The method of characteristics is used to numerically analyse the motion of a single solid capsule in a hydraulic horizontal straight pipe. The capsule is assumed to be a point mass and the coaxial-annular-flow model around the capsule is used to derive the boundary conditions for water flow at the capsule discontinuity. The results are compared with experimental measurements which were taken in a pipeline 28 m in length and with an inside diameter of 40 mm. The capsule had wheels to keep its position coaxial with the pipe axis and always had a higher velocity than the water flow. The measurements are explained quite well by the analysis.

The effect of gravity on a statistically homogeneous dispersion of small particles in fluid is to disturb the thermodynamic equilibrium slightly when the Reynolds and Péclet numbers associated with the resulting motion are small. In these circumstances the kinetic coefficients for the sedimentation velocities of two different species of particle should satisfy the Onsager reciprocal relation. It is shown analytically that the explicit expressions for the sedimentation velocities of the two species of spherical particle in a dilute bidispersion at small Péclet number found previously (Batchelor 1982) are in fact consistent with the reciprocal relation. It follows that the known kinetic coefficients for the Brownian diffusion of the particles down concentration gradients in a dilute bidispersion (Batchelor 1983) likewise satisfy the reciprocal relation.

A simple numerical scheme for the calculation of the motion of shock waves in gases based on Whitham's theory of geometrical shock dynamics is developed. This scheme is used to study the propagation of shock waves along walls and in channels and the self-focusing of initially curved shockfronts. The numerical results are compared with exact and numerical solutions of the geometrical-shock-dynamics equations and with recent experimental investigations.

Measurements of the wall shear stress with a floating element and with Preston tubes were conducted in turbulent boundary layers. Sudden application and removal of adverse pressure gradients resulted in boundary layers far from equilibrium. Positive and negative errors of the Preston-tube results were observed for adverse pressure gradients. The negative errors occurred mainly in regions with dτw/dx > 0. The relation between the error, the pressure gradient and the tube size (1.1) suggested by Frei & Thomann (1980) predicts only positive errors for dp/dx > 0. Therefore, it cannot be used for the present pressure distributions and is not as general as was expected. The present results show that indirect methods to determine the wall shear stress should not extend beyond y+ - 3 if accuracies of ± 1% are required for pressure distributions similar to the ones used in the present investigation. Predictions from Ludwieg & Tillmann's relation (4.21) agree to within ± 10% with the present measurements. The Preston-tube readings indicate velocities below the law of the wall in regions with a decreasing adverse pressure gradient. No local parameters could be found that correlated the errors of the Preston-tube results for the large pressure gradients used in the present investigation.