1. MAE 4261: AIR-BREATHING ENGINES
Integral Forms of Mass and Momentum Equations
January 17, 2012
Mechanical and Aerospace Engineering Department
Florida Institute of Technology
D. R. Kirk

2. CONSERVATION OF MASS Relative to CS Inertial
This is a single scalar equation
Velocity doted with normal unit vector results in a scalar
1st Term: Rate of change of mass inside CV
If steady d/dt( ) = 0
Velocity, density, etc. at any point in space do not change with time, but may vary from point to point
2nd Term: Rate of convection of mass into and out of CV through bounding surface, S
3rd Term (=0): Production or source terms

3. MOMENTUM EQUATION: NEWTONS 2nd LAW
Inertial
Relative to CS
This is a vector equation in 3 directions
1st Term: Rate of change of momentum inside CV or Total (vector sum) of the momentum of all parts of the CV at any one instant of time
If steady d/dt( ) = 0
Velocity, density, etc. at any point in space do not change with time, but may vary from point to point
2nd Term: Rate of convection of momentum into and out of CV through bounding surface, S or Net rate of flow of momentum out of the control surface (outflow minus inflow)
3rd Term:
Notice that sign on pressure, pressure always acts inward
Shear stress tensor, t, drag
Body forces, gravity, are volumetric phenomena
External forces, for example reaction force on an engine test stand
Application of a set of forces to a control volume has two possible consequences
Changing the total momentum instantaneously contained within the control volume, and/or
Changing the net flow rate of momentum leaving the control volume

4. HOW A ROCKET WORKS F Chemical Energy
Rocket Propulsion (class of jet propulsion) that produces thrust by ejecting stored matter
Propellants are combined in a combustion chamber where chemically react to form high T&P gases
Gases accelerated and ejected at high velocity through nozzle, imparting momentum to engine
Thrust force of rocket motor is reaction experienced by structure due to ejection of high velocity matter
Same phenomenon which pushes a garden hose backward as water flows from nozzle, gun recoil
Thermal
Energy
Kinetic
Energy

5. HOW AN AIRCRAFT ENGINE WORKS
Chemical
Energy
Thermal
Energy
Kinetic
Energy
Flow through engine is conventionally called THRUST
Composed of net change in momentum of inlet and exit air
Fluid that passes around engine is conventionally called DRAG
Excellent website for how internal components work: