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The flow problem of free overfall has been examined through hodograph transformations. It has been found that even with strong influence of the gravitational field, the stream function can be solved in the hodograph plane through numerical calculations. The velocity functions of the two free streamlines must be determined through iterations and it has been found that this iterative process is rapidly convergent. Favorable agreement of the results with the experimental data substantiates the fact that this method is effective in dealing with flow problems strongly influenced by gravitation. Comparison of results of calculations with analytical results by Clarke for the case of supercritical approach flow is also presented.

An analytical study of nonsimilar jet mixing is made for compressible, nonisoenergetic flows. The conservation equations are solved for each of the streams above and below the dividing streamline by using Meksyn’s asymptotic method of integration for solving boundary-layer problems. The problem of laminar mixing between two parallel streams is investigated for the case of a constant pressure gradient. It is found that the velocity and temperature profiles from the exact solution to the nonsimilar governing equations can be well approximated by the locally similar solution.

The problem of a potential flow discharge through a two-dimensional horizontal duct under the influence of gravitation is examined by the method of hodograph transformation. The stream function is considered and established in the hodograph plane, and the solution in the physical plane is established through additional integrations. The unknown boundary functions of the free jet must be determined as part of the solution. The initial pressure level and the discharge characteristics between the total head and the flow rate, have been established. Results are compared with those obtained previously by other method.

The effect of gravity on two-dimensional imcompressible potential nozzle flows has been studied using the method of hodograph transformation coupled with numerical computation. It has been demonstrated that although hodograph transformation is an inverse technique, it has the ability to allow curved walls to be prescribed a priori. Calculations have been performed for flows discharging from symmetric nozzles with horizontal lips. The variation of total head versus discharge rate can only be obtained from detailed consideration of the gravitational effect. Some general features of nozzle flows, including the possibility of early flow separation from the top nozzle wall, have been observed.

The problems of sluice gate and sharp crested weir were studied through hodograph transformations. Numerical calculations of the stream function in terms of hodograph variables were carried out after the hodographs were transformed into rectangles. Results were compared with the available experimental data and other results of calculations. Favorable agreement in all cases substantiated the fact that the method of hodograph transformation is effective in dealing with these problems strongly influenced by gravitation.

The original analysis on incompressible flow discharge from a vessel through an axisymmetric control valve has been extended to the discharge of a compressible fluid. The inviscid anlaysis is based on the method of hodograph transformation. While it is simple to account for the effect of compressibility for conditions of subcritical pressure ratios, special treatment must be applied to establish the sonic line and the free jet boundaries under conditions of supercritical pressure ratios. Discharge characteristics have been established for different pressure ratios and positions of the control valve. This series of investigations provides ample evidence that the hodograph transformation coupled with numerical computations is effective in dealing with problems of this nature.

The problem of an incompressible flow discharge through an axisymmetric control valve has been examined through the method of hodograph transformation. The boundary value problem in the hodograph plane has an unusual feature in that part of the boundary is overlapped. Certain manipulations have been applied to produce the realistic free streamline configuration. The rate of discharge is obtained for various locations of the valve. This investigation provides the evidence that the method of hodograph transformation coupled with numerical computation is indeed effective in dealing with problems of this kind.

A model is suggested to study the viscid-inviscid interaction associated with steady incompressible flow past wedges of arbitrary angles. It is shown from this analysis that the determination of the nearly constant pressure (base pressure) prevailing within the near wake is really the heart of the problem and this pressure can only be determined from these interactive considerations. The basic free streamline flow field is established through two discrete parameters which should adequately describe the inviscid flow around the body and the wake. The viscous flow processes such as boundary-layer buildup along the wedge surface, jet mixing, recompression, and reattachment which occurs along the region attached to the inviscid flow in the sense of the boundary-layer concept, serve to determine the aforementioned parameters needed for the establishment of the inviscid flow. It is found that the point of reattachment behaves as a saddle point singularity for the system of equations describing the viscous recompression process. Detailed results such as the base pressure, pressure distributions on the wedge surface, and the wake geometry as well as the influence of the characteristic Reynolds number are obtained. Discussion of these results and their comparison with the experimental data are reported.

A flow model has been devised to deal with the viscid-inviscid interaction of a class of two-dimensional incompressible separated flow problems. It is suggested that the corresponding inviscid flow of these problems is described by the free streamline theory with few unspecified parameters and their values are, in turn, determined by the viscous flow considerations. The problem of a flow past a backward facing step is selected for study in detail. The viscous flow components of turbulent jet mixing, recompression, and reattachment are delineated and studied individually. When they are later combined, it is found that the point of reattachment behaves as a saddle-point-type singularity in the system of differential equations describing the viscous flow process. This feature is employed to the determination of the aforementioned free parameters and thus the establishment of the overall corresponding inviscid flow field. The resulting base pressure coefficient for the specific case agrees reasonably well with the available experimental data. Additional calculations are performed to demonstrate the influence of higher Reynolds numbers and the values of the similarity (or spread rate) parameter σ of the “constant pressure” turbulent jet mixing process. Further studies of redevelopment of the viscous flow after reattachment, the turbulent exchange within the recompression and redevelopment regions, and the effect of wind tunnel-wall interference on the overall flow patterns have been suggested and discussed.

The problem of low-speed slip flow of a rarefied gas over a wedge has been solved using Meksyn’s asymptotic method of integrating the boundary-layer equations. Detailed results are given for slip velocity and developing velocity profiles for various wedge angles. The solution tends far downstream asymptotically to the Falkner and Skan profiles of conventional nonslip flow. In addition, the first correction to the skin friction due to velocity slip is found to be of the order of the first power of the molecular mean free path of the gas.

The problem of hypersonic rarefied viscous interaction over a semi-infinite flat plate has been solved using Meksyn’s asymptotic method of integrating the full nonsimilar boundary-layer equations. The primary phenomena of “incomplete compression”, velocity slip, and temperature jump are incorporated into the analysis. Results are obtained for induced wall pressure, skin friction, and Stanton number variation along the plate. Detailed results are also obtained for developing velocity profiles and shock location. The pressure plateau within the merged layer region is correctly predicted and the solutions merge far downstream with the strong interaction solutions where rarefied gas effects become negligible.