Preston's method of measuring skin friction, which makes use of a Pitot tube resting on the surface, depends upon the assumption of a region of flow similarity, adjacent to the wall, common to fully developed turbulent pipe flow and the turbulent boundary layer. Experiments performed elsewhere have cast considerable doubt on the validity of this assumption, and the present investigation was undertaken to establish whether or not it is justified.

Experiments were carried out in a short length of large-diameter pipe which could either form part of a very much longer pipe, giving fully developed turbulent pipe flow, or could be preceded by a conventional contraction and screens, giving a developing turbulent boundary layer.

Final results showed that for a given skin friction the Pitot tube reading was the same for both boundary layer and pipe flows, thus vindicating Preston's method and confirming the existence of a universal region of wall similarity. Initial experimental difficulties were found to be due to unexpectedly large circumferential variations in skin friction in the growing boundary layer.

Vortex-tube flows have been examined which lack the relatively quiescent, nearly isothermal, core common to those studied by other authors.

Observations were made of the vortex motion which occurs when a liquid is draining from a vessel through a hole in its bottom. It was found that, for relatively quiescent initial conditions, the direction of rotation reversed as the liquid surface approached the bottom of the vessel. An explanation of this phenomenon is proposed which is based upon the vorticity associated with the circumferential component of the flow in the boundary layer on the bottom of the vessel.

Under certain conditions, the motion caused in an annulus of fluid by rotating it about its (vertical) axis of symmetry and at the same time subjecting it to a radial temperature gradient has been shown by Hide (1958) to be mostly concentrated in a narrow jet stream which meanders between the inner and outer cylindrical boundaries of the fluid in a regular wave pattern: this wave pattern has a small angular velocity relative to the cylindrical walls containing the fluid. A theoretical solution has been found by Davies (1959) which is valid in the main body of the fluid: this solution neglects viscosity (which is permissible except near the boundaries of the fluid), and is related to the absolute angular velocity of the wave pattern. The present paper introduces viscous boundary layers between the main body of the fluid and the cylindrical walls, in an attempt to find a relation between the angular velocity of the wave pattern and that of the walls. That this is only partially successful is due to the presence of the boundary layer at the rigid surface at the bottom of the fluid (which is rotating with the same angular velocity as the cylindrical walls): this layer is ignored in the present theory. In addition to this contribution towards a complete explanation of the steady motion, the theory describes qualitatively certain periodic oscillations (vacillation) which were observed by Hide in his experiments.

The flow and deformation of single large air and liquid bubbles suspended in wetting liquids when moving under gravity in closed vertical tubes have been studied. The flow patterns in both phases and thickness of the liquid film surrounding the bubbles and the shape of the bubble ends were determined by direct observation through a microscope.

Quantitative agreement with a theory relating bubble velocity to film thickness in viscous flow, and to the tube radius in inertial flow was obtained. In viscous flow the deformation at a given interfacial tension was independent of bubble length and of the viscosity of the suspending liquid.

In viscous flow the end of the sedimenting bubbles were spheroidal, with the leading ends prolate and the trailing ends generally oblate. The axis ratio of the leading ends increased with increasing interfacial tension. Wave disturbances occurred at the trailing ends of the bubbles. In inertial flow the leading ends of rising air bubbles were hemispherical.

The classical theory of the instability of laminar flow predicts the growth (or decay) rate and phase velocity of two-dimensional small disturbance waves. In order to study the growth and dispersion of an originally localized spot-like disturbance, the initial disturbance is built up from all possible simple-harmonic waves. The propagation velocity and amplification rate for each vector wave-number then follows from the two-dimensional theory by Squire's generalization. The initial development can be solved explicitly by a power series in time, and the asymptotic behaviour is also predicted. For times between initial and final periods, exact numerical calculations have been made using an IBM 709 electronic computer. The role which localized disturbances can play in ultimate transition to turbulent motion is also indicated.

Two problems are considered. First, it is shown experimentally that the amount of viscous fluid left on the walls of a horizontal tube, when it is expelled by an inviscid fluid, reaches an asymptotic value of 0.60 of the amount required to fill the tube, when the parameter μU/T is increased, μ and T being the coefficients of viscosity and interfacial surface tension respectively, and U the velocity of the interface between the two fluids. Secondly, by neglecting the inertia terms in the equations of motion and the effect of gravity, a theory for the passage of this type of bubble is presented, together with experimental results in support of the theory. It is shown that such a solution is only valid under certain other restrictions, and then only to within half a tube diameter of the nose of the bubble.

In the thermal convection problem with free boundaries, the interaction of two ‘roll’ disturbances is considered. The problem is reduced to a pair of non-linear ordinary differential equations, which should also provide a model for the interaction of two disturbances in more general situations than that for which these equations have been derived. The equations contain several parameters which necessitates a discussion of various possible types of solution. Some representative results are: (1) under certain circumstances, an equilibrium state may be composed of a mixture of a linearly stable disturbance and a linearly unstable disturbance; (2) for the thermal convection problem, when the Rayleigh number is slightly above the minimum critical value, the equilibrium state will contain only one of two linearly unstable disturbances. These and other results are compared with experimental observations.

An apparatus is described for determining particle passages through any selected point on a tube cross-section. The method depends on the simultaneous blocking out of two mutually perpendicular light beams by a particle passing through their common region. The coincidence is registered and counted electronically. At higher particle concentrations coincidences are also registered arising from a pair-wise occupation of the light beams by two particles. An analysis is presented showing that these pair coincidences can be allowed for exactly in terms of experimentally measurable quantities.

The reliability and reproducibility of the method is discussed and illustrated by examples from sphere suspensions in Poiseuille flow.

It is shown that a rigid sphere transported along in Poiseuille flow through a tube is subject to radial forces which tend to carry it to a certain equilibrium position at about 0.6 tube radii from the axis, irrespective of the radial position at which the sphere first entered the tube. It is further shown that the trajectories of the particles are portions of one master trajectory and that the origin of the forces causing the radial displacements is in the inertia of the moving fluid. An analysis of the parameters determining the behaviour is presented and a phenomenological description valid at low Reynolds numbers is arrived at in terms of appropriate reduced variables. These phenomena have already been described in a preliminary note (Segré & Silberberg 1961). The present more complete analysis confirms the conclusions, but it appears that the dependence of the effects on the particle radius go with the third and not the fourth power as was then reported.

It is also shown that the description of the phenomena becomes more complicated at tube Reynolds numbers above about 30.