This paper analyses the development, according to the Navier-Stokes equations, of the two-dimensional flow in the neighbourhood of the rear stagnation point on a cylinder which is set in motion impulsively with constant velocity. The local flow is idealized to the extent that the cylindrical boundary is taken to be an infinite plane bounding a semi-infinite domain of fluid. The velocity field is taken to be a linear function of the co-ordinate measured parallel to the boundary, and the initial flow is taken to be the (unique) irrotational form of such a field, namely, inviscid flow away from a stagnation point. Thereafter this irrotational flow is maintained as the outer boundary condition at a large distance from the boundary.

It is suggested that, outside a viscous layer on the boundary, the asymptotic flow for large times is described by a similarity solution of the inviscid form of the governing equation, with a length scale normal to the boundary which increases exponentially with time. This inviscid solution has a steady velocity of slip along the boundary which is equal but opposite to that of the initial flow, so that the flow in the viscous layer ultimately becomes the well-known stagnation flow towards a boundary. The suggestion is supported by a numerical solution of the initial-value problem.

A detailed treatment of inviscid hypersonic flow past a circular cone is given, for small and moderate yaw angles, within the fremework of shock-layer theory. The basic problem of non-uniform validity associated with the singularity of the entropy field is examined and a valid first-order solution is obtained which provides an explicit description of a thin vortical layer at the inner edge of the shock layer. Analytic formulas for pressure and circumferential velocity are given consistent to the second-order approximation including the non-linear yaw effect.

The study of the entropy field (which is not restricted to the hypersonic case) also provides corrections to previous work on the yawed cone and confirms the validity of the linear yaw effect on pressure field in the Stone theory.

A related investigation of three-dimensional flow fields is presented with special reference to the flow structure near the surface of a pointed, but otherwise arbitrary body. The inviscid streamline pattern on the surface is given by the geodesics originating from the pointed nose as a leading approximation of shock-layer theory. Associated with this streamline pattern is a vortical sublayer which exists generally at small as well as at large angle of attack. At the base of the sublayer, enthalpy and flow speed remain essentially uniform.

The incompressible, inviscid, parallel flow of a layer of fluid over a slightly denser fluid, in the presence of gravity, is investigated for stability. Two idealized piece-wise-linear steady velocity profiles are examined analytically, and a comparison with related experimental results is made.

The dimensionless parameter U/(gh)½, where U is flow velocity, g the acceleration of gravity, and h the thickness of the upper layer, appears to have a critical value between 0.2 and 0.7, below which stable flows can persist. At the onset of instability disturbances of wavelength about h or 2h are predicted, with more violent disturbances of longer wavelength occurring at higher values of U/(gh)½ For continuous steady velocity profiles this instability phenomenon is found to be relatively insensitive to the ratio of the densities of the two fluids.

The steady incompressible flow of a non-viscous conducting fluid about thin airfoils and slender bodies is studied for the case of a uniform applied magnetic field aligned with the undisturbed fluid stream. Solutions are found, subject to the restriction of small perturbations to the applied field. This condition determines an upper limit on the range of conductivity to which the solution are applicable. Certain results for larger values of conductivity are presented and discussed.

The lift on airfoils is calculated, including the possibility of magnets and externally driven currents inside the airfoil, and a magnetohydrodynamic analogue to the Kutta condition is discussed. Drag formulae are presented for airfoils and slender bodies, and the distribution of internal currents and magnets for zero drag is shown. Optimum drag airfoils and bodies are discussed briefly.

Thin-airfoil theory is applied to steady, plane potential flow about vented or cavitating hydrofoils of arbitrary profile when there are two free-streamlines detaching from the foil and bounding the single cavity that extends downstream of the trailing edge. Cavity-termination models employed are the closed, the partly closed and the open models for which the thickness of the implied ’wake’ following the cavity ranges from zero to maximum for the open model. The general solution for given wetted-surface profile, cavity length and particular cavity termination is constructed by superposition of the profile's cusp-closure solution (angle of attack α+) plus the particular flat-plate solution to give the desired angle of attack α. Four related integrals involving the wetted-surface contour slope distribution lead to drag, lift, cavity pressure and α+vs cavity length. A comparison of theoretical and experimental lift and drag for a cavitating hydrofoil shows good agreement until the theoretical cavity closure nears the trailing edge.

This paper describes the use of a hot film flowmeter in the sea and presents experimental measurements of the ‘downstream’ component of turbulent velocity in a tidal channel. The Reynolds number of the flow is about 108 and the scale of the turbulence is so large that a ship is carried about to a considerable extent by the energy-containing eddies. Under these conditions, a velocity measuring probe attached to a ship cannot be used for reliable measurements in the energy-containing range of the spectrum. It is possible, however, to observe the intertial and dissipation ranges. Records have been made at various stages of the tide. The one-dimensional spectra are found to be proportional to $k|^{-{\frac {5}{3}}}$ for several decades in k as predicted by Kolmogoroff, and a value is given for Kolmogoroff's constant. In the dissipation range there is close agreement with both Kovasznay's theory and Heisenberg's theory. These two theories are not very different in the low wave-number end of the range and the observations do not extend to high enough wave-numbers to distinguish between them.

A new explanation of the vortex tube is presented. The proposed model leads to an equivalent unsteady-flow analysis for the development of the flow in the vortex tube. Using this analysis, radial distributions of velocity and temperature can now be calculated at successive axial positions in the tube. Many characteristics of these calculated profiles are found to be in qualitative agreement with corresponding experimental profiles. The qualitative similarity in the development of the calculated and experimental sets profiles with axial position is considered especially significant.

A theory of vortex-tube performance based upon an idealized three-dimensional flow pattern for the vortex tube is derived. Some experiments relating the idealized vortex tube analysed to previous vortex-tube measurements are described. The performance curves obtained from the theory resemble those measured. An important additional effect predicted by the theory is that both the hot and the cold temperature differences should increase as the effective height of the inlet nozzle increases, and this result has been substantiated by experiment.

The free-molecule limit of several free-flow problems is studied on the basis of the collisionless Boltzmann equation. It is shown that the density in the free expansion of a gas cloud obeys, under certain conditions, a diffusion equation with a coefficient directly proportional to the time, and the resulting flow field is described in terms of a thick ‘diffusion front’ travelling asympotically at a definite velocity and growing linearly with time. It is also show that in any free-molecule free expansion the stresses and heat flux can be expressed in terms of viscosity and conductivity coefficients, which however increase linearly with time but are such that the Stokesian relation is always valid and the Prandtl number has the value 5/6.

The flow field due to sources and jets is also discussed, and it is found that the jet has a width inversely proportional to the Mach number if the Mach number is sufficiently high. Finally, a procedure is indicated for taking approximate account of collisions among the molecules.

The instability of an annular coating of liquid on a wire or on the inside of a small tube subject to capillary forces at its free surface is discussed. It was found that for given values of s/a, the ratio of the two radii of the annulus, and S ≡ρTa/μ2, the reciprocal of the square of the Ohnesorge number, there is a disturbance of a certain wavelength (2πa/λ)*, which grows more rapidly than disturbances of any other wavelength. One would therefore expect the liquid to break up into a regular pattern of drops with spacing given by this wavelength. The dependence of (2πa/λ)* on s/a and S has been calculated and is presented graphically. Experimental observations on drop formation on wires and in tubes which agree with the calculations are given.