How Do You Convert Psi To Fps?

The Solution involves the use of two basic pressure formulas, namely

V= square root of 2hg where:

V= discharge velocity of nozzle or muzzle (ft/sec)

g= acceleration due to gravity (32 ft/sec/sec)

h= velocity head (ft)

An P = 0.433 h where:

P- pressure head (psi)

h=head(ft)

Take 75 psi

P= 75 psi = 0.433h

h=173.2 ft

V= square root of 2(32)(173.2)=105.3 ft/sec

Why are you using mixed units? Fps (feet per second) is "Imperial" (or American) measurement as is psi (pounds per square inch) and the area of the BB, while the others are metric. Do you want to crash your BB on Mars along with our space craft?
And 7mm is not a volume. At best in context it is diameter.
The best approximation of an answer would be to apply 600 psi to 0.1753 in^2 to get pounds force on the BB and then convert 0.25g mass to American mass units and pick a distance or time over which to apply the computed acceleration to get a velocity of feet per second. For example, the force might be applied for 1 foot along the length of the barrel. If you are need to know more about Psi To Fps conversions then use this unit converter.