The uniform, slow motion of a sphere in a viscous fluid is examined in the case where the undisturbed fluid rotates with constant angular velocity Ω and the axis of rotation is taken to coincide with the line of motion. The various modifications of the classical problem for small Reynolds numbers are discussed. The main analytical result is a correction to Stokes's drag formula, valid for small values of the Reynolds number and Taylor number and tending to the classical Oseen correction as the last parameter tends to zero. The rotation of a free sphere relative to the fluid at infinity is also deduced.

The heat transfer in a radial liquid jet is investigated. In the region where a similarity solution of the momentum equation is available solutions of the energy equation describing the effects of viscous dissipation, initial heating and wall heating are obtained in closed form. Two examples illustrating the work are discussed. In the second of these an approximate method, based on the heat flux equation, is used to describe the initial development of the thermal boundary layer.

Derived herein is a set of partial differential equations governing the propagation of an arbitrary, long-wave disturbance of small, but finite amplitude. The equations reduce to that of Boussinesq (1872) when the assumption is made that the disturbance is propagating in one direction only. The equations are hyperbolic with characteristic curves of constant slope. The initial-value problem can be solved very readily by numerical integration along characteristics. A few examples are included.

Using some recent results it is established that, for very general boundary conditions, time-independent subcritical instabilities do not exist for the non-linear thermoconvective stability problem.

An experimental investigation of the fluid dynamic forces on spheres suspended in a Poiseuille flow was performed. Small spheres of polystyrene, nylon, and Lucite, having diameters ranging from 0.061 in. to 0.126 in. were suspended in Poiseuille flows in a 0.419 in. diameter tube. Variations in particle size and density, the fluid properties, and the angle of inclination of the tube, resulted in a sphere Reynolds number (based on particle diameter and approach velocity) ranging from 80 to 250. The results are presented as curves which include the coefficients of lift and drag, and the dimensionless rotation speed plotted versus Reynolds number and a dimensionless shear parameter.

An approximate analytical solution is derived for the inclined non-inertial sinkage of a flat plate onto a smooth surface, for the case of small angles. The result is a modification to the existing solutions for parallel sinkage, in the form of a polynomial in the dimensionless angle of inclination. Even the smallest angle of inclination of plate to surface produces a large increase in the sinkage rate otherwise obtained. The results are confirmed experimentally.

Goldstein (1931) has considered the stability of a shear layer within which the velocity and the density vary linearly and outside which they are constant. Rayleigh (1880, 1887) had found that the corresponding, homogeneous shear flow is unstable in and only in a finite band of wave-numbers. Goldstein concluded that a small density gradient renders the flow unstable for all wave-numbers. This conclusion appears to depend on the acceptance of all possible branches of a multi-valued eigenvalue equation, and it is shown that the principal branch of this eigenvalue equation yields one and only one unstable mode if and only if the wave-number lies in a band that decreases from Rayleigh's band to zero as the Richardson number increases from 0 to ¼.

An experimental investigation was made of the stability of a two-dimensional jet at low Reynolds numbers with extremely small residual disturbances both in and around the jet. The velocity distribution of a laminar jet is in agreement with Bickley's theoretical result. The stability and transition of a laminar jet are characterized by the Reynolds number based on the slit width and the maximum velocity of the jet. When the Reynolds number is less than 10, the whole jet is laminar. When the Reynolds number is between 10 and around 50, periodic velocity fluctuations are found in the jet. They die out as they travel downstream without developing into irregular fluctuations. When the Reynolds number exceeds about 50, periodic fluctuations develop into irregular, turbulent fluctuations. The frequency of the periodic fluctuation is roughly proportional to the square of the jet velocity.

The stability of the jet against an artificially imposed disturbance was also investigated. Sound was used as an artificial disturbance. The disturbance is either amplified or damped in the jet depending on its frequency. The conventional stability theory was modified by considering the streamwise increase of Reynolds number. The experimental results are in agreement with the theoretical results.