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Es wird eine Methode fur die exakte Untersuchung der Geschwindigkeits- und Temperaturverteilung laminarer konvektionsfreier Stromungen in geschlossenen zweidimensionalen Hohlraumen dargestellt. Die Losung der Gleichungen (der Gleichung von Navier-Stokes und der Gleichung fur die Warmeubertragung) erhalt man durch eine Doppelreihen-Entwicklung der Strom- und der Temperaturfunktion nach orthogonalen Polynomen. Die resultierenden Gleichungen fur die Entwicklungskoeffizienten werden in zwei gekoppelte Systeme algebraischer Gleichungen umgeformt, und diese werden dann mit einem Rechenautomaten numerisch gelost. Die angegebene Methode ist z. B. besonders wirksam bei der Behandlung der Staupunkt-Erscheinungen in einem Thermosyphon, welche mit den bekannten Naherungsverfahren der Grenzschichttheorie nicht aus-reichend genau behandelt werden konnen. Die Ergebnisse der Untersuchung werden durch Bilder veranschaulicht. A method of exact analysis for the velocity and temperature distribution of the laminar free-convection flows in closed two-dimensional cavities is presented. The solution to the governing equations (the Navier-Stokes and the heat transfer) is obtained by the use of double series expansions of the stream and temperature functions into orthogonal polynomials. The resulting equations for the coefficients of expansions are reduced into two sets of coupled algebraic equations which are solved numerically with a computer. The present method is particularly effective in treating problems such as the stagnation phenomena in a thermosyphon which cannot be accurately treated with the existing approximate analysis of the boundary-layer theory. Illustrative results of the analysis are presented in the paper.

This article discusses turbulent dispersion of particles whose size and inertia are such that it cannot be assumed that they will follow exactly the fluctuations of the fluid elements with which they are associated. The turbulent field is assumed to be stationary, homogeneous and isotropic. Stationary, extraneous force fields for the particles may exist. The method of generalized harmonic analysis (Wiener) is used to determine the statistical particle-dispersion parameters in terms of the spectrum density of the turbulent field and the physical characteristics of the particles. The discussion is restricted to one-dimensional problems; it includes consideration of the relation between turbulent dispersion and Brownian motion of the particles due to molecular impacts. An illustrative example of dispersion calculation with a given turbulence spectrum is presented, and aspects of practical applications are discussed briefly.

A physical theory of pitot pressure in the transition-flow regime—i.e., the moderately-rarefied-gas-flow region—is proposed. The ratio X/& (the mean free path to the radius of the cavity opening) is assumed to be of the order unity or larger. A general formula for the perturbation to the pitot pressure in the free-molecule flow is given. This perturbation is attributed to the intermolecular collisions, which are neglected on the basis of the free-molecule hypothesis. The expected rate of collision is calculated for rigid spheres, using the classical kinetic theory. Although this is intended as an approximate theory, the theoretical results agree surprisingly well with the limited experimental data that are available. The present theory shows that the ratio Re/M (Reynolds Number to Mach Number) is the governing parameter for determining the intermolecularcollision effect on pitot pressure in the transition-flow regime.

The aerodynamic basis of using Pitot-tube pressure at supersonic speeds as an indirect measurement of the upper atmospheric density, pressure, and temperature, up to 80 km, is discussed. A special means of deduction of these ambient variables from corresponding Pitot-tube pressure and other relevant parameters is presented. A unique feature of the method is that it needs only the Pitot-tube pressure and the corresponding forward velocity of the Pitot tube (assuming negligible atmospheric wind-velocity) to determine the ambient variables. This simplification is made possible by invoking laws which describe the characteristic properties of the atmosphere. This simplification, in the physical sense, results in an integral equation for the ambient density. A special and effective method is developed for the solution of this equation.

The equation of rectilinear motion of a projectile which moves in an atmosphere, of which the density decreases exponentially with the altitude, is solved. It is found that the velocity of the projectile can be expressed explicitly in terms of confluent hypergeometric functions. This theory is applied to treat two specific problems: (1) the flight analysis of a sounding rocket during the freeflight period and (2) the calculation of ambient temperature from the trajectory of a spherical projectile.

Upper‐atmosphere air densities and temperatures have been calculated from the measured trajectory data of a falling sphere. Densities were calculated from the equation for the drag force on the falling sphere, and temperatures were then obtained by using the hydrostatic equation and the equation of state of a perfect gas. The aerodynamic background and instrumentation are described; the method of calculation and the errors are discussed. The results of four rocket flights which carried the experiment are given. Comparison with the average of other rocket measurements indicates agreement with these results.

Structure of infinitely strong shocks in a slightly ionized gas, suitable for the interstellar HI region, is discussed. The charge-separation field, in closed form, is obtained by using a bi-modal (beam-continuum) distribution and the Mott-Smith approach.

In this paper, two error-correcting algorithms for redundant residue number systems are presented, one for single residue-error correction and the other for burst residue-error correction. Neither algorithm requires table look-up and hence their implementations need a memory space which is much smaller than that required by existing methods. Furthermore, the conditions which the moduli of the redundant residue number systems must satisfy in these two algorithms are less restrictive than that of existing methods. Comparison of the approach on which these two algorithms are based and that of existing methods is given.

This paper discusses the effect of pressure‐diffusion flux upon the concentration distribution of gas mixtures in flow fields. The equation of concentration is formulated for a binary gas mixture in which the mass ratio is large and the concentration of the lighter gas is very small. An asymptotic solution to the steady‐state equation of concentration is given for an irrotational and incompressible flow.As an illustration, the diffusive separation (i.e., deviation from the original homogeneous state) of a mixture of helium and nitrogen along streamlines at the entrance to a long straight channel is calculated. It is assumed that the pressure inside the channel is 90% of that in the free stream, and that the diffusion coefficient of the mixture corresponds with the atmospheric conditions at 80‐km altitude.

Gas separation during flow of a mixture along a hot plate is described. If the mixture consists of gases of unequal molecular weights, thermal diffasion is set up so that the lighter gas tends to move to the hot region and the heavier gas to the cold region. The light gas mixture can be enriched by suction through slots or a porous material near the hot surface. A summary of the diffusive separation in the boundary layer along the hot plate with surface suction is given. (J.R.D.)

A variational approach is proposed to determine the induced electric field by charge separation in the near wake of a large negatively charged body moving at mesothermal speeds in a tenuous plasma. The presence of potential well is discussed.

The formula for the pressure‐drag coefficient of a sphere which moves at extremely high speeds is derived. In the derivation it is assumed that the nose of the shock contour follows exactly the frontal half of the spherical surface and the local pressure on the frontal spherical surface corresponds to the pressure behind the shock wave after the statistical equilibrium between the various degrees of freedom of the molecule has been reached. The chemical dissociation of the molecules behind the shock wave is taken into account in the analysis. The theoretical results of the drag coefficient of the spheres agree with the corresponding available measured value within the experimental error for the range of Mach number between 5 and 10.

A kinetic theory of sphere drag in the transition flows, based on the Boltzmann equation for the Maxwellian molecules, is presented. The exact binary collision integral, in the first order Knudsen iteration, is expanded as a function of Hermite polynomials in molecular velocity. The drag of a sphere at free stream temperature with molecular diffuse reflection is calculated. The results agree well with Millikan's measured values over a wide range of Knudsen number (0.5 < λ/d < 10). It is found that the sphere drag of the almost‐free molecular flows normalized by the corresponding collisionless drag is essentially independent of the speed ratio for the present range of calculations.