I will first define what I mean by a pipelauncher. A pipelauncher is essentially a pipe with one end capped. It's purpose is to be a launchpad for rockets which provides some speed to the rocket- a launch assist.
There are other things which can be classified as launch assist. Launching a rocket from a mothership [such as SpaceShipOne or Pegasus] is example of a launch assist. There are other ideas such as using a supergun or MagLev rail launcher- which generally focus on a assist launch which would be supersonic. A pipelauncher is NOT intended to give a assisted launch which is supersonic- getting any pipelauncher to add 500+ mph would be difficult. Instead the focus of a pipelauncher is provide a cheap launchpad which can located in the ocean. Generally speaking unlike other assist launcher the pipelauncher could launch very large rockets.

The Equator is generally the best place to launch, it would used in similar fashion the oil platform used by Sea Launch on the ocean and at the Equator. In a apples to apples comparison to oil platform type structure I think a pipelauncher could be cheaper. In this kind of comparison one would use a small pipelauncher which didn't add hardly any speed [say 30 mph] to a rocket because for comparison purposes the oil platform does not add any speed. The larger the pipe launcher the more speed it is capable of adding to the rocket. And the bigger the pipelauncher the more expensive it would be to make and operate. So what I mean by a small pipelauncher could be less 500' in length. A large pipelauncher could be more than 1 km in length. The limits of the size of pipelauncher would depend on things like the costs and markets, the strengths of material and ocean depth available. Though ocean pressure due to extreme ocean depth used by a pipelauncher is not a significant problem.

As I said a pipelauncher is a pipe with one end capped. So if you were to have a pipe 500' in length and 50' in diameter with say 1" thick steel pipe walls and the "top" capped and this were vertically lowered into the water [with open end down], the pipe would be lowered until such time as the inside air pressure would balance with the weight of the pipe. Now as a practical matter one could also have a plug in the open end, tow this out into the ocean, remove the plug, allowing water to come in to the pipe, so that end would lower and result in similar thing as [somehow] lowering it vertically. The result of doing either is you would have a pipe floating vertically in the water [cap end up and open end down]. And the idea is you would put a rocket on top of the capped end.

Now, with this 500' long pipe floating vertically, the top could be hundreds of feet in the air above sea level. The air pressure inside the pipe would be a higher pressure than the air pressure at sea level [1 atm].
If you add air inside the pipe, the pipe rises vertically. If you remove air from inside the pipe the pipe lowers vertically. If you heat the air inside the pipe, it rises, if you cool air inside the pipe, it lowers. Whether pipe raises up or down the air pressure inside the pipe remains fairly constant. If you add weight to pipelauncher the air pressure inside the pipe increases. If you have a pipe with bigger diameter the air pressure inside the pipe is generally less. For instance if the 500' pipe had instead 100' diameter and say 2" thick steel pipe walls, the air pressure would would less than compare to 50' diameter pipe. Let me check that:

500' with 1" walls 50' diameter is roughly equal to 500' by 157' 1" plate steel or 78500 sq feet or 6541.6 cu ft of steel
Water weights 62.416 and steel weights about 7.9 times water so steel weighs about 493 lb per cubic foot. So 3,225,574 lbs.
500' with 2" walls 100' diameter is roughly equal to 500' by 314 2" plate steel or
157079.5 sq feet or 26,180 cu ft of steel. So 12,906,699 lbs
Ok:
50' diameter has area of 282,743 sq inches. Divide 3,225,574 lbs by 282,743 equals 11.4 psi
100' diameter has area of 1,130,972.4 sq inches. Divide 12,906,699 lbs by 1,130,972.4 equals 11.4 psi.
Ok, so it's same.
Anyways, double the diameter with same thickness of pipe wall and it's half the pressure.

So, 11.4 psi inside the pipe means that water inside the pipe is pushed below sea level somewhere around 20'. If pressure was 14.7 psi it would 1 atm which is about 33', so precisely, it would be 25.59'.
Now, with the 50' diameter pipe which weighs 3,225,574 lbs, if you add 3,225,574 lbs to it, the pressure doubles as does the depth of water depressed inside the pipe.
OR if you double the pressure inside the pipe, the pipe accelerate vertically at 1 gee acceleration- a constant 1 gee acceleration IF the pressure inside the pipe is maintained at twice 11.4 psi [22.8 psi]. Now, maintaining this 22.8 psi may not be as easy as one might imagine. Or maybe you thinking the opposite:).

Ok let back up a bit. You got the 50' diameter 500' pipelauncher you drop it vertically in the water and it will submerge until the air pressure inside the pipe is 11.4 psi gauge [above the 14.7 psi sea level pressure]. If the air in the 500' pipe compresses into 250' of pipe the air pressure doubles [to 14.7 psi], so for 11.4 psi that means the air column inside the pipe will be more than 250' tall- which means that the capped end would higher than a 25 story building above the sea level.

To put a rocket on top of a pipelauncher you want the top lower than a 25 story building, so you could do this by letting the air out it. You could lower it to any level you want, even submerge to to below the sea level [if this would be somehow helpful to load the rocket].

So I guess next basic thing is how is this thing powered. There could numerous ways this could be done. I suppose it's even possible you *run it* with off hot rocks [even cold rocks:]- not very practical. Or one could use jet engines to add pressure. But probably the cheapest and simplest would be to use liquid air [or LOX] and some kind fuel like kerosene or Methane. And what one does is mostly heat up the liquid air [or LOX]- and btw you would get a small amount energy from the warmth of the ocean. The temperature range of the air could in the average range of -100 C to + 100 C [or 170 to 370 Kelvin- btw if you double Kelvin you double pressure- so operating in lower temperature range, generally works better].

In summary a balloon is a lighter than air machine; a pipelauncher is a lighter than water machine. Both depend upon buoyancy. Both are sort of antigravity machines- without gravity they don't work- or with higher gravity they function better [are more efficent] than compared to other types of machines.