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Unformatted text preview: Chapter 12: Compressible Flow Lecture 26 Stagnation Properties, Speed of Sound, Mach Number We will now consider problems where the density varies from location to location in the flow. Recall our governing equations for incompressible flow o Conservation of Mass r CV CS d d V ndA dt = 2200 + r r o Conservation of Linear Momentum r CV CS d F V d V V ndA dt = 2200 + r r r r r a vector equation with 3 components o : r x r CV CS dm d x F u d u V ndA dt = 2200 + & r r 142 43 o : r y r CV CS dm d y F v d v V ndA dt = 2200 + & r r 142 43 o : r z r CV CS dm d z F w d w V ndA dt = 2200 + & r r 142 43 o This set of equations is sufficient to solve incompressible flow problems. However, if density is no longer constant, we will need an additional relationship to solve the problem (one additional unknown requires one additional equation). We typically take the Conservation of Energy as the additional relationship: ( 29 2 net in shaft,net in 2 r CV CS d Q W...
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- Spring '08