The flow of an elastico-viscous liquid contained between two concentric spheres which are rotating with the same angular velocity about axes passing through the centre of the spheres is considered. The angle between these axes is small. The solution is obtained by expanding the velocity components in terms of a small parameter α2, which is usually associated with problems involving oscillatory flows. The analysis is shown to have a direct application to the Balance Rheometer. In particular, it is shown that inertial effects in this rheometer are likely to be very small.

A Symposium on Electrohydrodynamics sponsored by the International Unions of Theoretical and Applied Mechanics and of Pure and Applied Physics was convened at the Massachusetts Institute of Technology, Cambridge, Massachusetts, from 31 March to 1–2 April 1969. Authors from eight countries presented 44 papers to an invited audience of 112. The presentations illustrated the spectrum of scientific and engineering interests in the interactions of electric fields and moving fluids. Papers were grouped in seven sessions with the following titles: Steady flows; Bulk stability and dynamics; Interfacial dynamics: Static and steady-flow equilibria; Interfacial dynamics and stability: Drops; Basic formulation; Generation and other applications; Aerosol charging and dynamics. It is expected that the majority of authors will publish their papers in the formal literature. This brief review gives only an over-view of the Symposium as seen by the author.

A quantitative shallow water simulation technique for aerodynamic noise study is investigated. The technique is employed for the case of a free jet issuing from a nozzle with variable wall roughness.

The experimental results obtained are in remarkably good agreement with the theory. It is concluded that there is great potential for further work in even less well understood areas of aerodynamic noise research.

In this paper the problem of interaction of an oblique blast wave encountering a small bend along a plane wall is studied for the case when relative outflow from the reflected shock is supersonic. A theoretical solution is developed completely with the help of conformal transformations and complex variable techniques. Numerical results showing the pressure distribution along the wall have been obtained for two incident shock strengths.

Consideration is given to the flow of viscous and elastico-viscous liquids contained between two infinite parallel plates which rotate with the same angular velocity Ω about axes normal to the plates but not coincident. In the viscous case, it is shown that a simple exact solution of the relevant equations can be obtained. In the elastico-viscous case, certain formulae are derived which should facilitate the interpretation of experimental results obtained from the Maxwell orthogonal rheometer.

The problem considered is that of a strong shock propagating from a point energy source into a cold exponential atmosphere with radiative heat transfer in the flow behind the shock. The radiation mean free path is taken to be small compared to the shock radius, so that the shock may be treated as discontinuous and the radiative heat flux represented by the Rosseland diffusion approximation. The solution obtained is an approximate one based upon the ‘local radiality’ assumption and integral method previously utilized by Laumbach & Probstein for the case of adiabatic flow. The ‘thin shock’ concepts, which underlie the integral method, are extended to the present case of a radiating flow enabling an approximate integral of the differential energy equation to be obtained. A radiation parameter is developed, which provides an index as to when the effects of radiation may be neglected and the flow taken to be adiabatic. The physical interpretation of this parameter is that of the ratio of a characteristic radiation energy flux to a characteristic kinetic energy flux. When the value of this parameter is less than about 0·1, radiation effects may be neglected. It is shown that, when the radiation mean free path varies as a power of the temperature (Tn), where $n = -\frac{17}{6}$, the infinity of solutions for various polar angles can be transformed into two distinct solutions thereby essentially eliminating the parametric dependence on the polar angle and the atmospheric scale height. For fixed values of the radiation parameter the dependence on the explosion energy and the atmospheric density at the point of explosion is also eliminated. The results presented are for the mean free path–temperature variation indicated, but the technique of solution does not have this restriction, though for other temperature dependences some of the scaling advantages are sacrificed. The solution demonstrates the existence of an independence principle in which the flow becomes isothermal and independent of the detailed radiation mechanism when the radiation parameter becomes large. The limiting results of the present analysis for a uniform density atmosphere correspond quite, well with the exact solutions of Elliott & Korobeinikov. The radiating far field behaviour of the descending shock is shown to approach that for adiabatic flow, and, consequently, the asymptotic adiabatic solution obtained by Raizer is an appropriate limit to the present solution. However, the asymptotic results for the ascending shock show that the radiating flow does not approach an adiabatic one but rather an isothermal one.

The problem of flow from a large reservoir through a circular orifice is formulated by considering the velocity potential and Stokes's stream function as the independent variables and the radial and axial dimensions as the dependent variables, and a finite difference solution is obtained to the resulting boundary-value problem. This inverse formulation has the advantage over a finite difference solution in the physical plane that the region of flow is rectangular and consequently well adapted for minimum logic in programming a digital computer. The inverse finite difference solution is more readily obtained than a comparable solution in the physical plane, even though the inverse partial differential equation and associated boundary conditions are non-linear. The results from the inverse finite difference solution are in close agreement with other most recent results from approximate solutions to this problem.

The inverse method of solution is applicable to other free streamline as well as confined axisymmetric potential flow problems. The essential difference in other problems will be in the boundary conditions.Keywords: Orifice, Finite Differences, Non-linear Partial Differential Equation, Potential Flow.