A calculation taking into account the interaction of tube wall and ends with a falling sphere is presented, with a view to assessing the change in drag on the sphere due to the end proximity in practical viscometry. It is shown that when the sphere is more than one fall tube radius from the closed end, the extra drag resulting is less than 4·5 × 10−3 of the Faxèn drag, and is therefore usually negligible.

For smaller end-sphere distances the end-effect drag increases rapidly, reaching about 1·5 of the Faxèn drag when the sphere centre is 0·25 tube radius from the end. The drag curve lies substantially below that given by Ladenburg (1907). Satisfactory agreement with experiment is found. It is concluded that with the commonly used types of fall tubes, end effects due to a closed end and an open surface will not be detectable.

The flow of an incompressible second-order fluid due to torsional oscillations of an infinite plate when the fluid is infinite in extent as well as the case when it is bounded by another stationary parallel plate has been considered by expanding the velocity components and the pressure in powers of the amplitude of oscillation of the plate. In both cases the first-order solution consists of a transverse velocity and the second-order solution gives a radial-axial flow composed of a steady part and a fluctuating part. In the case of the unbounded plate the steady part of the radial flow does not vanish outside the boundary-layer region. Hence the equations are solved by another approximate method for the steady part of the flow. The effects of the non-Newtonian terms are to increase the non-dimensional boundary thickness and the shearing stress on the plate. In the case of two plates the velocity components and the shearing stresses on the plates have been expressed in powers of Reynolds number R for its small values. Their asymtotic behaviour for large R has also been studied. The asymtotic expansion of the fluctuating part of the radial-axial flow shows that the boundary layer is developed at both the plates.

The electrical conductivity of shock-ionized argon produced in an electromagnetic shock tube of low attenuation has been measured at shock speeds of March 10–33, with initial pressures of 0·01–2·0 mm Hg. These measurements extend considerably the range of previous measurements performed with pressure-driven shock tubes. With the higher initial pressures or at the highest Mach numbers the measured conductivity is in good agreement with the previous measurements and with the Spitzer–Harm (1953) formula for the conductivity of a fully ionized gas. With the lower initial pressures (which have not previously been investigated) and at the lower March numbers the conductivity falls to less than half of the Spitzer-Harm value. Order-of-magnitude calculations show that diffusion of atoms, and heat conduction by the plasma atoms from the plasma to the shock-tube walls, can cause appreciable plasma cooling (and hence a reduction of the electrical conductivity) with the lowest initial pressures. This mechanism in conjunction with non-attainment of equilibrium ionization appears to explain the observed diminution in conductivity at the lowest pressures, but not the reduced conductivity at the medium pressures.

Induced e.m.f. flow-velocity measurements indicate steady-flow conditions in the shock tube while photomultiplier measurements of the plasma radiation indicate that the column of shock-heated gas is 10–20 cm long; this latter figure is supported by the conductivity measurements. The fact that the length of the shock-heated gas column is not drastically shortened at low initial pressures in constrast to the work of Duff (1959), Roshko (1960) and Hooker (1961) is attributed to the fact that in this experiment both driver and driven gases are at high temperature.

Smooth- and rough-wall boundary layers and fully developed pipe and duct flow investigations are reviewed. It is shown that the effect of roughness on the flow away from the wall can be accounted for by using an equivalent viscosity νe. This viscosity is thought to depend only on the variables at the wall, such as shear stress τ0, fluid density ρ, viscosity μ and the roughness size and geometry and that the relationship between these variables is the same for both boundary layers and duct flow. However, experiments to date have been confined to the ‘rough régime’ and to boundary layers with a zero pressure gradient.

Experiments were performed and the results show that the above finding can be extended to boundary layers with adverse pressure gradients in the rough régime.

A general method for measuring the local boundary-layer characteristics, with roughness and pressure gradients present, is developed.

The process of mixing at the top of a turbulent cloud layer contains a new feature which has not been considered in previous studies of mixing; evaporation of liquid water can cause density changes which may affect the dynamics. A model experiment has been devised to study this problem, using liquids whose density behaviour is non-linear to simulate evaporation.

The existence of a moist, stable, turbulent region above cloudtop can be explained using the laboratory results, which suggest that this region can be regarded dynamically as part of the cloud. Comparison of the rates of mixing in the model experiments with and without ‘evaporation’ suggests that evaporation could cause a small decrease in the mixing rate for a given density difference, but the change would be negligible in practice. This result also sheds some light on the mechanism of mixing, in both the linear and non-linear cases.

