The normal reflexion of a plane shock wave from a plane wall is investigated experimentally using a new pressure gauge which has a rise time of 0.1 μsec and no overshoot. Wall-pressure histories of 5 μsec duration can be obtained with the present version of this gauge. The experiments were conducted on the end wall of the GALCIT 17 in. diameter shock tube.

Experimental results for three aspects of the reflexion process are presented and discussed: (1) effect of a cold wall, (2) effect of a vibrationally relaxing gas, and (3) profile for a reflecting shock front.

It is concluded that the effect of a cold wall introduces a comparatively minor perturbation to the wall-pressure history, since the ‘thickness’ of the shock-front profile exhibited by the wall-pressure history is comparable to the ‘thickness’ of the incident shock front, as measured by a stationary observer, and the pressure jump across the profile is about 90% of the theoretical value for a thermally insulated wall. Also, the wall-pressure history immediately behind the reflected shock front can be approximated by boundary-layer theory. The effect of a vibrationally relaxing gas was studied in carbon dioxide, and it is shown that the relaxation process behind the incident shock wave produces a large effect on the recorded pressure history, which provides a method for measuring the vibrational relaxation time in carbon dioxide at high temperatures.

This study is concerned with the phenomenon of a liquid jet impinging normally on the surface of a heavier immiscible liquid. In essence, the work is a continuation of a previous investigation which involved an air jet impinging on a water surface.

An analytical model is presented which relates the velocity of the jet in the neighbourhood of the interface to the depth of cavity created by the jet. The effect of interfacial tension is taken into account. Numerous experiments were conducted utilizing both circular and plane jets. An oil jet impinging on water and a water jet impinging on carbon tetrachloride were studied. The resulting experimental data were analysed in terms of the dimensionless quantities obtained from the analytical model.

Results obtained from the circular-jet experiments were in close agreement with the results of the previously conducted air-water tests. However, there were some discrepancies in the plane-jet results; side-wall boundary-layer effects may be the explanation. Depending on the relative values of the Froude and Weber numbers, interfacial tension may be important in determining the depth of cavity created by a jet. Finally two intriguing phenomena, viz. interfacial shearing and cavity oscillation, were observed in the plane-jet experiments.

Some of the processes relevant to the propulsion of small organisms are investigated using the simple mathematical model of two-dimensional waves passing through a sheet immersed in a viscous fluid. This model was first used by Taylor, who considered an inextensible sheet moving in an unbounded fluid of negligible inertia. Here the effects of fluid inertia, of straining of the wave-bearing surface, and of nearby walls are included in the study. The applicability of the results is restricted both by the unrealistic geometry of the model and by the method of analysis which gives results valid for small Reynolds numbers and for small wave amplitudes only. However, the following general results may have counterparts in nature.

The effect of fluid inertia is to increase the propulsive speed for a particular wave amplitude. Straining of the waving surface will probably reduce the propulsive velocity for a given amplitude, although there exist modes of surface straining that give augmented propulsion. If the wave celerity and the energy output in swimming remain constant in the presence of a solid wall, the amplitude of the wave is reduced as the wall is approached while the propulsive speed first rises slightly and then drops. It appears further that an organism swimming near a wall may induce a shear pattern which directs it away from the wall.

Three results on the flow of an infinitely conducting and inviscid fluid are presented in this paper. The first result is that all steady flows with magnetic lines coincident with streamlines are reducible to flows without a magnetic field. The second result is on the establishment of a steady irrotational and current-free flow with coincident streamlines and magnetic lines. It throws some light on the controversy between Stewartson (1960) and Sears & Resler (1959) concerning the possibility of such a flow. The third result concerns the flow of a fluid through a circular cylinder of radius R into a point sink with strength m when the fluid carries a current of density j0 at infinity. It is shown that the condition of uniform flow at infinity is impossible to maintain if a dimensionless number (kR)2 involving the current density j0 exceeds the value (3·831)2, and that the current has the effect of concentrating the flow near the centre line and of producing ring eddies which become longer and longer as (kR)2 is increased.

A method is presented in this article for deriving higher-order correction terms to the well-known asymptotic results for laminar forced-convection heat and mass transfer, and a formula is obtained for computing under fairly general conditions the first correction term to the asymptotic Nusselt number at large Péclet numbers for flows with small or moderate Reynolds numbers. This result is then applied to the problem of heat transfer from a solid, isothermal sphere in Stokes flow, to yield the asymptotic expression for the average Nusselt number,

for Pe→ ∞, Re→ 0, where and Pe are based on the radius of the sphere.

