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where m is the mass of the body being propelled (may be changing), FV is the sum of externally applied volumetric forces (gravitational or electromagnetic), FA the sum of externally applied surface forces at the wall, and ve outward normal vector ne and pe the exit velocity and pressure through any opening of area Ae with an . Rocket propulsion For steady horizontal motion of a body with just one exit (rocket) the momentum balance, in the direction of motion, reduces to (see Eq. 5.20): Tmv (p p)A (17.12) ee0e where p0 is the pressure in the surrounding media (acting on the impermeable walls), that may be zero in outer space, and the propulsion efficiency, p, is defined as the ratio of thrust power, Tv, to whole power emanating from the body, that is the sum of thrust power, Tv (communicated to the surrounding media) and residual kinetic power of the jet relative to the surrounding media, 12m(ve v)2 (communicated to the jet); i.e.: Tv pep0 mvv 2 p11e vv (17.13) Tv m(v v)2 mvv m(v v)2 e 2e e2e vve where the simplification of considering pe=p0 is always acceptable (it is true for subsonic exits, and for supersonic exits with 'adapted nozzle', and very approximate even for large pressure departures). Equation 17.13 is shown in Fig. 17.13. Fig. 17.13. Rocket propulsion efficiency vs. flight speed to exit speed ratio. Most rockets are heat engines because they transform the heating power of a fuel/oxidiser mixture into mechanical energy (the kinetic energy of the jet), and thus an energy efficiency may be defined by: 1mv2 e 2 e (17.14) mhP where hP is the heating power of the fuel/oxidiser mixture per unit mass of reactants. Notice that high energy-efficiency demands high exit speed, demanding also high flight speed to keep reasonable propulsion efficiencies; i.e., rocket propulsion is inefficient at low speed. Compressed-gas rockets are also heat engines, but new magnetohydrodynamic and electrodynamic rockets are not. Air-breathing propulsionPDF Image | THERMAL MACHINES AND HEAT ENGINES
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