Perturbations of a given flow are considered, and the equations which govern the one-dimensional, non-steady flow of an inviscid, ideal compressible gas are linearized in the neighbourhood of this known solution, assumed isentropic, by a formal perturbation expansion. The perturbed flow is not assumed isentropic. Explicit solutions are obtained for a basic flow which is uniform or a centred simple wave and for an arbitrary simple wave if the perturbed flow is isentropic.

The perturbation of a uniform shock and perturbations in a shock tube lead to functional equations of a particular type, and a discussion of their solution is given.

A similar analysis is used to discuss the flow in a tube of slowly varying cross-section.

A small-scale experimental model has been constructed for the study of steady-state slow free convection of water in saturated sand. The convection field is confined between coaxial cylinders maintained at constant temperature difference, and the upper and lower boundaries consist of planes with thermal and fluid insulation. Measurements of the temperature distribution within the convection space have been obtained for average boundary temperature differences (T1 − T0) of (I) 18·40° A, (II) 32·70° A, and (III) 46·68° A. Theoretical temperature values predicted from perturbation theory have been fitted by least squares. The first-order estimates of η/(T1 − T0), where η is the convection parameter or modified Rayleigh number, do not differ significantly from a constant value (± 3% S. D.) for the three given values of T1 − T0, indicating good agreement between theoretical and experimental results. First-order estimates are made also of the temperature coefficient of thermal conductivity b of the sand-water mixture, and of the coefficient of radiation loss c at the upper insulated boundary, but these estimates are less reliable. Separate determinations of η/(T1 − T0), b, c by direct physical measurement are in good agreement with the least-squares estimates.

An estimate is given of the distribution of skin frictional force per unit length, and of displacement area, on the outside of a semi-infinite cylinder, of arbitrary cross-section, moving steadily in a direction parallel to its generators. A Pohlhausen method is employed with a velocity distribution chosen to yield zero viscous retarding force on the boundary layer approximations. (The smallness of the fluid acceleration far from the leading edge has been pointed out by Batchelor (1954).) Like the Rayleigh method, this method is expected to yield reasonable results at large distances from the leading edge. However, for a large class of cross-sections, which includes all convex cross-sections and locally concave cross-sections with re-entrant angles greater than ½π, the method yields the expected square root growth of the boundary layer at the leading-edge, with a fairly close approximation to the coefficient, and it is supposed that the skin-frictional force and displacement area are given with reasonable accuracy along the whole length of the cylinder.

Results for the elliptic cylinder and the finite flat plate are given in closed form, valid for the whole length of the cylinder, and are expected to be in error by at most 20%. In addition, some estimate is given of the effect of corners on skin frictional force and displacement area.

A mathematical model is constructed for cavitating flow past a wedge with sides of equal length but with its axis of symmetry placed at an angle to the incident stream. The model involves a subsidiary cavity with a re-entrant jet at the vertex. Only the case of zero cavitation number is considered. The flow field is worked out in some detail for small angles of incidence, and the lift, drag and moment coefficients are calculated as far as first-order terms in the angle of incidence. It is shown that the effect of the rate of loss of momentum in the re-entrant jet on these force coefficients is negligible to this order.

Experimentally, it is shown that the secondary cavity does exist under suitable conditions, and the force coefficients obtained agree with the theory.

A comparison is made between various methods for the calculation of the pressure distribution on an elliptic cone in supersonic flow. In particular, a criterion first put forward by Van Dyke (1956) is reconsidered. The paper is presented in two parts under separate authorship, taking the form of a discussion of some controversial aspects of this subject.

In a stationary weak sound wave the four gas dynamical quantities, entropy, stagnation enthaply, mass flow per unit area and impulse per unit area are constant. The six processes in which pairs of these four variables are kept constant are studied for the case of any single phase fluid or mixture of fluids in equilibrium, and it is shown that the remaining variables are stationary at sonic points. Such points are shown to occur once only in each process and are identified as maxima or minima, on the assumption that the fluid is a normal one which expands on heating at constant pressure and for which (∂2p/∂v2)s is positive.

Newton's theory of sound assumed that the fluid temperature was invariant. Across a stationary Newtonian sound wave, the four quantities, temperature, mass flow and impulse per unit area, and a dynamical variant of the Gibbs function are constant. The six processes in which pairs of these four variables are kept constant are studied, and it is shown that the remaining variables are stationary at points where the fluid speed equals Newton's sound velocity. These points are shown to occur once only in each process and are identified as maxima or minima with the further proviso that (∂2p/∂v2)T is positive.

The two sets of processes have one member in common, that usually referred to as the Rayleigh line. The Fanno line and the usual isentropic ‘nozzle’ process also belong to the first set.

Finally, the variation of stagnation temperature and pressure in some of the processes and in stationary shocks is investigated.