The peeling of a flexible strip from a rigid surface to which it is attached by a thin layer of adhesive is discussed, treating the adhesive as a Newtonian viscous fluid. This makes it possible to examine the flow and stress distributions ahead of the point where separation occurs. The conditions at this point are taken to be the same as those observed in other cases where a stream of viscous fluid separates into two. In particular, the effect of surface tension at the separating meniscus on the speed of peeling is predicted.

Experiments are described in which a sheet of ‘Melanex’ 4μm thick was laid on a sheet of fluid covering a piece of plate glass. The apparatus was designed to ensure that this was peeled off at a constant angle, and the speed of the separation meniscus, as well as the load on the sheet, was measured. The experimental results are analysed in the light of the theory and shown to be consistent with it.

An interesting feature is the prediction that at low peeling speeds there is a great reduction in the thickness of the adhesive layer immediately ahead of the line of separation. Although the initial thickness of the layer dictates the scale of the shape adopted by the strip ahead of this line, it exerts no effect upon the relation between the external variables.

It is noted that, when the adhesive layer remains intact ahead of separation, the physical appearance of commercially available tapes in slow peeling can resemble that of simple viscous adhesives.

In this paper systems of non-linear integral equations are formulated which are equivalent to the Krook kinetic equation for steady problems in two and three space-dimensions. The boundary conditions used are discussed and some of the properties of the equations which are significant in their numerical solution pointed out. This work will then serve as a basis for the consideration of a sequence of particular problems to be presented in subsequent papers.

Measurements of grid turbulence have been obtained for grid Reynolds numbers ranging from 2·4 × 106 to 1·2 × 105. The decay law and the effect of Reynolds number on the turbulence level are established. The measured power spectra of the turbulence are consistent with Kolmogoroff scaling for kη > 0·1 (k is the wave-number and η is the Kolmogoroff length); but for kη < 0·1, the spectra of the stream-wise turbulence velocity component and of the cross-stream component do not appear to be isotropically related. However, the stream-wise spectrum does display a $-\frac{5}{3}$ region, which increases in extent with increasing Reynolds number.

Calculations are presented for two-dimensional Bénard convection between free bounding surfaces for ranges of Rayleigh and Prandtl numbers. The variables are expanded in a series consisting of the eigenfunctions of the stability problem and the system is truncated to take into account only a limited number of terms. The amplitudes of the eigenfunctions are evaluated by numerical integration of the resulting non-linear equations. In all cases considered, the system achieves a steady state with the motion consisting of a single large cell. Results for Nusselt number vs. Rayleigh number are given for a range of Prandtl number varying between 0·01 and 100 and show that heat flux increases slightly with decreasing Prandtl number. The calculations agree with those of Kuo where the ranges of Rayleigh number overlap. A simple heuristic argument based on the assumption that turbulent boundary layers exist is also given and the conclusions of the latter indicate that heat flux should decrease with decreasing Prandtl number. Thus the behaviour is qualitatively different from that of the calculations. The reason appears to be associated with the fact that the single large cell in the computed cases enables the fluid to accelerate through repeated cycles until it achieves a steady state with the amplitude of the motion much larger than could be acquired by a single turbulent blob free-falling in the gravitational field.

The problem of flow through rotating channels of almost arbitrary cross-section is considered. It is shown that when the ratio of the Rossby number and the Reynolds number is small (ε = Ro/Re [Lt ] 1) and when the Reynolds number is not too large (Re [Lt ] ε−1): (1) the viscous effects are important only in thin boundary layers along the channel walls; (2) the flow in the interior is geostrophic; and (3) the inertia effects may be neglected everywhere. Solutions for the geostrophic region and the boundary layers are obtained and are combined to give the complete velocity field. Experimental results for a circular conduit are presented which are in good agreement with the theory.

The problem solved concerns the disturbance to a stream of shallow water due to an immersed slender body, with special application to the steady motion of ships in shallow water. Formulae valid to first order in slenderness are given for the wave resistance and vertical forces at both sub- and supercritical speeds. The vertical forces are used to predict sinkage and trim of ships and satisfactory comparisons with model experiments are made.

The incompressible viscous flow along a right-angle corner, formed by the intersection of two semi-infinite flat plates, is considered. The effect of the three-dimensional geometry on the second-order ‘boundary layer’ flow away from the corner is determined and an interesting secondary flow is deduced. It is observed that this cross-flow prescribes the necessary asymptotic boundary conditions for the equations governing the flow inside the ‘corner layer’. A systematic matching scheme is specified and the corner flow problem is reformulated in terms of the ‘corner layer-boundary layer’ matching conditions.

