Similar solutions of the boundary layer equations for incompressible flow with external velocity u1 ∞ xm and suction velocity υw ∞ x(m-1)/2 are obtained for negative values of m, in the range −0-1 to −0-9, and a wide range of suction quantities.

The results are used, in combination with, existing solutions for positive m, to provide a guide to the ranges of m and suction parameter [(υw/u1√x] for which a general form of the classical asymptotic solution can be regarded as a good approximation to the exact solution.

It is shown that the values of both m and suction parameter are generally important in this comparison, but for values of the latter greater than about 8 the approximation is a very good one for all values of m considered. For m≃−0·14 the approximation is good (i.e. the error is less than about 1 per cent) down to values of the suction parameter as low as 1·0.

The paper describes an “explicit” method of predicting the flow properties of a turbulent boundary layer; particular attention is paid to the region in which the growth of the layer is characterised by the decay of a velocity maximum. The validity of the method is tested against the data of Wieghardt and against new data of the present authors; it is shown to be satisfactory. The integral flow properties predicted by the method are used, together with a further assumption, to predict velocity profiles; these closely resemble the measured ones.

Simple expressions are derived for predicting the spread of turbulent jets issuing into parallel moving airstreams. Difficulties with applying these expressions to practical problems are discussed and comparisons with experimental results are given.

It is shown that considerable improvement is achieved in the most popular classical approach to the vibration of structural members by giving new meaning to the generalised coordinate term in the infinite series expansion of the product of the generalised coordinate and eigenfunction. A transform employing the eigenfunction as a kernel efficiently generates a universal solution that embraces arbitrary loading, time-dependent boundary conditions, and such in-span conditions as supports and changes in cross section, axial load, and elastic foundation modulus. The method is applied to the Timoshenko beam as a representative structural member.

An earlier paper described a method of calculating the turbulent boundary layer flow over the rear of an infinite swept wing. It made use of an entrainment equation and momentum integral equations in streamwise and cross-flow directions, together with several auxiliary assumptions. Here the method is adapted to the calculation of the turbulent boundary layer flow along the attachment line of an infinite swept wing. In this case the cross-flow momentum integral equation reduces to the identity 0 = 0 and must be replaced by its differentiated form. Two alternative approaches are also adopted and give very similar results, in good agreement with the limited experimental data available. It is found that results can be expressed as functions of a single parameter C*, which is evidently the criterion of similarity for attachment-line flows.

Flight tests on the Handley Page suction wing showed that turbulence at the wing root can propagate along the leading edge and cause the whole flow to be turbulent. The flow on the attachment line of a swept wing was studied in a low speed wind tunnel with particular reference to this problem of turbulent contamination.

The critical Reynolds number, RθL, of the attachment-line boundary layer for the spanwise spread of turbulence was found to be about 100 for sweep angles in the range 40°–60°. A device was developed to act as a barrier to the turbulent root flow so that a clean laminar flow could exist outboard. This device was shown to be effective up to an Rθ of at least 170, so that experiments were possible on a laminar boundary layer at Reynolds numbers above the lower critical value. A spark was used to introduce spots of turbulence into the attachment-line boundary layer and the propagation speeds of the leading and trailing edges were measured. The spots expanded, the leading edge moving faster than the trailing edge, at high Reynolds numbers, and contracted at low values.

The behaviour of Tollmien-Schlichting waves was also investigated by exciting the flow with sound emanating from a small hole on the attachment line. Measurements of the perturbation phase and amplitude were made downstream of the source and, although accurate values of wave length and propagation speed could be found, difficulties were experienced in evaluating the amplification ratio. Nevertheless, all small disturbances decayed at a sufficient distance from the source hole up to the highest available Reynolds number of 170.

In recent papers Messiter and Hida have proposed a first-order correction to simple Newtonian theory for the pressure distributions on the lower surfaces of lifting conical bodies with detached shocks. The method involves the solution of an integral equation which Messiter solved numerically for thin delta wings, while Hida gave an approximate solution for thick wings with diamond and bi-convex cross-sections. It is shown in the present paper that Hida’s approximate solutions give poor agreement with experiment, and a series of more precise numerical solutions of the equation are given for wings with diamond cross-sections. The pressures, and shock shapes, obtained from these solutions are in very good agreement with experiment at Mach numbers as low as 4·0.

The method has also been extended to Nonweiler wings at off-design when the shock wave is detached from the leading edges. Again the agreement with experiment is good provided the integral equation is solved numerically.