An analysis has been made of the two-dimensional flow of an incompressible constant-conductivity fluid through an elliptically shaped solenoid containing a constant magnetic field directed normal to the flow plane. The effect of both Hall current and ion slip has been included in the generalized Ohm's law used for the fluid. The analysis is based on a perturbation procedure in two parameters, one being the magnetic Reynolds number Rm and the other the ratio S of magnetic force per unit area to dynamic pressure. Calculations have been carried to the first order in each parameter, and closed-form analytic expressions have been obtained for the force and moment on the solenoid, the current density, stream function, magnetic field and other pertinent physical quantities.

It was found that, to the zeroth order, there is a force but no moment on the solenoid. To the first order in S, where the flow field is modified but the magnetic field is not, there is a moment and a force, the latter being anti-parallel to the zeroth order force. To the first order in Rm, where the magnetic field is modified but the flow field is not, there is a moment but no force. Thus, to the first order the lift to drag ratio is the same as in the zeroth order. Graphs which illustrate some of the effects of angle of attack, fineness ratio of the ellipse, Hall current and ion slip, on the forces and moments are presented.

Shock waves generated in a shock tube by use of hydrogen or helium as a driver gas and air, nitrogen, oxygen or argon as a driven gas have higher velocities than predicted by simple theory when sufficiently large diaphragm pressure ratios are used. Expected shock-tube performance curves have been constructed using the equilibrium Hugoniot for the driven gas, both for the usual model of shock tube flow, which assumes instantaneous diaphragm removal, and for a suggested model based on a finite rupture time for the diaphragm. Agreement between experiment and the latter model is in general good, and the differences are qualitatively accounted for by the pressure waves expected to result from mixing between driver and driven gases at the contact surface. These waves may be either compression or expansion waves, depending on the relative heat capacities of the two gases. The maximum shock strength observed as a shock goes down the tube was found to occur at a distance from the diaphragm which increases with the shock strength, and the strongest shocks were found to be still accelerating at the end of a 42 ft. long shock tube of 3 1/2 in. square cross-section. Diaphragm breaking time has been measured and found to be consistent with the observations on the shock formation distance.

A set of two-dimensional subsonic flows past certain cylinders is obtained using hodograph methods, in which the true pressure-volume relationship is replaced by various straight-line approximations. It is found that the approximation obtained by a least-squares method possibly gives best results. Comparison is made with values obtained by using the von Kármán-Tsien approximation and also with results obtained by the variational approach of Lush & Cherry (1956).

Gravity waves occur on the surface of a liquid such as water, and the manner in which they propagate depends upon its depth. Although this dependence is described in principle by the equations of the ‘exact linear theory’ of surface waves, these equations have not been solved except in some special cases. Therefore, oceanographers have been unable to use the theory to describe surface wave propagation in water whose depth varies in a general way. Instead they have employed a simplified geometrical optics theory for this purpose (see, for example, Sverdrup & Munk (1944)). It has been used very successfully, and consequently various attempts, only partially successful, have been made to deduce it from the exact linear theory. It is the purpose of this article to present a derivation which appears to be satisfactory and which also yields corrections to the geometrical optics theory.

The effects of compressibility on a radial laminar wall jet are investigated. On the assumption that the coefficient of viscosity is proportional to the temperature, it is shown that a similarity solution for the velocity distribution exists, which is expressible directly in terms of the corresponding solution for an incompressible wall jet. For arbitrary Prandtl number the energy equation is studied in detail and solutions are obtained for a variety of temperature conditions.

In this paper transonic small-disturbance theory is applied to a simplified model of the flow near the front of a ducted body. The body is assumed to consist simply of two parallel flat plates which extend from the inlet station to infinity downstream. The velocity far upstream is sonic, and the velocity far downstream in the duct, which is assumed to be known, is slightly subsonic. Air is therefore ‘spilled’ around the intake edges. An analytic solution is found for the resulting flow field up to the ‘limiting Mach wave’, and asymptotic solutions are found for the supersonic flow and for the shock wave far from, and near, the intake edges. The pressure distribution along the outside walls is then known at both ends, and its computation is completed by an empirical procedure. Distributions of pressure along the centre-line and along the inside and outside walls are shown. These results may be used to compute the drag of sharp-edged intakes with a very small frontal area.

The results of calculations of the compression of air by repeated shock waves are compared with the perfect-gas values given by Evans & Evans (1956). The comparison emphasizes the increasing divergence of real from perfect-gas results as shock strengths are raised. The equations relating conditions across a shock wave are obtained in a convenient form for solution using a Mollier diagram.