Four aspects of the problem of describing the phenomena governing the flow pattern in a lake are investigated with the aid of simple mathematical models. Analogies are pointed out between the two-dimensional models and the corresponding problems in the elastic deformation of thin rigid plates. A. The dependence of the flow pattern in a longitudinal vertical cross-section of a lake on a given temperature distribution within the lake is studied with the aid of a two-dimensional lake model of semicircular vertical cross-section. A stream function satisfying the two-dimensional non-homogeneous biharmonic equation is introduced. Solutions are found consisting of a through flow function having a source and sink at the ends of the diameter plus a circulation function which is obtained in terms of a Green's function and the horizontal density gradient. The total stream function satisfies the conditions of no slipping at a solid boundary and zero stress at a free surface. Two cases of simple density structure are considered, and streamlines are drawn for several ratios of circulation to through flow. B. The departure of the lake surface from the horizontal required to maintain a pressure head sufficient to overcome eddy viscosity is estimated by considering the pressure distribution in the case of the through flow function introduced above. C. The effect of Coriolis forces on the flow in a canal is investigated with the aid of a three-dimensional semi-oylindrical model. It is shown that the effect on the shape of the canal surface is negligible. For a sufficiently low value of vertical density stratification the effect of Coriolis forces may show up in the tilting of constant density surfaces. D. The effect of wind stress on circulation in a vertical lake cross-section is investigated mathematically with the aid of a two-dimensional model. The results are found to agree quite closely with experiments on the deformation of a semicircular plate recently reported in the literature. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

This study investigates the stability of a simple surge tank operating in conjunction with a turbine. The turbine is assumed to be governed for constant power output or for constant gate opening, depending on whether the instantaneous head acting on the turbine is greater or smaller than the rated head. Early investigations on the stability of oscillations assumed that the governor on a turbine ensured constant power output. In practice, the governor on a turbine can maintain constant power output only when the oscillations remain above the rated head and the full-gate position is not reached. For this case, a computer study showed that results of the investigation are in close agreement with the results of several investigators. A revised form of the Thoma's formula for surge tank stability with oscillations of large amplitude is proposed. When the head during the maximum downsurge falls below the rated head of the turbine the constant gate opening condition must be considered. A computer program was developed to study the stability of oscillations of large amplitude under constant gate opening condition. The transient conditions for three cases of load demand with initial steady state discharge of zero, one quarter and one half of the final steady state discharge were studied. The graphical form of the results allows the prediction of surge tank stability for oscillations of large amplitude for a simple surge tank. The graphs for all three conditions show that an increase in the rated head has a stabilizing influence on surge tank oscillations. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

No description available.

No description available.

No description available.

Note:

Note:

No description available.

Inaug.-diss.--Technische Hochschule, Karlsruhe.

Thesis (Ph. D.)--University of South Florida, 2003. / Includes vita. Title from PDF of title page. Document formatted into pages; contains 185 pages. Includes bibliographical references.