Measurements of the amount of fluid left behind when a viscous liquid is blown from an open-ended tube are described.

A long bubble of a fluid of negligible viscosity is moving steadily in a tube filled with liquid of viscosity μ at small Reynolds number, the interfacial tension being σ. The angle of contact at the wall is zero. Two related problems are treated here.

In the first the tube radius r is so small that gravitational effects are negligible, and theory shows that the speed U of the bubble exceeds the average speed of the fluid in the tube by an amount UW, where $W \simeq 1\cdot 29(3 \mu U|\sigma)^{\frac {2}{3}}\;\;\; as\;\;\; \mu U|\sigma$ (This result is in error by no more than 10% provided $\mu U |\sigma \; \textless \;5 \times 10^{-3}\rightarrow 0$). The pressure drop, P, across such a bubble is given by $P \simeq 3\cdot 58(3\mu U|\sigma)^{\frac {2}{3}}\sigma|r \; \; \;as\; \; \; \mu U|\sigma \rightarrow 0$ and W is uniquely determined by conditions near the leading meniscus. The interface near the rear meniscus has a wave-like appearance. This provides a partial theory of the indicator bubble commonly used to measure liquid flowrates in capillaries. A similar theory is applicable to the two-dimensional motion round a meniscus between two parallel plates. Experimental results given here for the value of W agree well neither with theory nor with previous experiments by other workers. No explanation is given for the discrepancies.

In the second problem the tube is wider, vertical, and sealed at one end. The bubble now moves under the effect of gravity, but it is shown that it will not rise at all if $\rho gr^2| \sigma \; \textless \; 0 \cdot 842,$ where ρ is the difference in density between the fluids inside and outside the bubble. If $0 \cdot 842 \; \textless \; 1 \cdot 04,$ then $\rho gr^2| \sigma - 0 \cdot842 \simeq 1 \cdot 25 (\mu U|\sigma)^{\frac {2}{9}} + 2 \cdot 24(\mu U|\sigma)^{\frac {1}{3}},$ accurate to within 10%. Experiments are adduced in support of these results, though there is disagreement with previous work.

It is shown to be probable that a large proportion of the drag exerted by a water surface on the wind is in the form of wave drag. As a result the usual relation between the wind profile and the surface stress and roughness length are modified. In particular, close to the surface the relation between the transport of momentum and that of heat and water vapour are different from that obtaining over a rough solid surface.

The transient effects generated when a shock wave is suddenly disturbed by a field of cellular vortices have been studied. Both the pressure disturbance on the shock and the local shock velocity are found to be strong functions of the cell geometry. Disturbances are resolved into transient components and sinusoidal components of constant amplitude. The transients are found to die out as t−3/2, t being the interaction time, except for one particular case of the cell geometry for which they diminish as t−1/2. Furthermore, the analysis indicates that the initial magnitude of the transient components may be quite appreciable in comparison with the sinusoidal component. The theory is extended to treat the convection through the shock of a single column of vortex cells.

Three-dimensional periodic oscillations in the shear flow region between two parallel streams are considered up to that second order of the oscillation amplitude. It is shown that, as an integral part of the oscillation, there is a mean secondary flow in the nature of a longitudinal vortex. Despite the dissimilarity in the profile of the basic flows, several of the principal features of the calculated results can be compared with those observed for the Blasius flow by Schubauer and Klebanoff & Tidstrom at the National Bureau of Standards.

Linearized methods developed in earlier papers (Spence 1956, 1961) are used to discuss the non-stationary flow of a wing with a jet-flap. We consider a thin twodimensional wing at zero incidence in a steady stream of speed U, with a thin jet emerging parallel to the chord at the trailing edge, and study the motion following an instantaneous deflexion of the jet through an angle τ0. If the momentum-flux coefficient CJ of the jet is [Lt ] 4, the governing equations can be put in a form in which CJ does not appear explicitly, and a similarity solution then gives the shape of the jet at small times t from the start of the motion as a function of $(x -c)\mu ^{-\frac {1}{3}}t^{-\frac {2}{3}}$, where x= c is the trailing edge and $\mu = \frac{1}{2}C_J$. The solution is obtained from a certain third-order integro-differential equation, by constructing the Mellin transform of the non-dimensional shape. When t is large the jet near the wing approaches the shape given by the known results for steady flow, but its shape at distances of the order of Ut downstream changes diffusively under the action of the starting vortex. A similarity solution is also found for the flow in this region in terms of $(x -c)\mu ^{-\frac {1}{3}}t^{-\frac {2}{3}}$, without restriction to small μ. Expressions for the lift coefficient at small and large times are found, and the case of an oscillating deflexion angle is treated by the same methods.

The present paper is concerned with the conditions of flow in tanks containing stirred fluids. An attempt is made to apply the theoretical concepts of local isotropy to explain the behaviour of liquid in liquid dispersions, subjected to turbulent agitation. Relations describing quantitatively the influence of turbulence on both break-up and coalescence of individual droplets are derived and are compared with experimental evidence. A special type of dispersion is described in which droplet size is controlled by the prevention of coalescence due to turbulence. The dependence of droplet size on energy dissipation per unit mass, as predicted by the theory of local isotropy, is put to an experimental test using geometrically similar vessels of different sizes.

Though the results are not entirely conclusive, experimental evidence suggests that the hypothesis of locally isotropic flow may be applicable to the flow conditions described in the paper, and that statistical theories of turbulence can be of practical value in estimating droplet sizes in agitated dispersions.

This paper is concerned with the boundary layer on a semi-infinite flat plate in a uniform stream of conducting fluid, with a magnetic field in the stream direction such that the Alfvén speed is less than the undisturbed fluid speed. Series solutions are derived which are applicable for large and small values of the electrical conductivity, and which give a guide as to the validity and limitations of theories which assume the fluid to have infinite or zero conductivity.

An I.B.M. 704 electronic computer was used to integrate the differential equations, which determine the shock singularity, when the velocity after the shock on a body is subsonic. The results are given in twenty-two cases corresponding to three different bodies; the procedure followed was outlined in a previous paper (Cabannes 1952).

An investigation has been carried out on the behaviour of a thin sheet of liquid in connexion with the new method of lacquer application known as ’curtain coating’. A method is described for measuring the velocity of the sheet and an equation deduced for calculating this for a liquid of any viscosity. The minimum liquid flow rate required to maintain a stable sheet is discussed, and some effects of the impingement of the sheet on a rapidly moving surface are described.

The results of Proudman & Pearson (1957) for a sphere are generalized to apply to all ellipsoids of revolution both prolate and oblate.