When a thin film of viscous fluid is produced by passing it through a small gap between a roller or spreader and a flat plate, it often presents a waved, or ribbed, surface. An analysis is given here in terms of lubrication theory to show why in many cases flow leading to a uniform film is unstable. Account is taken of surface tension which proves to be a stabilizing factor. The most unstable values of the wave-number, n (characterizing the disturbance), are calculated as functions of the dimensionless variable T/μU0, and of the geometry of the system; T is the surface tension, μ the viscosity and U0 a representative velocity of the fluid. For the particular case of a spreader in the form of a wide-angled wedge, these predictions are compared with experimental observations. Agreement is obtained for values of T/μU0 between about 10 and 0.1, but for smaller values of T/μU0 it is clear that other considerations, involving only viscous and pressure forces, determine the nature of the secondary flow.

Approximate equations of motion, continuity and mass transport are given for a viscous liquid of variable density moving very slowly between vertical and impermeable parallel planes. These equations are used to calculate approximate stability criteria when the liquid is at rest under a vertical density gradient. The results are applicable to the problem of the stability of a viscous liquid of variable density to two-dimensional disturbances in a porous medium.

An exact stability analysis for the liquid between parallel planes is also given, and expansions in powers of the disturbance wave-number are obtained for the critical Rayleigh number at neutral stability. The previous approximate results are found to correspond to the leading terms of the series expansions. For the most unstable type of disturbance, the velocity distribution closely resembles plane Poiseuille flow, which was the form assumed in the approximate equations.

An asymptotic expansion is derived for the critical Rayleigh number at neutral stability in a long vertical channel, or duct, the cross-section of which is a thin rectangle. The typical neutral disturbance possesses a ‘boundary layer’ at each end of the cell cross-section, and this has a small stabilizing effect.

The critical Rayleigh number for a long vertical channel of rectangular cross-section is found experimentally by comparing the density gradient of the liquid in the channel at neutral stability with the corresponding density gradient in a vertical capillary tube. There is better agreement with the exact theory than with the approximate theory, the experimental result being about 4% higher than the value predicted by the ‘exact’ asymptotic expression, and about 10% higher than the value predicted by the simple approximate theory.

In the steady flow of an incompressible, inviscid, conducting fluid past a magnetized sphere, the first-order effects of the magnetic field and the conductivity are studied. Paraboloidal wakes of vorticity and magnetic intensity are formed, the former being half the size of the latter. The vorticity, generated by the non-conservative electromagnetic force, is logarithmically infinite on the sphere. For the case of a dipole of moment M at the centre of a sphere of radius a, the drag coefficient is $C_D = \frac {144 \mu^{\prime 2}}{5(2\mu + \mu^{\prime})^2} \beta R_M,$ where μ and μ′ are the permeabilities of the fluid and sphere, respectively, β is the ratio of the representative magnetic pressure μM2/2a6 to the free-stream dynamic pressure, and RM is the magnetic Reynolds number.

The Stokes flow problem is concerned with fluid motion about an obstacle when the motion is such that inertial effects can be neglected. This problem is considered here for the case in which the obstacle (or configuration of obstacles) has an axis of symmetry, and the flow at distant points is uniform and parallel to this axis. The differential equation for the stream function ψ then assumes the form L2−1ψ = 0, where L−1 is the operator which occurs in axiallysymmetric flows of the incompressible ideal fluid. This is a particular case of the fundamental operator of A. Weinstein's generalized axially symmetric potential theory. Using the results of this theory and theorems regarding representations of the solutions of repeated operator equations, the authors (1) give a general expression for the drag of an axially symmetric configuration in Stokes flow, and (2) indicate a procedure for the determination of the stream function. The stream function is found for the particular case of the lens-shaped body.

Explicit calculation of the drag is difficult for the general lens, without recourse to numerical procedures, but is relatively easy in the case of the hemispherical cup. As examples illustrative of their procedures, the authors briefly consider three Stokes flow problems whose solutions have been given previously.

The pressure measured at a static pressure hole differs slightly from the true static pressure, by an amount which depends on the hole size and shape. The present investigation extends the range of previous work to determine the error in static pressure measurement in incompressible turbulent flow. The observed static pressure was always greater than the true static pressure. The results are presented in dimesionless form as a function of the Reynolds number based on hole diameter and friction velocity.

This article has a twofold purpose: (1) to analyse the available theoretical and experimental knowledge concerning flow in the inlet region of a smooth round tube, and (2) to point out that the e9 amplification factor method apparently predicts natural transition correctly over a significant fraction of the entire inlet lenght of the tube. The successful prediction indicates, but does not prove, that flow in a smooth round tube becomes turbulent at higher Reynolds numbers because transition occurs in the inlet lenght—not in the fully developed Poiseuille régime. The close agreement between theory and a test result obtained by Pfenninger indicates that the e9 method is valid for a wide variety of flows having x Reynolds numbers of transition ranging from 570,000 to 40 million. The results are applicable to both plane and axially symmetric flows.

The equations for planar two-dimensional steady flow of an ideal dissociating gas are linearized, assuming small disturbances to a free stream in chemical equilibrium.

As an example of their solution, the flow past a sharp corner in a supersonic stream is evaluated and the variations of flow properties in the relaxation zone are found. Numerical illustrations are provided using an ‘oxygen-like’ ideal gas and comparisons made with a characteristics solution. The flow past a sharp corner can be studied in a conventional shock tube and it may be possible to verify the present theory experimentally. In particular it may prove feasible to use the results to obtain a measure of the reaction rates in the gas mixture.

The paper describes an experimental investigation of the pressures developed at the seat of collapse of cavities in water. Single transient cavities, generated by a spark discharge, are allowed to collapse on the end of a piezoelectric pressure-bar gauge which measures the variation of thrust with time. It is shown that both the peak force and duration of the cavity collapse pulse are functions of the cavity lifetime. From an estimate of the minimum radius attained by the cavity and the peak force, the peak pressure on collapse is found to be at least 10,000 atm. Streak schlieren photographs of the collapse process show that a shock wave is radiated into the water at the moment of collapse and that the cavity rebounds. At the collapse of the rebound cavities the pressures developed are comparable with those developed by the collapse of the initial cavity, and these probably contribute materially to cavitational surface damage.

An electronic computer has been employed to calculate the ratio between the initial radii of curvature of the attached shock wave and the body for an axially symmetrical body in a uniform supersonic stream. The results are obtained with 4 exact digits for more than 200 cases. They extend results obtained previously (Cabannes 1951) by means of numerical integration.

The flow produced by an infinite rotating disk when the fluid at infinity is in a state of solid rotation is investigated numerically. When the fluid at infinity is rotating in the same sense as the disk, physically acceptable solutions exist in all cases. When the fluid at infinity is rotating in the opposite sense to that of the disk, the only physically acceptable solutions appear to be those in which there is a uniform suction present acting through the disk.

A theory of a jet in a rotating, viscous fluid is developed. It is suggested that it may be related to a jet observed in an experiment with a rotating spherical shell of liquid and, in addition, may partly explain the existence of the subsurface equatorial current in the Pacific Ocean. The fundamental physical idea is that of a balance of vorticity brought into the jet by advection and diffused by friction. The necessary approximations are borrowed from boundary-layer theory. The linear case is solved completely and inferences about the non-linear jet are obtained by dimensional reasoning.