A two-dimensional, semi-infinite tank, closed by a vertical wall at one end, is initially filled to a certain level with an in viscid liquid at rest. A gate in the lower part of the wall is suddenly opened to a region where the gas pressure is greater or less than the gas pressure over the free liquid surface in the tank. The liquid escapes (or moves inwardly) through the gate under the combined action of gravity and the driving pressure differential. The fluid motion, the shapes of the two free surfaces, and the discharge through the gate are calculated for small times after the opening.

An experimental investigation of a large long air bubble moving into stationary water in a horizontal channel of rectangular cross-section is presented and three well-defined flow régimes for the water discharged beneath the bubble are described. The influence of surface tension on the bubble velocity is explained using the hypothesis that the radius of curvature of the two-phase interface close to the upper wall does not vary greatly with channel depth and is close to the theoretical value for a channel of such depth that the bubble is just motionless.

We give further consideration to flow situations which are steady in the sense that ∂/∂t ≡ 0 but for which individual fluid elements are subjected to a small sinusoidal deformation. The particular situation studied involves the flow between eccentric circular cylinders which rotate about their axes with the same angular velocity Ω. The eccentricity is assumed to be small. It is shown that measurements of the force on the inner cylinder can be used to determine the complex dynamic viscosity of an elastico-viscous liquid.

The theory provides the necessary mathematical background for the operation of a new commercial rheometer. Consideration is given to the possibility of ‘on-line’ use of such an instrument for control purposes.

The error minimization technique is introduced as a method of obtaining the simultaneous solution to a set of partial differential equations. Because this numerical technique is at worst neutrally stable, it is believed to have fundamental advantages over existing techniques. The method is formulated in general for the steady fluid dynamic conservation equations and then applied to a specific case of irrotational isentropic flow of a perfect gas through a nozzle. Flow-field solutions were found in nozzle contours having a throat radius of curvature as low as 0·5. Comparison between experimental Mach number contours and the theoretical solution for a finite inlet nozzle with a conical exit is excellent.

The instability of Poiseuille flow in a pipe is considered for small disturbances. An asymptotic analysis is used which is similar to that found successful in plane Poiseuille flow. The disturbance is taken to travel in a spiral fashion, and comparison of the radial velocity component with the transverse component in the plane case shows a high degree of similarity, particularly near the critical point where the disturbance and primary flow travel with the same speed. Instability is found for azimuthal wave-numbers of 2 or greater, although the corresponding minimum Reynolds numbers are too small to compare favourably with either experiments or the initial restrictions on the magnitude of the wave-number.

The cross-correlation technique has been used to obtain statistical properties of scalar density fluctuations. Two schlieren instruments with their optical beams intersecting in the turbulent field each give a signal proportional to the density gradient in the flow direction but integrated along the beam path. Cross-correlation of the two signals gives an area integral of the density-gradient covariance. For locally isotropic conditions the area integration can exactly compensate for the two gradients giving a result proportional to the local mean-square density fluctuation at the beam intersection point.

Experiments performed in the shear layer of a subsonic jet show results which tend to verify the principles of crossed-schlieren measurement. Intensity levels are close to those predicted assuming density fluctuations are related isentropically to local, incompressible pressure fluctuations.

The break-up mechanism of axisymmetric liquid sheets formed by the impingement of two co-axial jets has been examined. Three break-up regimes in the Weber number range from 100 to 3 × 104 are reported. In the first break-up regime, droplets are formed through successive mergings of liquid beads along the nearly circular periphery of the sheet. The formation of beads is caused by Rayleigh instability. In the transition regime, Taylor's cardioid wave pattern prevails in the first half of this regime, while the sheet begins to flap in the second half.

In the second break-up regime, antisymmetric waves on the sheet grow radially. A semi-empirical equation has been deduced to predict the break-up radius of the sheet. The motion of an axisymmetric vibrating membrane with radially decreasing thickness has been studied to include Helmholtz instability as an analogue of the wave motion of the expanding circular sheet. A distorted progressive wave equation has been solved by the WKBJ method to indicate the effect of cylindrical geometry. The calculated wave speed agrees fairly well with experimental data at low Weber numbers.

