This paper presents experimental investigations of the diffraction of plane strong shocks by several cones, a cylinder, and a sphere. The diffraction pattern, in particular the loci of Mach triple points and the shape of the diffracted shocks are compared with theoretical results obtained from a diffraction theory proposed by Whitham (1957, 1958, 1959). The agreement between theory and experiment is shown to be good. Also given are extensive numerical results supplementing Whitham's papers, and theortical considerations applying Whitham's theory to very blunt bodies.

The Stokes flow problem is considered here for the case in which an axially symmetric body is uniformly rotating about its axis of symmetry. Analytic solutions are presented for the heretofore unsolved cases of a spindle, a torus, a lens, and various special configurations of a lens. Formulas are derived for the angular velocity of the flow field and for the couple experienced by the body in each case.

The physics of shock-waves with vibrational relaxation regions is recapitulated, and it is shown that exact methods of analysis can be developed from the classical Rayleigh-line equations by treating the real gas as an ideal gas with heat transfer. By using these methods to analyse experimental records of density distributions in relaxation regions, a large number of local values of the relaxation frequency, rather than a single over-all value, may be obtained from each shock-wave record.

The validity of various solutions for the vibrational relaxation region in shock-waves, and of the assumptions on which they are based, has been assesed by comparison with an exact solution obtained by numerical integration of the relaxation equation, and also by use of the Rayleigh-line equations. Estimates of errors in the values of the relaxation frequency, determined by means of these solutions, are given.

In an earlier contribution (Francis 1956), a report was made of the speed of small solid bodies floating in the upper layers of a free surface stream. The bodies were cylinders of several diameters floating with their axes vertical and ballasted to the same draft. All the floats travelled at the same speed in the long, wide stream which was of constant depth and was strongly sheared, and this speed was the mean speed of the upper layers of the stream. It was pointed out that this result is unexpected, since the solid boundaries of the floats prevent turbulent interchange there, so that the floats are not locked to the stream in the same way as the corresponding volume of turbulent water would be locked. Thus the floats would be expected to travel a little faster than the stream, large diameter floats travelling faster than small floats.

Electrical power of 0·32MW has been extracted for a period of 100 μsec from a plasma of shock-ionized argon travelling at 4×105cm per sec through a magnetic field of 10,000 G. Currents of more than 10,000amp are drawn and the resulting modification of the applied field is considered.

Maximum power is obtained when the external load is matched to the plasma generator which has an internal impedance equivalent to its own electrical resistance in series with a resistance arising from its behaviour as a compressible fluid.

Values of the electrical conductivity of the plasma obtained in these experiments (about 3 × 103mho per metre) show that the plasma resistance is controlled by electron motion and these values are in good agreement with those found by other methods.

The paper gives the result of a study on the efflux of gases through circular apertures. The problem is considered as an example of a transition from the gasdynamic to the gaskinetic régime.

The mass flow of helium, argon and nitrogen was measured for a range of upstream pressures corresponding to (mean free path)/(aperture diameter) from about 50 to 5 × 10−3; within this range the transition from molecular effusion to inviscid, transonic flow takes place. The theory for the two asymptotic limits is discussed and first-order corrections to the free molecular and inviscid limit formulae are given.

A study of the stability of a plane laminar flame front is made. The effects of disturbances on the flame structure are investigated by a small perturbations technique, taking into account the mechanism of diffusion, heat conduction and unsteady combustion. By use of a simplified model of the flame structure, and the assumption that the flame thickness is small compared with the wavelength of disturbances, a formula for the perturbation of the flame propagation velocity is derived. The flame velocity is shown to depend on the curvature of the flame, and on the rates of change of fluid velocities at the flame boundary. From stability analysis it then follows that properties of the mixture, as expressed in terms of the coefficient of heat conductivity and various coefficients of diffusion, play an important role in determining the stability picture. For some estimated values of these parameters the theoretical results are shown to agree with the general trend of the experimentally observed behaviour.

Many salient features of fully developed turbulent jets, plumes and wakes with steady mean flow are shown clearly by the relationship between the momentum flux and the mass flux in the column of moving fluid. Using a simple model for the flows, this relationship can be found from the solution of a single ordinary differential equation and the character of many related flows can be represented immediately (except for actual distribution in space) on a single momentummass flux diagram.

In this note some approximate solutions based on dimensional arguments are outlined briefly for cases of buoyant and non-buoyant wakes and jets directed along the axis of a uniform main stream, and momentum-mass flux curves are presented.

Recent work by Hall and Vinen has established that mutual friction between the normal and superfluid components of liquid helium II is caused by interactions between quantized vortex-lines and the normal fluid. If the mean separation of the vortex-lines is small compared with the channel width, the general character of the flow may not depend on the discrete nature of the lines except in so far as this is the cause of the mutual friction. Equations of motion are developed which refer to components of the velocity field with a scale large compared with the line separation, and these are used to discuss the nature of possible turbulent motions. Reasons are given for believing that isothermal flow is very similar to that of a Newtonian fluid, and the theory is developed for turbulent pressure flow along a channel and a circular pipe. The predicted variation of flow rate with pressure gradient is in good agreement with experimental measurements for Reynolds numbers (based on tube diameter and normal fluid viscosity) above 1400, and it is likely that turbulent flow can exist only above this critical Reynolds number. For Reynolds numbers which are not too small, the equations of motion apply to steady ’laminar’ flow and these lead to a relation between flow rate and pressure gradient in reasonable agreement with experiment.

If the viscosity and specific weight of a fluid are variable, the equations governing its flow in a porous medium are non-linear and in general very difficult to solve. It has been found, however, that steady flows of a fluid of variable viscosity but constant specific weight can be reduced to those of a homogeneous fluid by a remarkably simple transformation, which indicates that the flow patterns of the fluid are the same as those of a homogeneous fluid with the same boundary conditions, and that only the speed need be modified. The speed of the actual flow is obtained by dividing the speed of the homogeneous-fluid flow by a factor proportional to the actual viscosity. The transformation is also used to derive the equations governing steady two-dimensional flows and steady axisymmetric flows of a fluid of variable viscosity and specific weight. In a good many cases of practical importance these equations are exactly linear, in spite of the fact that the governing equations obtained without the use of the above-mentioned transformation are non-linear. An exact solution for a steady two-dimensional flow with prescribed boundary conditions is given. Two inverse methods for generating exact solutions for two-dimensional flows are presented, together with two illustrative examples. The theory also applies to Hele-Shaw flows, so that it can be easily verified in the laboratory.

The flow engendered by the steady motion of a cylindrical insulator through an inviscid, incompressible fluid of small conductivity σ is not close to potential flow when the applied magnetic cross-field H0 is sufficiently strong. Here we determine the limiting form of this flow as σ → 0 with $\sigma H^2_0 \rightarrow \infty$, the latter representing the ponderomotive force.

The limit equations do not have a unique solution, but it is possible to make a selection by taking into account the inertia of the fluid during the limiting process, i.e. without recourse to considerations of how the motion was set up from rest. The forces on the cylinder are found to be asymptotically proportional to $\surd {\sigma} H_0$.

The case of an elliptic cylinder and that of a flat plate are worked out in detail.