As my teacher was going through the 'open the oxygen valve 1/4
turn' part (which is EXACTLY what they had told me at my tank
place), the student mentioned that since the oxygen is used at
such high pressures it actually needs to be turned on *all the
way*, and then closed back 1/4 turn.
It's not clear from your post if you're talking about the valve on
the tank or the torch.
Oxy is stored at about 2,000 PSI in a full tank. The valve on the
tank is a double sealing valve. That means it is sealed when it's
closed & when it's 'fully' opened. If the valve on an Oxy tank isn't
fully opened, there's a very good probability of more oxy leaking
out around the valve stem than will be used by the torch. The
packing used around the valve stem can't contain the oxy under
2,000 PSI. That's the reason the valve is opened fully; so it gets
sealed against the 'open' valve seat.
The fuel gas, on the other hand, is stored at a much lower pressure.
Therefore a standard single sealing (shut only) valve is used on
fuel gas cylinders. The valve stem packing can contain the gas in an
open valve. Typically the fuel gas tank valve is only opened a 1/4
turn (or something less than a full turn).
If you stop to think about what's required for a flame, it's oxy & a
fuel. It's impossible to get rid of the source of oxy, it's in the
air all around us. If there's a undesired fire with a torch & you
want to extinguish it quickly, removing the oxy won't do it.
Removing the fuel will. That's one of the reasons for only opening
the valve on the fuel gas tank of a welding combination less than a
full turn. It doesn't take as long to stop the flow of fuel gas.