Taylor (1953, 1954a) showed that, when a cloud of solute is injected into a pipe through which a solvent is flowing, it spreads out, so that the distribution of concentration C is eventually a Gaussian function of distance along the pipe axis. This paper is concerned with the approach to this final form. An asymptotic series is derived for the distribution of concentration based on the assumption that the diffusion of solute obeys Fick's law. The first term is the Gaussian function, and succeeding terms describe the asymmetries and other deviations from normality observed in practice. The theory is applied to Poiseuille flow in a pipe of radius a and it is concluded that three terms of the series describe C satisfactorily if Dt/a2 > 0·2 (where D is the coefficient of molecular diffusion), and that the initial distribution of C has little effect on the approach to normality in most cases of practical importance. The predictions of the theory are compared with numerical work by Sayre (1968) for a simple model of turbulent open channel flow and show excellent agreement. The final section of the paper presents a second series derived from the first which involves only quantities which can be determined directly by integration from the observed values of C without knowledge of the velocity distribution or diffusivity. The latter series can be derived independently of the rest of the paper provided the cumulants of C tend to zero fast enough as t → ∞, and it is suggested, therefore, that the latter series may be valid in flows for which Fick's law does not hold.

This paper discusses the linear theory of the transmission of an acoustic pulse through a plane discontinuity of velocity. It is shown that elementary ideas of geometrical acoustics which have received much attention in the recent literature lead to the erroneous prediction of a zone of silence. It is in precisely this zone that unstable disturbances and broad-fronted pulses of enhanced intensity propagate, having been triggered-off by the arrival of the pulse at the vortex sheet. The apparent qualitative agreement between geometrical acoustics and experimental data regarding sound radiation from the interior of supersonic jets is shown to be purely fortuitous, and it is argued that a complete analysis of such problems must depend on a deeper and possibly non-linear treatment.

Using a simplified wave-diagram and the gas-speed/sound-speed diagram, it is shown how the oscillations start and grow within a resonance tube. It is found that the oscillation amplitude tends to a limiting value which is obtained when the jet is fully swallowed by the tube during the phase of compression of the cycle. Experiments are carried out for jet Mach numbers from 0·1 up to 2. To achieve an adequate evacuation of the tube in the expansion phase, a thin cylindrical body must be used, which is laid along the axis of the jet to produce a wake and a correlative local deficiency of the kinetic energy of the jet. Measured amplitudes of pressure fluctuations are in good agreement with theoretical values.

A Boussinesq fluid is heated from below. The applied temperature gradient is the sum of a steady component and a low-frequency sinusoidal component. An asymptotic solution is obtained which describes the behaviour of infinitesimal disturbances to this configuration. The solution is discussed from the viewpoint of the stability or otherwise of the basic state, and possible stability criteria are analyzed. Some comparison is made with known experimental results.

A similarity solution has been obtained for a radiation-driven shock wave. Radiation propagating radially inwards is completely absorbed in the shock layer of a spherical, expanding shock wave. For a strong shock wave and a constant power input a similarity solution is obtained. It is found that the radial position of the shock wave rs ∼ t⅗. The shock wave propagates as an overdriven detonation. The jump conditions and complete flow field are obtained.

The slow motion of a body through a stratified fluid bounded laterally by insulating walls is studied for both large and small Peclet number. The Taylor column and its associated boundary and shear layers are very different from the analogous problem in a rotating fluid. In particular, the large Peclet number problem is non-linear and exhibits mixing of statically unstable fluid layers, and hence the drag is order one; whereas the small Peclet number flow is everywhere stable, and the drag is of the order of the Peclet number.

Experiments conducted elsewhere show that a mean fluid motion can be induced in a channel by a travelling thermal wave. An analysis is carried out, linearized under the assumption that the induced motion is slower than the speed of the heat source. The expression for the mean motion is obtained for any Prandtl number and circular frequency of the thermal wave, to complete the results presented by Davey (1967) for low and high frequency ranges.

In the problem of the flow between two parallel plates, it is found that with a temperature profile symmetric about the centre of the channel, the induced flow does not exert a net shear force on either plate, while with a non-symmetric one, the plates are subjected to equal and opposite forces.

For the problem that the upper surface of the fluid is free and thermally insulated, an approximated result can be deduced from that of the previous problem by a simple transformation. It should agree with the result of Davey, obtained through a more elaborate procedure, except in the low frequency range when the surface deformation becomes important.

In agreement with the experiments, our analysis indicates that the induced mean motion is always in a direction opposite to that of the thermal wave, and its magnitude increases rapidly with decreasing Prandtl number. According to the theory, some of the previous experiments were not conducted under the optimum situations, and improved experimental conditions are suggested.