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lecture_2 - 16.512, Rocket Propulsion, Prof. Manuel...

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16.512, Rocket Propulsion, Prof. Manuel Martinez-Sanchez Lecture 2: Rocket Nozzles and Thrust Rocket Thrust (Thermal rockets) = ∫∫ i ne A e mu d ρ A e Solid A A ee surfaces P dS P dA u u dA = n e () −= xx x int. n (Tanks included) dm i Note: so subtract, x x .,int , aa e s Ae PdS PdA 0 () ( ) x int. −+ ae a e Solid A A P P dS P P dA u u dA Thrust F 16.512, Rocket Propulsion Lecture 2 Prof. Manuel Martinez-Sanchez Page 1 of 7
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In general then, define x = ∫∫ ne A e e A e uudA u ud A ρ and = x x ee A e e e PdA P A () ⇒= +− i x ea e e Fm u P PA If things are nearly constant on spherical caps, modify control volume to spherical wedge: = i r A e mu d A () ( ) ( ) x x int. . −− − = ax eae r AA solids P P dS P P dA u u dA θ == x x cos cos er dA dA u u 16.512, Rocket Propulsion Lecture 2 Prof. Manuel Martinez-Sanchez Page 2 of 7
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Define x = ∫∫ i r A e e uudA u m ρ ; x x = ee A e e e PdA P A and use 2s i n = dA r rd π θθ For ideal conical flow, ,, r uP are constant over e A . Then 2 2 0 0 1 cos sin i nc o s 2 1c o s i n == = r A e e rr r A e ud A rd uu u A α ρθ πθ θ πθθ or o s 2 + = er uu Also, since const on the exit surface, = e P = PP 16.512, Rocket Propulsion
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This note was uploaded on 11/07/2011 for the course AERO 16.512 taught by Professor Manuelmartinez-sanchez during the Fall '05 term at MIT.

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lecture_2 - 16.512, Rocket Propulsion, Prof. Manuel...

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