Does anyone know the gas pressure and volume needed to cycle an AR?

SRM

Your average AR-15 chamber pressure is around 52,000 PSI...

That's max chamber pressure but by the time the bullet passes the port, pressures are significantly reduced.  Maryland AR15 site has good data, but IIRC in the rifle, port pressure is down around 14,000 psi, in a carbine length system it's higher, 24,000-25,000 psi, but that's just from memory.

It's all a game of modifying the gas port size to deliver the right amount of gas to the carrier considering how much dwell is needed to get the job done.  Shorties/SBRs, while port pressure is high, often need larger port sizes because the dwell (remaining barrel length past the port) is so short that they need a burst of gas.  Rifles have smaller port sizes because their dwells are longer.

I can remember reading some where that its between 8-14,000 psi... Its the size of the port hole that determines the amount of pressure that is released into the gas tube...
To much gas can result in erratic cycling that can cause excessive recoil, unnecessary wear on parts and extraction problems... To little pressure will cause short stroking problems...