Momentum, chaps
Force (thrust) is rate of change of momentum. That's the time derivative of the product of mass and velocity coming out versus going in.
Thrust = [d(mv)/dt at exhaust] - [d(mv)/dt at intake]
In the case of constant exhaust and intake velocity, this is renard's formula from post 2.
Thrust = (v_exhaust - v_intake) dm/dt
Fuel burnt adds a little to mass, bleed air takes a bit away.
-
For a rocket, the product of m and v at the intake is zero, and the change of momentum comes entirely from the exhaust speed and the burn rate of the fuel and oxidiser.
Thrust = (v_exhaust m/s) x (burn rate - Kg/s)
-
How fast you end up going (horizontally) is controlled just by drag.
If drag is very small, then a little bit of thrust is enough to reach a speed that can be much higher than v_exhaust: in fact the exhaust velocity hasn't got much to do with it, other than for efficiency.
In the limit that drag is very high you get a test rig, where there's a substantial static force on the pylon, but no motion (OK - with the exception of a tiny change in earth rotation).