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adiabatic amplitude angle axis Bernoulli's equation body boundary conditions boundary layer calculation characteristics co-ordinates coefficient combustion constant corresponding cross-section cylinder denote derivative determined detonation wave dimension direction distance drag energy flux entropy equation of continuity equations of motion equilibrium Euler-Tricomi equation Euler's equation expression finite flow past fluid velocity flux density formula frequency function gas velocity given gives grad gradient heat Hence ideal fluid increases infinite infinity integral intersection laminar Laplace's equation lift force mean mechanical equilibrium moves obtain occurs oscillations parameters particles perturbations pipe plane potential flow pressure PROBLEM propagated quantities radius rarefaction wave result Reynolds number shock wave simple wave small compared solution sound wave sphere spherical streamlines subsonic Substituting superfluid supersonic surface of discontinuity temperature tensor thermal conduction thermodynamic turbulent flow vector velocity component velocity of sound viscosity volume wake weak discontinuity zero