The boundary conditions of this virtual flow may be established by the boundary conditions of the complex velocity on the physical plane, thereby the boundary value problem is solved. The formulae for calculating the lift, drag and the shape of each free streamline are obtained. In addition, certain limiting cases are discussed.

In thin paper, ths traditional problems of Complex potential, complex Velocity, elevating force and force moment in the flow around rocket tail profile have been studied by usingthe theory of boundory value problem of analytic functions.

In this paper, a method of calculating synthetic seismogram contained mulitiple and attenuation using complex velocity in the case of layered medium and normal incidence in the frequency domain has been presented.

The complex velocity w(z) is then expended into Laurent series and if the coefficients of the first three terms in series are determined, the hydrodynamie characteristics of a circular arc hydrofoil can be derived.

This kind of tomography inversion with a rectangular block cell, that could process the directive wave and refraction as well as transmission wave, can model and invert the complex velocity structure. It is unnecessary to cognize wave styles and it calculates velocity quickly.

In this paper, both the exact solution of the complex velocity induced by a horizontal flat plate moving vertically near a plane wall and the pseud-steady approximate solution to the same problem for the plate still having horizontal velocity are obtained together, by using the theory of elliptical functions.

Ray tracing techniques are widely applied in seismology, among which the shortest path method (SPM) is robust for 3-D ray tracing in complex velocity structures.

This phenomenon is resulted from the complex velocity struc- ture of down-faulted strata and incorrect reflection migration from poststack time migration.

- The only way to make an excessively complex velocity model suitable for application of ray-based methods, such as the Gaussian beam or Gaussian packet methods, is to smooth it.

The accuracy of hypocenter locations based on regional data is affected by the complex velocity structures characteristic of subduction zones, but the problems are now well-understood.

This paper reviews applications of the finite-difference and finite-element methods to the study of seismic wave scattering in both simple and complex velocity models.

Jeffreys-Bullen P and PKP travel-time residuals observed at more than 50 seismic stations distributed along Italy and surrounding areas in the time interval 1962-1979, indicate the complex velocity pattern of this region.

Turbulent swirling water flow in a pipe has complex velocity distributions with special measurement problems tor experimental work.

The pressure distribution of noncavitating potcnial flow around gate piers shown in Fig. la has been analysed. The analysis has its practical significance in that the minimum-pressure coefficient is closely related to the incipient cavitation number. After the W plane was mapped on to, the t plane with known transformations except an unknown parameter m, the complex velocity was expressed by Eq. (10) in terms of an unknown function Ω (t). Eqs. (13) and (16) indicate that along the boundary f and g are...

The pressure distribution of noncavitating potcnial flow around gate piers shown in Fig. la has been analysed. The analysis has its practical significance in that the minimum-pressure coefficient is closely related to the incipient cavitation number. After the W plane was mapped on to, the t plane with known transformations except an unknown parameter m, the complex velocity was expressed by Eq. (10) in terms of an unknown function Ω (t). Eqs. (13) and (16) indicate that along the boundary f and g are respectively related, to the magnitude of the boundary velocity and the boundary geometry. Three equations to solve for the three unknowns are furnished by the conditions along the boundary: (1) The angle τ is given as a function of z. (2) f and g, being the real and imaginary parts of an analytic function, are related to each other. (3) The points of tangency are transformed to points on the real axis of the t plane. For the case in which the nose curve is composed of circular arcs, Eqs. (22), (28) and (29) were derived. The functions f and g were found numerically by iteration, and m was computed from Eq. (28). The distribution of velocity and that of pressure along the line of symmetry and the boundary were computed and plotted in Fig. 5, in which the pressure distribution from wind tunnel tests was also included. Preliminary results on incipient cavitation number were plotted in Fig. 6, to be compared with the theoretical |C_(pm)| curve. More tests are being done to study the scale effects.

The method of functions of complex variable is used in solving the problem of small amplitude surface waves on water generated by a vibrating side wall, the general formula for the complex velocity is given, and three different types of wall vibrations are discussed in some detail.Two different methods were used for the measurements and recording of surface waves. The experimental results in the case of small amplitude agree well with theory. Some observation and recording were made with large amplitudes....

The method of functions of complex variable is used in solving the problem of small amplitude surface waves on water generated by a vibrating side wall, the general formula for the complex velocity is given, and three different types of wall vibrations are discussed in some detail.Two different methods were used for the measurements and recording of surface waves. The experimental results in the case of small amplitude agree well with theory. Some observation and recording were made with large amplitudes. Second subharmonic vibrations were observed in the surface waves when the driving frequency is above a certain critical value. This phenomenon is yet to be accounted for theoretically.

In this paper, formulas to calculate the lift, drag and moment coefficients of a supereavitating circular arc hydrofoil with zero thickness are derived by using the linearized theory developed by Geurst. Similar to the method used in aerodynamics, we integrate the Cauehy type integral in Geurst solution by means of contour integral, the velocity field of a circular arc hydrofoil can be represented analytically. The complex velocity w(z) is then expended into Laurent series and if the coefficients of the...

In this paper, formulas to calculate the lift, drag and moment coefficients of a supereavitating circular arc hydrofoil with zero thickness are derived by using the linearized theory developed by Geurst. Similar to the method used in aerodynamics, we integrate the Cauehy type integral in Geurst solution by means of contour integral, the velocity field of a circular arc hydrofoil can be represented analytically. The complex velocity w(z) is then expended into Laurent series and if the coefficients of the first three terms in series are determined, the hydrodynamie characteristics of a circular arc hydrofoil can be derived. The object of this paper is to investigate the camber effect of a supercavitating hydrofoil upon its performance characteristics, hence the results obtained are useful in analysing the performance of the blade section of a supercavitating propeller or the hydrofoils of a high speed hydrofoil craft. The numerical calculations show that when the cavitation number and the angle of attack are sufficiently small the results may be used as the first approximations.