Recently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

The buckling behaviour of elastic beams, plates and shallow shells must often be investigated by calculating the slope at the instant of buckling of a curve relating the applied loading and the deformation parallel to the undeformed middle surface. This paper demonstrates the circumstances under which this slope can be calculated exactly without taking into account changes in the mode shape as the buckle amplitude increases.

Recently Messiter has proposed a first-order correction to simple Newtonian theory for the pressure distribution on the lower (compression) surfaces of lifting conical bodies. Although the basic theory holds for bodies with and without attached shock waves, solutions have so far only been obtained for bodies with detached shocks. In the present paper an approximate method of applying the theory to bodies with attached shocks is given. In spite of the approximations involved the calculated shock shapes and pressure distributions are in good agreement with some exact solutions for flat wings, except near the incidence for shock detachment. Like the detached shock case, the present solution can be applied to Nonweiler wings in certain off-design conditions. The combined results for the detached shock and for the attached shock enable the off-design behaviour of Nonweiler wings to be discussed in a systematic manner.

An experimental study of bow-wave trajectories for a sphere in CO2 has been made in a shock tube, using a drum-camera-schlieren technique, for incident shock Mach numbers of 2·4, 2·8 and 4·0. Results show that vibrational relaxation has only a slight effect on the bow-wave formation time but significantly affects the stand-off distance in steady flow.

The solution has been obtained for the problem of a uniformly compressed and symmetrically loaded circular ring plate of linearly varying thickness. Four particular cases have been discussed and numerical values of the maximum deflection have been obtained for various sizes of the hole of the ring.

A theoretical analysis is presented for a two-dimensional air strut with walls consisting of thin membranes which are joined by many inextensible strings. The strut is deflected through large angles so than an appreciable portion of each membrane is buckled and lies along the solid plates which form the ends of the strut. Numerical solutions are obtained for two cases and, in particular, the resultant force on each end plate is determined.

The wholly supersonic flow past a two-dimensional wedge is analysed on the assumption that release of chemical energy into the stream can be accomplished across a thin discontinuous plane flame front attached to the apex. Forces experienced by the wedge are calculated and representative flow patterns exhibited. Some typical interactions between the flame and shocks or centred simple waves are discussed, with emphasis on the use of pressure-flow-deflection diagrams to obtain results.

General solutions for two-dimensional incompressible potential flow occurring between two equipotential planes perpendicular to the x-axis are given. The first form is the two-dimensional analogue of Thwaites’s solution for axisymmetric flow and allows the calculation of the flow when the axial velocity distribution is specified as a Fourier cosine series in x. The second form of solution, obtained by “inverting” the first form, allows the calculation of the flow when the shape of the “boundary streamline” is specified by a similar series in the velocity potential ϕ.

It is shown how the second form of solution may be utilised to design contracting channels between equipotential planes. The computation of the contraction shapes and velocities is straightforward. In particular, contractions are derived from smoothing conditions similar to those used by Thwaites, and from a flow having a single (ϕ, y) step-discontinuity. It is shown in the Appendix that the latter flow possesses a closed form representation in terms of elliptic functions.