An exact derivation of HAMILTON's principle has been shown for the non-viscous fluid dynamics. The principie of virtual work has been applied to the LAGRANGE-type dynamic equation of the fluid. The conservation laws of mass and energy as well as the geometrical boundary condition have been treated as subsidiary conditions. In the present variational method, a new concept of substantial variations of the state variables has been introduced in order to describe the subsidiary conditions in the correct forms. By use of this concept, it has been found that HAMILTON's principle for the fluid dynamics can be exactly derived from the principle of virtual work through the familiar manner in the classical dynamic problems. And also the theoretical foundation has been given to HERIVELLIN's principle.
This paper presents an experimental study of shock wave/turbulent boundary-layer interaction induced by a sharp fin placed normal to the side wall of the wind tunnel. The experiments were carried out in a 8×10cmcm2 supersonic wind tunnel at free stream Mach numbers of 1.98 and 2.48. Corresponding free stream REYNOLDS numbers per meter were 4.1×107 and 2.7×107 for the former case and 4.1×107 for the latter case. A set of 3 fin models with wedge type leading edge of 20°, 30° and 40° half angle were used in this study. Surface static pressure measurements, oil flow studies and SCHLIEREN photographs of the flow field were made. It was found that, the separation shock angle and the pressure ratio though separation are insensitive to the shape of fin's leading edge. The length of the upstream influence point and the separation point measured along the centerline from the fin's leading edge were found to increase linearly with the increase of wedge angle. Furthermore, with the increase of wedge angle, the pressure distribution became qualitatively similar to the hemi-cylindrical blunt fin case.
In this paper, the stresses in the plane cantilever beam are expressed by addition of the elementary stresses and the deviation stresses from them. The unknowns included in the deviation stresses are determined so as the distortion at the fixing end of the beam is constrained at five points, and the principle of minimum strain energy is satisfied. The numerical results are shown. Next the stresses are expressed by the higher approximation, and by similar treatment the distortion along the fixing end is satisfactorily decreased. By the above treatments, it is shown at the fixing end that the fiber stress distribution across the neutral axis is curved and not linear, and the shear stress distribution is concave and not parabolic. Moreover, many numerical results are contributed.
The dynamic pitching characteristics of peripheral jet ACV which have a stability curtain are investigated analytically and experimentally. The measured values of moment, lift and cushion pressure are compared with the numerical results calculated by the theory which was developed by the authors and it is proved that the theory is applicable to the pitching motion. The response of ACV to the sinusoidal pitching oscillation of the ground are also studied.