4: Thrust of a Jet Propulsion system

x-momentum:

Assume that pressue and velocity are constant over the entire control surface except at the exhaust area Ae.
Thus,

Using continuity,

      , or       .

Now,


Thus,


Net momentum outflow from the control volume is



Thus,

    , or    

Define a fuel-air ratio



Thus,



Note: Thrust comes from:
a) Increase in momentum of the air + fuel (momentum thrust)
b) Pressure at the exit plane being higher than the outside pressure (pressure thrust).   When the exit velocity is subsonic,   Pe = P1 because a pressure difference cannot be maintained across a subsonic jet.   Thus, for subsonic jet exhausts,   For engines with bypass flow (some flow going through a fan or propeller, but not going through the burner), the thrust equation is where   is the bypass ratio  

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