The usefulness of zero pressure gradient, flat plate closure relations in providing approximate solutions for the boundary layer momentum and energy integral equations is examined. Expressions are obtained for skin friction, surface heat transfer rate and local Reynolds analogy factor under general compressible flow conditions. For laminar flows the predictions are compared with well known similarity solutions, with some exact solutions for non-similar flows and with experimental heat transfer data for high speed flow over a blunt cone. Consideration is also given to situations in which the surface temperature is a function of position. For turbulent flow situations comparisons are made with experimental data obtained from two-dimensional and axi-symmetric tests. Conditions vary from low Mach number incompressible flows through to high Mach number compressible flows with highly cooled walls. Some comparisons are also made with other prediction techniques.

A simple closed-form formula for the coefficient of surface pressure, Cp is given in this paper. The formula is based on first and second approximations of the full problem and can be used for the Newtonian flow past two-dimensional thin airfoils at small angles of attack and with attached shock waves. It thus extends Cole's zero order theory to the effects of non-zero (γ – 1) and finite values of Mx where γ is the ratio of the specific heats of the gas and Mx is the free stream Mach number. The analysis presented relies on a previous recent formulation of the hypersonic small disturbance theory which has proved to be more advantageous than the hypersonic small disturbance theory. The results are compared with other approximate methods and the agreement is found to be generally good.

An inviscid model for a steady two-dimensional aerofoil-spoiler at low speeds is applied to an aerofoil-spoiler-plain flap configuration. The model is extended to an aerofoil-spoiler-slotted flap configuration. The flow through a slotted flap can result in either attached flow or separated flow about the flap. The location of the separation point on the flap has to be assumed, it is taken empirically to fit experimental data. The inviscid model is extended to the aerofoil-spoiler-slotted flap configuration with the spoiler oscillating in small amplitude simple harmonic motion about a mean spoiler angle. Although both the steady and unsteady models for the aerofoil-spoiler-flap configuration are crude, the results look encouraging.