The exit velocity "v" of gas from a nozzle, or engine core, or fan is determined by adiabatic effficiency (I'll call it "effy"); the specific heat ratio k (usually called gamma), Gas Constant R, stage temperature T and the pressure ratio across the stage
Pr.
Thus u = sqrt[2*"effy"*(k/k-1)RT[1-(
Pr)^(k-1)/k].
A nice treatise is found in Mechanics and Thermodynamics of Propulsion by Hill & Peterson ISBN 0201 146592 pp184-185 mainly but they do go through the maths for all stages.
Also
http://www.anirudh.net/seminar/ge90.pdf is handy for B777 people.
The mixing of fan and core streams mucks these undergrad figures about a bit by 1 or 2%