The unsteady flow field pertaining to a drop moving vertically under gravity is obtained from the Stokes equations applicable to low-Reynolds-number flow. A proof is given that there is no variation in the normal stress over the drop surface. In consequence unsteadily moving drops remain spherical, subject only to the criterion of low Reynolds number. Numerical results are presented for a water drop moving through air. A small-time analysis of the motion provides a comparison between the motion of any drop, or bubble, with that of the presented water-drop solution.

The classical hydrodynamical problem of a body submerged beneath a free surface is considered. The flow is two-dimensional and the cross-section of the body and its motion are arbitrary. In the limit as a typical body dimension becomes small compared with its depth the method of matched asymptotic expansions becomes applicable and expressions for the forces and moment experienced by the body can be found. Several cases are considered in detail where the body is permitted to move in response to the forces and moment. We also find the additional forces, due to the free surface, experienced by a lifting body - a body about which there is a circulation.

An analysis is presented of the shock-wave configurations which will occur when a plane shock is incident on a double wedge for which the second wedge may have a greater (concave case) or a smaller (convex case) inclination than the first wedge. It is shown that seven different reflection processes may be expected depending on the Mach number of the incidnet shock Mi and the two wedge angles θ1w and θ2w. These processes may be defined by seven regiouns in the (θ1w,θ2w)-plane, for a given value of Mi. Each of the seven processes has been verified by sequences of shadowgraph and schlieren photographs.

A shock-polar analysis of each of the seven processes has provided infomation about the pressure changes and the wave structures which develop immediately behind the main reflections along the wedge surfaces. These wave structures have been verified experimentally, and two types have been observed; one normal to the reflecting surface, and the other in the form of a regular reflection. The criteria to determine which of thses configurations will occur have not yet been established.

It is believed that the present study will be of value in predicting the loading of shock waves on structures, and may lead to a better understanding of shock reflections form concave and convex cylindrical surfaces.

The steady-state motion of a gas bubble inside a non-isothermal, spherical, liquidfilled container is described by taking into account the effects of gravity, the thermally induced gradient of the gas-liquid interfacial tension, and the finite size of the liquid container. The flow fields inside and outside the bubble located at the centre of the container are calculated using a low-Reynolds-number approximation of the fluid equations. The temperature fields are determined by using a low-Prandtl-number approximation of the heat equations. A general expression is obtained for the steady-state migration velocity of the bubble which, under certain conditions, reduces to expressions previously derived by a number of investigators. Finally, an expression for the vertical temperature gradient that will maintain a stationary gas bubble at the centre of the container is formulated.