previous StackExchange post on the topic, the technology necessary existed by the late 1800s.
It appears that winch strength and not the ability of the structure to ovecome pressure was the limiting factor on the maximum depth of the Bathysphere, and that is a problem that could have been overcome in the steam age by a more ambitious funding source.
The pressure at the bottom of the Mariana trench is about 8 tons per square inch... about 1000 atmospheres. You can't make water hot enough to boil at that temperature, so your boiler would need to be inside the submarine's pressure vessel.
A steam engine needs a source of heat... a lot of heat. That is, you'd need to sit alongside the firebox and boiler inside a sealed steel can.
So you'd run out of air very quickly, you've got a fire in there not just a few people, the people attempting it would die of asphyxia way before they got that deep . It's worse than running an IC engine in a sealed container... submarines could never run sub-surface on diesel or petrol engines, they either needed breather tubes or they ran on batteries when they were running any deeper than just under the surface prior to nuclear submarines. Look at the 'best' that could be done using steam and under water vessels in the 1860s... the USS Monitor for instance, sunk because water got in through vents
If you run a steam engine in a submarine, you need to get the drive to propellers outside the pressure vessel. So you need rotating seals that can survive 1000 atmosphere pressure without leaking. That's a huge ask for technology that is only just inventing the steam engine.
So in an early steam era you have to have a source of heat that doesn't involve a fire (you need a working nuclear industry?) and you need some way to get drive through a pressure vessel (you need working generators and electric motors?). You are asking for a very imbalanced development cycle, a world with nuclear reactors and generators that doesn't have steam engine technology already... that's a bit like expecting mediaeval knights to be equipped with light-sabres.
It's impossible because Challenger Deep wasn't well known in steam engine times.
Challenger Deep was found in 1875, but it's true deep was not known until 1950s. A hypothetical submarine trying to reach it in 1876 would be designed to whitstand only 8.000 meters. But it's real deep is 11.000.
In his book "Seven Miles Down" Jacques Piccard tells that only ten years before his historical travel to the bottom of the deep in 1960 he believed the Philippine Trench to be the deepest place on Earth.