The limiting lines, which are given by the solutions of the basic equation derived by making use of the independent variables of velocity and stream function, are studied. The first three examples are the supersonic flows along a wall, in which the limiting line is split into three parts for the certain values of Mach number and sometimes a narrow continuous stream exists along the wall. Next example is the case of a spiral sinking transonic flow, where a nearly circular limiting line takes place. The last example is a transonic flow given by an approximate solution. It is the flow between two arbitrary walls.

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The output energy gain in inertial confinement fusion is estimated for a single-shell target which is irradiated by ion beams. The target consists of the three layers of tamper, pusher and DT fuel. In this paper, the effect of self-heating due to alpha-particles which are produced by fusion reactions is taken into considerations. Three kinds of beam particle, proton (H), lithium (Li) and lead (Pb) are chosen as the energy driver. Three types of target are used. 'Type 1' target consists of Pb as the tamper, of Al as the pusher, 'type 2' of Al as the tamper and pusher and 'type 3' of Al as the tamper and Li as the pusher. Optimized target parameters, such as fuel mass and energy deposition rates in the layers (layer thickness), and optimized particle energy for 'type 1, 2 and 3' targets are obtained for the fixed amount of beam input energy. The particle energies which extract the maximum fusion output energies from 'type 1' target irradiated by H, Li and Pb beams of 6 MJ is 3. 5 MeV, 30 MeV and 2.75 GeV, respectively. The output fusion energy from 'type 3' target irradiated by Pb beam is less than that from 'type 1'target.

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The flows over sand-ripples induced by wave action are characterized by the periodic flow separation and the vortex formation. In order to calculate such flows, a linearization is proposed to emphasize a convective acceleration effect of the flow. A new boundary condition which provides a vorticity supply from a boundary is introduced instead of a non-slip condition.
It was confirmed through experiments and trial-and-error calculations that the value of turbulent kinematic viscosity was twenty-five times that of kinematic viscosity ; and it was also shown that the proposed model gives good results.

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The present paper deals with the two-dimensional flow field around a circular cylinder moving slowly along the central plane parallel to side planes in a viscous liquid bounded by two parallel side planes. It is solved semi-analytically by applying the collocation method for the determination of unknown coefficients of the general solution. From the stream function determined, experssions of velocity, pressure and viscous stress are obtained and are discussed on the basis of numerical results. It seems to be quite all right to consider the present solution to be reasonable. The pressure drag and the friction drag of the cylinder are determined from the pressure distribution and the viscous stress distribution at the surface of a circular cylinder, respectively. It is shown that the pressure drag is larger than the friction drag and the ratio of the former to the latter decreases with an increase in the distance between two parallel planes. Concerning the total drag of a circular cylinder, Faxen's formula about the two parallel planes effect on the drag is discussed on the present analytical results and a modified formula is proposed. The new formula is useful in a wider range of the distance between two parallel planes.

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