The changes in stagnation pressure produced by movement of rows, arrays and sheets of vortices are derived. By applying Preston’s result for a single row of moving vortices to continuous vortex sheets, the time mean stagnation pressure downstream of a row of blades with fluctuating circulation is derived. It is shown that if the blade circulation varies due to the potential flow fields of the neighbouring blades then the time mean stagnation pressure may change with location.

For caret waveriders at the design condition the attached shock wave in the plane of the leading edges may correspond to either a strong or a weak oblique shock wave when viewed normal to the edges. In cases when the design shock wave corresponds to the strong oblique shock the off-design behaviour of the wing is not completely understood. In this note some measured results are analysed in an attempt to understand this off-design behaviour.

The method of characteristics and an implicit finite-difference scheme are used to investigate the interaction between the internal flow field and laminar boundary layer in ducts of circular cross-section under the conditions of high Mach number and low Reynolds number. The displacement thickness is added on to the body to form a new “effective body shape” which is used to re-calculate the inviscid flow. Iterations are performed and a solution is obtained when the surface pressures in two consecutive iterations converge to within a specified tolerance. The calculated surface pressures on a 10 degree conical duct placed in a hypersonic stream at M∞=8·34, Re∞=7·5 × 106 and M∞=10·4, Re∞=4·625 × 106 with γ=1·4 show good agreement with experiments. The results are computed for constant wall temperature, using a value of Tw/Tstag=0·23, and the Prandtl number is assumed to be constant and equal to 0·7 throughout the calculations. The type of shock-wave interaction near the axis of symmetry is determined and the computation terminates after the fluid properties behind the reflected shock have been calculated.

The natural frequencies and mode shapes of vibration of cantilever aerofoil cross-section blades of pre-twist angle in the range 0 to 90 degrees are obtained. The beams are 152·4 mm long and the width / thickness ratio is such that they may be regarded as slender. Theoretical frequency ratios and mode shapes of vibration, neglecting shear and rotary inertia effects, are obtained for two sets of beams, one with clockwise pre-twist relative to the root cross-section and the other with anti-clockwise pre-twist. The effect of variation in the value of the centre-of-flexure coordinates upon the natural frequency ratios and mode shapes of vibration is investigated. The theoretical results are compared to corresponding experimental results.

The prediction procedures of Bradshaw and Ferriss and Spalding and Patankar are compared with a wide range of experimental data obtained in turbulent, supersonic, two-dimensional flow. Both procedures are shown to result in satisfactory predictions of mean velocity profiles and wall shear stress in adiabatic-wall situations: in addition, the procedure of Spalding and Patankar is shown to be satisfactory in heat transfer situations. The Bradshaw and Ferriss procedure employs a turbulent energy hypothesis in contrast to the mixing-length assumptions used in the present version of the Spalding and Patankar procedure. The close agreement between the predictions of the two procedures indicates a lack of experimental data obtained in flow configurations with suddenly imposed or relaxed pressure gradients.

Two alternative presentations are given of Patel’s Preston tube calibration. In the first, Δp/τw is tabulated as a function of Δpd2/ρν2; in the second, cf is plotted as a function of Δp/½ρU2 and Ud/ν, so that values of cf, can be read off directly.

A closed-form expression is derived which gives an approximate solution to the lift generated on a two-dimensional thin aerofoil in incompressible flow with a normal velocity component of the form exp [i (ωt–xx+yy)]. The inaccuracy of the solution when compared with other published work is compensated by the simplicity of the final expression, particularly if the result is required for the calculation of the sound power radiated by an aerofoil in a turbulent flow.