The analysis given previously for predicting the average pressure and length of the region of recirculating flow enclosed by a low-speed turbulent jet, issuing parallel to a flat plate, has been modified to take into account the different rates of entrainment by the two edges of the curved jet, the initial mixing region and the pressure forces near reattachment. There is improved correlation between theory and experiment. The analysis has been applied to the flow due to a jet emerging at an angle to a flat plate, and gives good prediction of the length and average pressure of the recirculation region for a particular value of an entrainment-ratio parameter.

Curvature has a considerable effect on the rates of entrainment, but a first-order mixing-length theory indicates that this need not necessarily be accompanied by a marked deviation in jet velocity profile from that of a plane jet.

The detailed structure of the relaxation region in shock waves in oxygen was investigated using Blackman's experimental results. Oxygen was found to display a behaviour similar in many ways to that found previously for carbon dioxide with the relaxation frequency, as defined by the simple relaxation equation, depending on the departure from equilibrium as well as on temperature. The previous results for carbon dioxide were further analysed by means of a separate relaxation equation for each mode.

The calculation by shock-expansion theory of supersonic aerofoil flow fields with varying entropy is simplified by assuming the flow behind the curved attached shock to be a small perturbation of a simple wave. A characteristic perturbation method is used.

In this paper methods are given for establishing qualitative and quantitative measures of the effects of rotation in supercavitating flows past slender bodies. A linearized theory is developed for steady, two-dimensional flow under the assumption that the flow has a constant rotation throughout. The stream function of the rotational flow satisfies Poisson's equation. By using a particular solution of this equation, the rotational problem is reduced to a problem involving Laplace's equation and harmonic perturbation velocities. The resulting boundary-value problem is solved by use of conformal mapping and singularities from thinairfoil theory. The theory is then applied to asymmetric shear flow past wedges and hydrofoils and to symmetric shear flow past wedges. The presence of rotation is shown to create significant changes in the forces acting on the slender bodies and in the shape and size of the trailing cavities.

The results of an experimental investigation are presented to show that the stability of the steady laminar wake behind a circular cylinder is strongly influenced by the proximity of the walls of the confining experimental equipment.

The small-perturbation theory for steady, inviscid, non-equilibrium flow is extended to include the transonic speed range. The resulting transonic small-perturbation equation for the velocity potential is solved for flow inside a wavy cylinder. It is shown that this solution gives a representation of transition through sonic speed at the narrowest sections of the cylinder. This extension of the theory is applied to non-equilibrium nozzle flow.

Assuming that the Stokes flow past an arbitrary particle in a uniform stream is known for any three non-coplanar directions of flow, then the force on the body to O(R), for any direction of flow, is given explicitly in terms of these Stokes velocity fields. The Reynolds number (R) based on the maximum particle dimension is assumed small. For bodies with certain types of symmetry it suffices merely to know the Stokes resistance tensor for the body in order to calculate this force. In this case the resulting formula is identical to that of Brenner (1961) and Chester (1962). However, for bodies devoid of such symmetry, their formula is incomplete—there being an additional force at right angles to the uniform stream which remains invariant under a reversal of the flow at infinity. As this additional force is a lift force, it follows that the Brenner-Chester formula furnishes the correct drag on a body of arbitrary shape; moreover, this drag is always reversed to at least O(R) by a reversal of the uniform flow at infinity.

Exactly analogous formulae are derived using the classical Oseen equations, and it is shown that although this gives both the correct vector force on bodies with the above types of symmetry and the correct drag on bodies of arbitrary shape, it gives in general an incorrect lift component for completely arbitrary particles.

Finally, the singular perturbation result for the force on an arbitrary body is extended to terms of O(R2log R). This higher-order contribution to the force is given explicitly in terms of the Stokes resistance tensor, and has the property of being reversed by a reversal of the flow at infinity, regardless of the geometry of the body.

These results are collected in the Summary at the end of the paper.

A method developed by Roshko (1953a, b) has been applied to the case of flow round a right-angled elbow, in which the fluid separates at the inner corner at a speed which may be higher than the velocity of the separated flow far downstream. Numerical results have been evaluated and are presented for values of the ratio of the channel widths, downstream to upstream of the elbow, equal to 0·1 and 1·0.

The elbow may be regarded as one half of a two-dimensional representation of an axisymmetric plate valve, on which experiments indicate considerable variation in performance, the discharge coefficient being found to depend to a marked extent on the length of the valve land.

The interaction of a pitching circular disk with the motion induced by the disk in the surrounding fluid is investigated in this paper. MacCamy's (1961) method of simplifying the three-dimensional problem of a circular disk to the two-dimensional problem is found to apply in the present analysis. The integral equation is solved numerically to determine the dependence of pressure, added moment of inertia, and damping coefficient on the frequency of the oscillation.