It would depend on the height of the vessel, but potentially quite a bit.

How much head space you going to have?

Under primary fermentation I would suspect that the CO2 being produced would probably be enough to push out any O2 to remove the chance of oxidation occuring. I guess after primary ferment has finished you always flush the headpsace with CO2 if you were worried.

(From my just recently completed SCUBA class:) Air is very compressible, liquid is not. Now for the guessing part. I'm thinking that the issue is with air pressure the CO2 produced during fermentation can't come out of solution, and that inhibits the yeast. I don't think it is the pressure of the liquid.

unsure f the exact amount of headspace...but now i think my guy has backed out on giving them to me so it may all be a wash...ill have to see what happens. Either way you guys have brought a lot of info forward for me to digest and i thank you.

As far as coming out of solution is concerned to the CO2 a headspace filled with air looks like a near vacuum (under the idealization that air and CO2 are ideal gasses which they are approximately). One deals in partial pressures of the individual gasses. In air the partial pressure of CO2 is 0.0003% atmosphere (if you believe the warming alarmists it's climbing rapidly, however). Thus CO2 would be freely evolved. If the CO2 can't escape, of course, the partial pressure of CO2 in the headspace rises and this causes more of the CO2 to stay in solution thus carbonating the beer. Right now, for example, I have CO2 pressure of 1 MPa (14.7 psig) in the headspace of one fermenter because I want the corresponding level of CO2 in the beer when I go to kegs in a day or 2.

Obviously, you want the evolving CO2 to blanket the surface of the fermenting beer at first and then later displace the air so the fermenter is open to the atmosphere through a "lock" which in the case of a larg fermenter is usually a hose connected to the CIP ball (at the top) at one end with the other end in a bucket of sanitizer. When the fermenter is spunded a pressure releif valve takes over holding whatever pressure you set for the desired level of carbonation.

Hydraulic pressure is significant in tall fermenters. If a fermenter is filled with beer to a depth of 30 ft then the hydrostatic pressure at the bottom will be approximately (dpending on the density of the beer) 1 atmosphere. The total pressure in the cone will be that 1 atmosphere plus the pressure of the atmosphere itself i.e. 2 atmospheres (absolute, 1 atmosphere gauge). If the pressure in the headspace is 1 amtomsphere gauge then the yeast in the cone will see 3 atmospheres total. This is a consideration in the design of breweries with huge fermenters.