A method of successive approximations for the solution of problems in the fields of diffusion, boundary-layer flow, and heat-transfer is illustrated by solving problems in each of these fields. In most of the examples, the approximate solutions are compared with known accurate solutions and the agreement is shown to be good.

The Euler equations for the rotation of a solid body are applied to the problem of the motion of ultracentrifuges. Particular attention is paid to the problem of the passage of an ultracentrifuge rotor through the critical velocity. The factors that affect the passage of rotors through the critical point are stressed.

By an analysis of the Navier-Stokes equations it is shown that the aerodynamic coefficients of an infinite rectangular swept wing in an isothermal or adiabatic flow of a compressible gas can be determined from the aerodynamic coefficients of the unswept wing. When the flow is neither isothermal nor adiabatic, a three-dimensional boundary layer theory is developed and applied to the special case of a swept flat plate.

An explanation based upon reaction kinetics is presented to account for the deviation of measured ionization levels obtained from reflection experiments from the values computed assuming chemical equilibrium. The heat transfer to the unburned fuel is also considered.

Memorandum presenting three papers regarding aerodynamic balance of control surfaces. The specific topics covered include some general remarks regarding aerodynamically balanced control surfaces, aerodynamically equivalent systems for various forms of control surfaces within the scope of two-dimensional wing theory, and comparative calculations concerning aerodynamic balance of control surfaces.

This report discusses the need for considering a wide variation in certain of the basic flutter parameters in conducting a flutter analysis. Conclusions are drawn stating that design charts or simple rules may be misleading. Due to inherent difficulties, dynamic model testing may also yield misleading results. The general flutter equations and various methods of solution are discussed. Of particular interest, curves are presented showing computational effort plotted against a number of degrees of freedom used in a flutter analysis.

For compressible flow with friction in a cylindrical pipe the momentum, continuity, and heat-transfer equations are examined to determine whether an increase in Mach number ("thermal" Laval nozzle) is obtainable through heat conduction from the gas through the pipe walls. The analysis is based on the assumption that the wall temperature is negligibly small in comparison with the stagnation temperature of the gas. The analysis leads to a negative result. When the gas cooling is increased by also considering radiation to the wall, a limited region at high temperatures is obtained where Mach number increases were theoretically possible. Obtaining this condition practically is considered impossible.

"The shell shall be considered as a three-dimensional continuous medium; for the coordinate surface, the middle surface of the shell shall be assumed parallel to the bounding surfaces. Let alpha and beta be the curvilinear orthogonal coordinates of this surface, coinciding with the lines of principal curvatures, and gamma the distance along the normal from the point (alpha,beta) of the coordinate surface to any point (alpha, beta, gamma) of the shell" (p. 1).

The performance of a jet power plant consisting of a compressor and a turbine is determined by the characteristic curves of these component parts and is controllable by the characteristics of the compressor and the turbine in relation to each other. The normal. output, overload, and throttled load of the Jet power plant are obtained on the basis of assumed straight-line characteristics.

Among the information presented are included displacement, momentum, and kinetic energy thicknesses, shearing stress distributions across boundary layer, and surface friction coefficients. The Gruschwitz method and its modifications are examined and tested. An energy theorem for the turbulent boundary layer is introduced and discussed but does not lead to a method for the prediction of the behavior of the turbulent boundary layer because relations for the shearing stress and the surface friction are lacking.

The chemical reaction of two substances (fuel and oxygen) accompanied by the formation of new substances of the products of combustion and the liberation of heat is considered. General equations are provided as well as an analysis of the equation and the distribution of products of the reaction.

"The mechanism of flame propagation has been qualitatively formulated. In accordance with this formulation, the chemical reaction initiated in some layer brings about an increase in the temperature; because of the heat conduction, the temperature is raised in the neighboring layer where in turn the chemical reaction is initiated. In this manner the flame is propagated" (p. 1).

A comparatively rapid method is presented for determining theoretically the bending stresses of helicopter rotor blades in forward flight. The method is based on the analysis of the properties of a vibrating beam, and its uniqueness lies in the simple solution of the differential equation which governs the motion of the bent blades.