An experimental study of the transition from laminar to turbulent flow in a long 0·248in. I.D. pipe is reported for both water and dilute water solutions of polyethylene oxide which exhibit turbulent flow drag reduction (the Toms phenomenon). The drag-reducing solutions, ranging in effectiveness from near zero to the maximum attainable, are observed to undergo transition in a similar way to the Newtonian solvent in that the solutions exhibit intermittency and the growth rates of the turbulent patches are essentially equal to those of the pure solvent. The growth rate of turbulent patches indicates that drag reduction is associated with the small-scale structure of the turbulence near the pipe wall while patch growth is associated with the larger-scale turbulence in the outer flow. For low-disturbance pipe inlet conditions the strong drag-reducing solutions are observed to undergo transition at lower Reynolds numbers than the pure solvent.

An approximate binary collision procedure is devised for the loaded-sphere molecular model and is used with Bird's direct simulation technique for computer experiments on diatomic gases. The collision procedure is tested by simulating the approach to equilibrium of a constant-speed gas of loaded spheres and good agreement with Jeans's (1904) theoretical prediction is obtained. The procedure is then used to study the structure of normal shock waves in the diatomic gas, giving mean velocity, density and temperature profiles. It is found that the present procedure consumes considerably more computer time than comparable simulations of monatomic gases.

The deformation of a liquid drop immersed in a conducting fluid by the imposition of a uniform electric field is investigated. The flow field set up is due to the surface charge and the tangential electric field stress over the surface of the drop, and the rotationality of the Lorentz force which is set up by the electric current and the associated magnetic field. It is shown that when the fluids are poor conductors and good dielectrics the effects of the Lorentz force are minimal and the flow field is due to the stresses of the electric field tangential to the surface of the drop, in agreement with other authors. When, however, the fluids are highly conducting and poor dielectrics the effects of the Lorentz force may be predominant, especially for larger drops.

Previous analyses of gas and particle motion around bubbles in fluidized beds have concentrated on idealized isolated bubbles. In this paper three non-idealities are considered using the theoretical models of Davidson and Murray. Gas flow patterns are derived for indented and elongated bubbles and for pairs of interacting bubbles. Cloud boundaries are predicted for these situations and some effects on gas-solid contacting are discussed.

The stability of spiral flow between rotating and sliding cylinders is considered. In the limit of narrow gap, a’ modified’ energy theory is constructed. This theory exploits the consequences of assuming the existence of a preferred spiral direction along which disturbances do not vary. The flow is also analyzed from the viewpoint of linearized theory. Both problems depend strongly on the sign of Rayleigh's discriminant, – 2Ωζ. Here Ω is the component of angular velocity, and ζ is the component of total vorticity of the basic flow in the direction perpendicular to the spiral ribbons on which the disturbance is constant. When the discriminant is negative, there is evidently no instability to infinitesimal disturbances, and the spiral disturbance whose energy increases at the smallest R is a roll whose axis is perpendicular to the stream. This restores and generalizes Orr's non-linear results for disturbances having a preferred spiral direction. When the discriminant is positive, the critical disturbances of linear theory and the modified energy theory are spiral vortices. The differences between the energy and linear limits can be made smaller in the restricted class of disturbances with coincidence achieved for axisymmetric disturbances in the rotating cylinder problem in the limit of narrow gap. For the sliding-rotating case, the critical disturbance of the linear theory appears as a periodic wave in a co-ordinate system fixed on the outer cylinder. This wave has a dimensionless frequency equal to - ½ a sin (χ-ψ), where a is the wave-number, χ is the angle between the pipe axis and the direction of motion of the inner cylinder relative to the outer one, and ψ is the disturbance spiral angle.

Instability limits, frequencies and wave-numbers are computed numerically when the cylinder gap is not narrow. These are in even closer agreement with Ludwieg's experimental results than the approximate results which were given in part 1.

The linear initial-value problem of a partially mixed cylindrical wake in a, uniformly stratified fluid is formulated and exact solutions are given for the density and velocity fields inside and just outside the original cylinder. An asymptotic expression for the far-field internal wave radiation is given and the corresponding solutions for a spherical wake geometry are noted. The treatment emphasizes the inadequancy of the usual linear Boussinesq approximation to describe the detailed nature of similar problems, in particular the fully mixed wake-collapse problem.