A generalized wave equation is derived for sound disturbances in a gas when relaxation effects connected with, for example, molecular vibration or dissociation are important. Solutions involving discontinuous wave fronts are presented, and it is shown that, under certain assumptions, the complete wave equation reduces to a variant of the telegraph equation. Detailed solutions are presented for disturbance fields produced by a wavy wall in subsonic and supersonic flow and a simple wedge in supersonic flow. This study is viewed as a step in the development of a theory of small disturbances of a high-temperature gas, as is found behind the shock in hypersonic flight. Symbolsy a 0 T/ 8 e V e # X = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = constant, Eq. (44) inclination of wave front, Eq. (46) and Fig. 3 equilibrium sound speed, Eq. (17) frozen sound speed, Eq. (16) wave attenuation, Eq. (46) transformation factor, Eqs. (35) and (39) quantity defined in Eq. (18c) internal energy per unit mass slope of surface as function of £ slope of surface as function of X Bessel function of the first kind, of an imaginary argument function of k and M, Eq. (22) ratio of sound speed, a c /a f Mach Number based on frozen sound speed, u/a f static pressure heat of dissociation per unit mass gas constant inclination of discontinuous wave front translational temperature time velocity in x direction velocity in y direction transformed x coordinate, Eq. (21) coordinate (in stream direction for steady flow) transformed y coordinate, Eq. (21) coordinate (normal to stream direction) fraction of diatomic molecules dissociated quantity subject to relaxation (either aort?) ratio of specific heats for frozen process amplitude of wavy wall related to difference of sound speeds [ = (1 -K 2 )/2] transformed Y coordinate, Eqs. (35) wedge angle vibrational temperature wavelength of wavy wall v = dimensionless frequency, Eq. (42) £ = coordinate measured normal to frozen waves a-= quantity defined in Eq. (18d) r = relaxation time for constant p and T T * = relaxation time for adiabatic process cb= velocity potential w = variable of integration SubscriptsSubscript notation is used for partial differentiation d pertains to dissociative relaxation e -equilibrium conditions / = frozen conditions v pertains to vibrational relaxation w = evaluation at a surface r denotes distance at which /3 effectively reaches equilibrium

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An approximate solution for coupled, nonequilibrium chemistry along streamlines of inviscid, blunt-body airflows is described. The solution is derived from a correspondence between the chemical relaxation zone along a streamline and that behind a normal shock. This correspondence applies in general for Newtonian flows with binary kinetics. Along the stagnation streamline, binary kinetics are not required. The approximate solution is compared with exact numerical solutions of the blunt-body problem and is found to be accurate for the high enthalpies corresponding to hypersonic flight.

The ability of two small cyclones to separate Freon drops from water and from an ice-brine slurry was measured for various flow rates and drop sizes. A theory developed for solid-liquid extraction was used to predict separation efficiencies, based on drop size distributions measured in the feed. For the larger cyclone, agreement between theory and experiment was good. For the smaller one, the data fell below the theory. This was attributed largely to drop breakup within the cyclone.