Conditions for the existence of similar solutions for the two-dimensional and axisymmetric boundary layers are obtained for the steady or unsteady flow for purely viscous non-Newtonian fluids, where the shear stress is proportional to the nth power of the velocity gradient and n > 0. These conditions are shown to be a generalization of the similarity conditions for Newtonian fluids. In particular it is found that the velocity at the outer edge of the boundary layer must be proportional to {R(x) + A}m or exp [AR(x)] for steady flows and to (t + A)m, (dx + A)/(t + B) or exp [At] for unsteady flows. Here x is the distance along the wall from the forward stagnation point, t is the time, R(x) = x for two-dimensional flows and for axisymmetric flows, r is the distance from the axis to the wall, and A, B, d, m are constants.

Several examples of the similar solutions are calculated analytically for both steady and unsteady pseudoplastic flows (n < 1). In these solutions the velocity in the boundary layer tends to the outside velocity in such a manner that the difference tends to zero as an inverse power of the distance from the wall, whereas such a difference tends to zero exponentially for the corresponding flow in Newtonian fluids.

The equations of motion of an incompressible viscous fluid are given in a rotating helical co-ordinate system, which is non-orthogonal. Partial differential equations are derived for the boundary-layer flow on a rotating helical blade. Numerical solutions of these equations show that the radial flow in the boundary layer is strongly dependent upon the stagger and speed of rotation of the blade.

Density waves in low-pressure are discharges have been observed travelling towards the anode with speeds near . A dispersion relation for these waves is developed, taking into account the boundary effects, namely, the continuous loss of ions to the containing walls. This theory is in fair agreement with experiment, except in its prediction of a rather high value for the wave damping. However, by allowing for the effect of electrostatic instabilities on anode-approaching waves, due to electron drift, this discrepancy is satisfactorily explained.

The Laplace equation for the pressure drop across curved liquid-gas interfaces is applied to the solution of the profile of a static liquid meniscus on the outside of a wire of circular cross-section. The resulting differential equation is integrated numerically, an operation complicated by the existence of boundary conditions at two points making a trial-and-error solution necessary. The accuracy of the solution is substantiated by comparison of computed profiles with experiments in which menisci of a blue dye in water are photographed clinging to the outside of brass wires, whose diameters lie within the range of technological interest.

Two-dimensional thermal convection of air between horizontal plates of length much greater than their separation distance is studied numerically by solution constraining motions to lie in a single vertical plane. Rayleigh numbers from 105 to 107 are employed. Steady rolls with wavelength twice the plate-separation were obtained in both cases. As the experimental two-dimensional constraint is relaxed, short-period turbulent fluctuations in temperature develop, the rolls or cells become only quasi-steady, and their wavelength increases. For the three-dimensional case, very large width-to-height ratios and averaging periods are found necessary before the temperature variance in time approaches the variance in the horizontal.

The inviscid stability of the laminar mixing of two parallel streams of a compressible fluid is investigated with respect to three-dimensional wavy disturbances. The flow is more unstable as the angle between the disturbance-wave-number vector and the principal-flow direction exist even at very high Mach number, and the flow is still unstable. However, it is also found that increasing the Mach number of the flow tends to stabilize the flow.

An accurate measurement of low-Reynolds-number sphere drag has been made. Some of the inaccuracies of previous measurements are revealed. Comparison with the theoretical studies shows that the Oseen formula is as accurate as any in predicting sphere drag below a Reynolds number of 0·4.

The drag of a sphere has been measured as it moves along the axis of a rotating, viscous fluid. Rotation has been found to modify the classical low-Reynolds-number flow so that the drag is increased and the effects of finite Reynolds number, R, and of wall proximity are reduced as the rotation parameter, the Taylor number T, increases. The results confirm the theory of Childress (1963, 1964) when both Reynolds number and Taylor number are small. The rate at which the sphere rotates with respect to the rotating fluid frame has also been measured and was found to be less than the values calculated by Childress (1964) for small T and R, but to approach the theoretical values in a reasonable way.

The forced motion of a liquid heated non-uniformly from below and subject to a non-constant basic temperature profile is examined. The problem is formulated as a two-point boundary-value problem which is solved by a numerical method. In agreement with previous work, the presence of a positive vertical lapse rate of basic temperature tends to decrease the forced motion. It is found that constant heat generation within the fluid produces a parabolic basic temperature profile, and this tends to increase the forced velocity components.

Theoretical and experimental results are presented for the reflexion and transmission of water waves, passing over a step bottom between regions of finite and infinite depth. Two-dimensional motion is assumed, with the wave crests parallel to the step, and in the theory linearized irrotational flow is assumed. By matching ‘wavemaker’ solutions for the two regions at the cut above the step, an integral equation is derived for the horizontal velocity component on the cut. This integral equation is solved numerically and the reflexion and transmission coefficients and associated phase shifts are obtained. These results are compared with the long-wave theory and significant frequency effects are found, even for quite long waves. Experimental results are presented, which are in fair agreement with the theory.