A series of flat-plate laminar boundary layer experiments carried out in an arc-heated supersonic wind tunnel is described. Measurements of the static pressure distribution, the total pressure profiles through the boundary layer, and the heat-transfer rates to catalytic and non-catalytic surfaces at moderately high enthalpies are given and compared with various theoretical predictions. The observations indicate that the dissociation fraction affects the boundary-layer profiles through its influence on the local transport properties. It is confirmed that the atomic recombination at the surface is retarded by using a non-catalytic oxide coating, and hence the heat transfer to the wall is reduced.

The dynamical properties of a fluid, occupying the space between two concentric rotating spheres, are considered, attention being focused on the case where the angular velocities of the spheres are only slightly different and the Reynolds number R of the flow is large. It is found that the flow properties differ inside and outside a cylinder [Cscr ], circumscribing the inner sphere and having its generators parallel to the axis of rotation. Outside [Cscr ] the fluid rotates as if rigid with the angular velocity of the outer sphere. Inside [Cscr ] the fluid rotates with an angular velocity intermediate to the angular velocities of the two spheres and determined by the condition that the flux of fluid into the boundary layer of the faster-rotating sphere is equal to the flux out of the boundary layer of the slower-rotating sphere at the same distance from the axis. The return of fluid is effected by a shear layer near [Cscr ] and we show that it has a complicated structure for it can be divided into three separate layers, two outer ones, of thickness $\sim R^{-\frac{2}{7}}$ and ∼R−¼, and an inner layer of thickness $\sim R^{-\frac{1}{3}}$.

The characteristics of the laminar boundary layer on a continuous moving surface are described and an experiment is performed to demonstrate that such a flow is physically realizable. The hydrodynamic stability of the flow is analysed within the framework of small-perturbation stability theory. A complete stability diagram is mapped out. The critical Reynolds number is found to be substantially higher than that for the Blasius flow and, correspondingly, the critical layer lies closer to the wall. The disturbance amplitude function and its derivative are numerically evaluated, from which are derived the vector flow field of the disturbance, the resultant flow field (main flow plus disturbances), the root-mean-square distributions of the disturbance velocity components, and the distributions of the kinetic energy and the Reynolds stress. The energy criterion for stability is also investigated and is found to be consistent with the solutions of the eigenvalue problem.

A method is proposed for obtaining regular solutions of the boundary-layer equations near a point of vanishing skin friction for steady incompressible laminar two-dimensional flow. The boundary-layer equations are integrated numerically in the usual way until the separation point is approached; then the displacement thickness is prescribed as a regular function of the distance along the surface, leaving the pressure gradient to be calculated from the consequent solution. Numerical solutions are obtained with reversed flow and shallow separation bubbles inside the boundary layer without the occurrence of a singularity at the separation point.

Experimental evidence suggests that it may be profitable to separate the discussion of the high-frequency components of jet noise from low-frequency components. Theory then leads one to the recognition that the physical mechanism of noise generation is slightly different for the two components and for this reason one may speak of high-frequency ‘self noise’ and low-frequency ‘shear noise’ (Lilley 1958; Ribner 1964).

Both theory and experiment indicate that mean-flow refraction effects on self noise are appreciable. Using geometrical acoustics a description of the far-field radiation pattern of the high-frequency end of the jet-noise spectrum is obtained, in good qualitative agreement with observations. A conservation law of acoustic energy, applying between the frame of reference in which the sound sources move, and the fixed frame in which the observations are carried out, results in the absence of the convection amplification effect (over and above the U8 law) for total sound power at high frequencies, a result which helps explain the uniform validity of the U8 law.

An analysis of the shear-noise source term suggests that this part of the sound radiation is due to a combination of quadrupoles which have at least one axis parallel to the jet. This then explains the observed concentration of low-frequency noise around the jet axis.

A technique has been developed to measure the instantaneous shear stress at the boundary over which a liquid is flowing. It is being used to study turbulence in the immediate vicinity of a pipe wall. A reaction is conducted on an electrode mounted flush with a solid wall at high enough voltages to reduce the concentration of the reacting species to zero at the surface. Under these conditions, the rate of reaction is controlled by the rate of mass transfer. The electrode is analogous to a constant-temperature hot-wire anemometer in that the surface concentration is kept constant and the current flowing in the circuit is related to the surface shear stress. For fully developed turbulence the limiting velocity intensity, based on the local average velocity, is 0·32. Some of the velocity fluctuations are as large as the local average velocity and their distribution is nearly symmetric about the average. The ratio of the longitudinal to circumferential scale is about 30 : 1, because the circumferential scale is very small. There is some indication that close to a wall the velocity fluctuations in the circumferential direction are much smaller than the longitudinal fluctuations.