A method is described for obtaining the displacements (and hence the stresses) of a linear elastic system under a given transient load in a more accurate and more expeditious manner than is possible by the standard method. For simplicity, ho account is taken of damping forces in describing the method.

The method is of interest to engineers and others who require to obtain numerical answers to problems of the type described above. It depends upon the fact that in many practical cases of transient loads the inertia forces in the series of normal modes of an elastic system converge rapidly, compared with the series of “normal” loadings in terms of which the spatial distribution of the applied load can be expressed.

From an analysis of the work of Crocco and others, semi-empirical formulae are derived for the skin friction on a flat plate at zero incidence with a laminar boundary layer. These formulae are

for the general case of heat transfer, and

when there is no heat transfer.

The problem of heat transfer and the effect of radiation are discussed in the light of these formula;. The second formula is then utilised in the development of an approximate method for solving the momentum equation of the boundary layer on a cylinder without heat transfer. The method indicates that with increase of Mach number there is a marked forward movement of separation from a flat plate in the presence of a constant adverse velocity gradient.

Following a brief discussion of various methods of measuring combustion efficiency in gas turbine chambers, the superiority in accuracy of applied gas analysis is stated. Factors leading to inefficiencies in combustion are outlined and the exhaust constituents requiring measurement are deduced. The chief difficulty in the past in the application of gas analysis methods to combustion efficiency determination has been the time consumed in actual analysis of samples; at Thornton Research Centre means of overcoming this difficulty have been investigated and several rapid and accurate analytical techniques have been developed and used successfully. These techniques are described, together with other promising methods at present under development. The broad requirements of obtaining exhaust gas samples for analysis are discussed and typical sampling systems described; precautions necessary in applying these systems are given. Formulse for the calculation of combustion efficiency from analytical results, together with any assumptions made, are given in the text and their derivation explained in an Appendix. The techniques described have been developed primarily for use in conjunction with rig testing of aircraft gas turbine combustion chambers; the broader application—for instance, to engine testing—of the principles involved are considered briefly.

This note is concerned with a general and exact solution of the two-dimensional equations of motion of a compressible fluid, which is steady, irrotational and isen-. tropic. The solution arrived at is the generalisation of the Prandtl-Meyer celebrated “wedge solution” to include an expansion around any smooth (or abrupt) convex boundary.

We shall obtain the solution of equations for the most general type of motion in which the Cartesian components of velocity are connected by some functional relation throughout the field of flow.

Taking into account the conditions of continuity, zero rotation and Bernoulli's equation, together with the fundamental assumption, which implies that the components of fluid velocity are each a function of fluid speed only, it is found that the motion is necessarily supersonic.

It is shown that the lines of equal speed, pressure (isobars) and density are all straight lines, although they are not necessarily concurrent as in the original Prandtl-Meyer theory, and further that the component of fluid velocity perpendicular to the isobar is equal to the local velocity of sound.

The extended Prandtl-Meyer solution for the flow past an arbitrary fixed boundary is obtained analytically.