## Fluid Mechanics and Thermo-Acoustic WavesA derivation of the averaged balance equations of fluid mechanics is presented including compressibility with alternative equations of state, viscous and thermal dissipation contributions, stream tube end boundary motion, and chemical reaction. Explicit utilization of the energy equation, or enthalpy equation in combination with the linear momentum and mass balances is investigated. Both the vorticity and Bernouilli equations are provided in alternative forms with thermodynamic energy assumptions to be used in engineering analysis and to discern assumptions. |

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Acoustic Waves Acoustical Society analysis applied assumed average balance equations boundary condition calculus rheology model chemical kinetic chemical kinetic equations chemical reactions coefficient complex component constant constitutive equation continuum continuum mechanics cross covariances deﬁned denotes density diagonal differential equation diffusion dimensionless dispersion dr dr dynamical eigenvalues energy equation Engineering equations of motion equilibrium extra stress ﬁeld equations ﬁrst Fluid Mechanics follows Fourier fractional calculus fractional calculus rheology frequency number gradient heat ﬂux inertial integrating internal energy Journal of Acoustical linear momentum Margulies material Mathematics matrix mixture modiﬁed multiphase Newtonian ﬂuid Nonlinear ofthe parameters particles perturbation phase phoresis pressure random reaction progress References represents shear viscosity solution solved stress tensor temperature theory thermal conductivity thermodynamic thermophoresis total mass transform universal gas constant variables vector velocity visco-elastic volume ﬂow rate vorticity wave propagation written yields York zero