It is shown that in an incompressible fluid in which the magnetic diffusivity λ is much less than the kinematic viscosity ν, certain magnetic field distributions of limited spatial extent (conveniently described as magnetic eddies) can exist on a length scale such that the associated Reynolds number and magnetic Reynolds number are respectively small and large compared with unity. The Lorentz forces are in equilibrium with the dynamic forces associated with the fluid motion. The boundary condition imposed on this motion is that at a large distance from a magnetic eddy the velocity field should be a uniform axisymmetric irrotational straining motion. The eddies are steady in the limit λ → 0, but decay slowly in a fluid of finite conductivity. Two particular eddies are considered in detail: a disk-shaped eddy in a compressive straining motion, and a spherical eddy in an extensive straining motion. Possible applications to turbulence in interstellar gas clouds are qualitatively considered.

The motion of a bounded shallow liquid, initially of arbitrary shape, in an arbitrary state of motion and lying on a paraboloid of revolution (including a level surface as a special case) can always be separated into three parts:

1. the motion of the centre of gravity, which is entirely independent of the other motions and is governed by a pair of simple ordinary linear differential equations;

2. an isotropic two-dimensional dilatation and rotation which are also governed by a simple linear differential equation;

3. the motions that remain after removal of the velocity fields associated with the preceding motions; these will be called additional motions.

The additional motions exert a ‘pressure’, determined by their total energy, which tends to increase the spread of the liquid. If the spread does increase then the additional motions lose energy which then appears as energy associated with the dilatation.

The effect of the dilatation and rotation on the additional motions can be described by transformation into a co-ordinate system that rotates and dilates with the liquid. In these co-ordinates, with a properly adjusted time scale, the additional motions satisfy equations that are isomorphic with the original equations of motion; however, the liquid now appears to be lying on a parabola that is always concave upwards.

Lamb's analysis of small-amplitude, shallow-water oscillations in a rotating paraboloid, interpreted by him in the inconsistent context of an approximately plane free surface, is re-interpreted to obtain results that are valid for $0 \le \omega^2l|2g \; \textless \;1$ (ω = rotational speed, l = latus rectum of paraboloid); no equilibrium is possible for ω2l/2g > 1. It is shown that the frequencies of the dominant modes for the azimuthal wave numbers 0 (axisymmetric motion) and 1 are independent of ω for an observer in a non-rotating reference frame and that the frequencies of all other axisymmetric modes are decreased by rotation (Lamb concluded that they would be increased). An axisymmetric mode of zero frequency, which was over-looked by Lamb, also is found.

Exact solutions to the non-linear equations of motion, which reduce to the aforementioned dominant modes for small amplitudes, are determined. The axisymmetric solution is inferred from similarity considerations and is found to contain all harmonics of the fundamental frequency. The finite motion of azimuthal wave-number 1 is a quasi-rigid displacement of the liquid and is found to be simple harmonic except for a second-harmonic component of the free-surface displacement (but the horizontal velocity at a given point remains simple harmonic).

Previous results on the over-all density ratio of shock waves in CO2, confirming experimentally the theoretical equilibrium value, have been extended to a shock Mach number of 7·3. The discrepancy between our results and earlier Princeton results approaches 18% at a Mach number of 7. Possible reasons for this are discussed, with particular reference to the interferometer technique, but no explanation has been found.

This is a study of the longitudinal and vertical turbulent velocities which were measured both near the surface and near the bottom of an estuarine tidal current. The turbulence spectra, representing mainly the energy-containing eddies of the flow, were derived, and it was also possible to determine values for the Reynolds stresses at different depths and to make an estimate of the scales of the turbulence. The results are compared with similar observations in the open sea and certain features are discussed which resemble those of measurements of turbulent flow in laboratory experiments and in the atmosphere.

A systematic procedure is presented for the determination of uniformly valid successive approximations to the axisymmetric incompressible potential flow about elongated bodies of revolution meeting certain shape requirements. The presence of external disturbances moving with respect to the body under study is admitted. The accuracy of the procedure and its extension beyond the scope of the present study—e.g. to problems in plane flow - are discussed.

Function-theoretic techniques are used for determining the supersonic flow past a wing of infinite length having a straight leading edge. The problem is reduced to a set of dual integral equations which are solved by function - theoretic methods. This approach is shown to be useful for treating more general - type leading edges yielding closed - form solutions which heretofore have been unobtainable. The general solutions obtained here are shown to be in complete agreement with previous solutions for the flow at large distances downstream on the aerofoil. For a wing of infinite span, the solution reduces to the well - known perturbation potential for a distribution of sources in a horizontal plane.