The transfer of energy through a dissociated diatomic gas in Couette flow is considered, taking oxygen as a numerical example. The two extremes of chemical equilibrium flow and chemically frozen flow are dealt with in detail, and it is shown that the surface reaction rate is of prime importance in the latter case. The chemical rate equations in the gas phase are used to estimate the probable chemical state of the gas mixture, this being deduced from the ratio of a characteristic chemical reaction time to a characteristic time for atom diffusion across the layer. The influence of the surface reaction appears to spread outwards through the flow from the wall as gas-phase chemical reaction times decrease. For practical values of the surface reaction rate on a metallic wall, the energy transfer rate may be significantly lower in chemically frozen flow than in chemical equilibrium flow under otherwise similar circumstances.

Similar phenomena to those discussed will arise in the more complicated case of boundary layer flows, so that a treatment of the simpler type of shear layer represented by Couette flow may be of some value in assessing the relative importance of the various parameters.

This paper examines the flow characteristics of a body of small slope planing at high Froude number over a water surface. An equation is obtained relating the slope of the planing surface to an integral containing the pressure distribution on the planing surface. The equation is expanded for large Froude number and a solution is obtained by an iteration process. At each stage of the iteration process the integral equation of ordinary thin aerofoil theory is solved. The pressure distribution on the planing surface is derived as a series in inverse powers of the Froude number F, as far as the F−4 term. Computations are performed for the planing of a flat plate, a parabolic surface, and a suitable linear combination of these shapes which results in a flow without a splash at the leading edge.

The subterranean mixing in permeable media of sea water and ground water is studied. The model for this mixing process which was suggested by C. K. Wentworth is adopted, but is soon discarded in favour of a more tractable formulation whose equivalence to the original model is established. The analysis is carried to the point where the determination of the salinity distribution of the ground water in a given subsoil requires only the solution of an elementary linear ordinary differential equation.

A mechanism is proposed by which cellular convective motion of the type observed by H. Bénard, which hitherto has been attributed to the action of buoyancy forces, can also be induced by surface tension forces. Thus when a thin layer of fluid is heated from below, the temperature gradient is such that small variations in the surface temperature lead to surface tractions which cause the fluid to flow and thereby tend to maintain the original temperature variations. A small disturbance analysis, analogous to that carried out by Rayleigh and others for unstable density gradients, leads to a dimensionless number B which expresses the ratio of surface tension to viscous forces, and which must attain a certain minimum critical value for instability to occur. The results obtained are then applied to the original cells described by Bénard, and to the case of drying paint films. It is concluded that surface tension forces are responsible for cellular motion in many such cases where the criteria given in terms of buoyancy forces would not allow of instability.

A shock wave is generated by a uniform compressive piston motion and passes into a channel of slowly varying cross-section. A relation in closed form is obtained between shock strength and the area of the channel and is used to discuss converging cylindrical and spherical shocks.

A simple mathematical model is proposed to describe the steady melting of a body of ice which presents a plane surface transverse to a stream of hot air; the temperature of the air is such that vaporization does not occur.

The analysis takes into account the convection of heat away from the surface by the water released in melting and the results show that the rate of transfer of heat to the body and thus the rate of melting, is reduced by as much as 46% by this convection.

Simple approximate expressions are obtained for the rate of melting, the thickness of the water layer, and the thickness of the thermal boundary layer in the ice, in terms of a basic parameter S which can be calculated in terms of known quantities. These results are compared with those obtained by a separate Pohlhausen calculation and are found to be in good agreement.

It is also shown that there exists a thermal boundary layer, in the body, of thickness much greater than that of the boundary layer in the air, in which the temperature changes rapidly from its value at the melting surface to its value in the far interior.

A direct current electric arc has been developed as a heating device for argon gas. Negligible amounts of electrode material are consumed during an operating time of several minutes. Under normal operating conditions 50% to 90% of the input electric power is transferred directly to the gas. The remaining power is absorbed by the water-cooled electrodes. Measurements were made to determine the total gas enthalpy and the proportion of the enthalpy in directed kinetic energy, random particle motion, and ionization energy. From these measurements it is postulated that the gas is initially in a non-equilibrium state on leaving the arc, but approaches equilibrium relatively quickly when confined to a constant diameter jet outside the arc. The gas temperature range in these experiments varies from 5000°K to 15000°K.

A formal solution to the initial value problem for a plane vortex sheet in an inviscid fluid is obtained by transform methods. The eigenvalue problem is investigated and the stability criterion determined. This criterion is found to be in agreement with that obtained previously by Landau (1944), Hatanaka (1949), and Pai (1954), all of whom had included spurious eigenvalues in their analyses. It is also established that supersonic disturbances may be unstable; related investigations in hydrodynamic stability have conjectured on this possibility, but the vortex sheet appears to afford the first definite example. Finally, an asymptotic approximation is developed for the displacement of a vortex sheet following a suddenly imposed, spatially periodic velocity.