Steady two-dimensional viscous motion within a circular cylinder generated by (a) the rotation of part of the cylinder wall and (b) fluid entering and leaving through slots in the wall is considered. Studied in particular are moving-surface problems with continuous and discontinuous surface speeds, simple inflow–outflow problems and the impinging-jet problem within a circle. The analytical solutions at zero Reynolds number are given for the last two types of problem. Numerical results are obtained at various Reynolds numbers from the integral representation of the solution. At zero Reynolds number this approach involves a quadrature around the circumference of the cylinder. At other Reynolds numbers it involves an iterative–integral technique based on the use of the ‘clamped-plate’ biharmonic Green's function.

Self-diffusion coefficients were determined experimentally for lateral dispersion of spherical and disk-like particles in linear shear flow of a slurry at very low Reynolds number. Using a concentric-cylinder Couette apparatus, recurrent observations were made of the lateral position of a particular radioactively labelled particle. The self-diffusion coefficient D was calculated by means of random-walk theory, using the ergodic hypothesis. Owing to great experimental difficulties, the calculated values of D are not of high accuracy, but are correct to within a factor of two. In the range 0 < ϕ < 0·2, D/a2ω increases from zero linearly with ϕ up to D/a2ω ≅ 0·02 (where ϕ = volumetric concentration of particles, a = particle radius, ω = mean shear rate of suspending fluid). In the range 0·2 < 0·5, the trend of D/a2ω is not clear because of experimental scatter, but in this range D/a2ω ≅ 0·025 to within a factor of two. Within the experimental accuracy, spheres and disks have the same value of D/a2ω.

Work recently reported by the authors (Perry & Abell 1975) on smooth-walled pipe flow showed support for the Townsend (1976) structural similarity principle as regards viscosity not being directly relevant in controlling the mean relative motions and the energy-containing turbulent motions. The work also supported a universal spectral behaviour in the wall region of the flow. In many hypotheses for rough-walled pipe flow, surface roughness, like viscosity, enters the problem only via external boundary conditions. Data obtained in a rough pipe are reported here and on first appearance the results seem to contradict the Townsend hypothesis and to threaten the very foundation upon which many similarity laws for rough-walled flows are based. However, on closer examination of the spectrum scaling of smooth-walled pipe flow the low and high wavenumber energy not necessarily associated with the universal similarity range can be accounted for. The broad-band longitudinal turbulence results for a rough-walled pipe can then be predicted from the smooth-wall scaling. The conclusion is that, despite the apparent anomalies, the turbulence structure in a rough pipe appears to follow the same scaling laws as for a smooth pipe, given a sufficient length of flow development in both cases. The deduced functional forms are consistent with Townsend's (1976) attached-eddy hypothesis.

A Lavrentiev model of the flow about a blunt two-dimensional body with a separation bubble is considered. Physical bases of the model are discussed in relation to other wake models. The Lavrentiev wake bubble contains a pair of closed free streamlines enclosing the regions of vorticity. It is shown, by means of conformal mapping, that the complex potential can be expressed in terms of elliptic functions, and a one-parameter family of exact solutions has been constructed for a normal flat plate and truncated wedges, for both an unbounded and a bounded stream. A procedure for relating the value of the parameter to the Reynolds number of the real fluid flow is indicated.