This paper presents an experimental investigation of the displacement of the total-head profile in a shear flow from its true position when it is measured with a flat-ended round Pitot tube. The experiments showed that at least two forms of displacement may exist depending on the flow conditions.

In a wake the displacement of the effective centre of pressure towards the higher velocity was found to obey the law deduced theoretically by Hall (1956), provided that changes in flow direction were not large. In the presence of large eddies the behaviour of the Pitot is further modified by its characteristics in yaw. This introuduces a total-head error reducing the observed total head.

In a turbulent boundary layer the experiments showed that the displacements were an order of magnitude smaller than in a wake and could be regarded as negligible for a round Pitot, even when it was touching the wall.

An empirical method for correcting the observations made with a round Pitot which is of the same width as the wake is given in an appendix.

This paper describes theoretical and experimental studies of the effects on shock tube flows of a monotonic convergence at the diaphragm section. Systematic flow equations are developed for tubes of uniform bore and tubes having either a monotonic convergence or a convergence-divergence in the diaphragm section. Except across the shock front itself, isentropic processes and ideal-gas behaviour have been assumed. Simplified procedures are presented for predicting the ideal-flow parameters over a wide range of operating conditions, as well as for comparing straight and convergent tubes. Such comparisons made by other investigators are found to be incomplete or in error. The experiments described utilize a very simple device for altering the diaphragm section convergence and a multi-station measurement of shock velocity. The expected effect of convergence is verified over a wide range of Mach numbers. Even at Mach numbers where the processes of shock formation can no longer be ignored, it is found that the relative performance between a uniform and convergent tube is preserved.

The boundary layer on a hot flat plate which is fixed at zero incidence in a slow stream carrying a progressive sound wave is investigated. Formulae are obtained for the skin friction and the heat transfer in the extreme cases when the frequency is very low and very high. In addition, different methods of simplifying the boundary layer equations in unsteady compressible flow are briefly compared.

The linearized equations of motion show that in a viscous heat-conducting compressible medium three modes of fluctuations exist, each one of which is a familiar type of disturbance. The vorticity mode occurs in an incompressible turbulent flow, the entropy mode is familiar as temperature fluctuations in low speed turbulent heat transfer problems, and the sound mode is the subject of conventional acoustics. A consistent higher order perturbation theory is presented with the only restrictions being that the Prandtl number is 3/4 and the viscosity and heat conductivity are monotinic functions of the temperature alone. The theory is based on expansion of the disturbance fields in powers of an amplitude parameter α. The non-linearity of the full Navier-Stokes equations can be interpreted as interaction between the three basic modes; in order to help physical insight the interactions are classed as ‘mass-like’, ‘force-like’, and ‘heat-like’ effects.

Besides the amplitude parameter α there is another subsidiary non-dimensional parameter ε which indicates the relative importance of viscosity and heat conduction effects as compared to the inertial effects, ε is proportional to the ratio of the molecular mean free path and the characteristic length of the flow pattern (Knudsen number). The main contribution of the paper is the outline of a consistent successive approximation for an arbitrary order in α and the presentation of explicit formulae for the second order (bilateral) interactions.

A special case of rather general significance is treated in more detail. This is when all three basic modes have intensities and length scales of the same orders of magnitude and in addition to α the parameter ε is also small; the second-order interactions are then relatively few and easily identifiable and are shown in table 1.

The present analysis also sheds some light on the ‘zero order’ approximation which treats the vorticity and entropy disturbances as a ‘frozen pattern’ and the sound field as propagating nondissipative waves. The interpretation of hot-wire measurements relies heavily on these simplified models and the present paper lends some support to these current hot-wire practices.

A simple approximate model is set forth for the flow field between the nose of a blunt body of revolution and its detached shock wave. The model tends to explain the poor convergence of Chester's solution, which is based on an improvement of the Newtonian approximation. It suggests a modification of his series for the body shape which appears to improve its convergence considerably.

Experiments have been performed with a viscous fluid contained in a rotating cylinder heated from below. Previous theoretical explanations of the flow patterns obtained in these experiments assumed that the convective terms in the heat transfer equation were negligible. The present paper gives a treatment which includes one of these convective terms. The results confirm the physical reasoning that, when the laps rate is positive, the stability is increased and that the motion is therefore decreased.

Differentiation of the Hugoniot function $H (p,v) = E(p,v)-E(p_0,v_0)+\frac {1}{2}(p + p_0)(v_0 - v)$ and use of the first and second laws of thermodynamics leads to the relation dH = T dS+dA, where dA is the element of area in the (p, v) plane swept out (in a counter-clockwise direction) by the line segment (p0, v0) → (p, v) as the point (p, v) is moved from some point (p1, v1) to a neighbouring point (p1+dp1, v1+dv1). This relation, together with rather general assumptions regarding the shape of the isentropic curves dS = 0 for the material behind the shock, makes possible the geometrical derivation of a number of properties of the function H and of the Hugoniot curves dH = 0.