Theory of Hydraulic Models

Abstract

PrefaceThe present book concerns the design of hydraulic models. Theory cannot cover all the complications that are encountered in practice, so that almost every major project in the field of hydraulic engineering undergoes a 'model test' where, on a small scale model, the flows and their consequences corresponding to various versions of the scheme may be observed, and the relevant quantities measured. As a result of these observations and measurements, the most effective and rational design of the scheme can be determined.A hydraulic model is a precision device for the experimental investigation of a hydromechanical phenomenon, which can give reliable information only if its scales are determined according to certain definite rules; that is, if it is designed correctly. If the design is not correct, then the model is wrong in principle. In that case, the employment of the most sophisticated instrumentation and measurement methods can only help to increase the accuracy of the wrong predictions. A small scale reproduction of a physical phenomenon can be a scientifically valid model only if a certain set of its measurable characteristics are related to their counterparts in the actual phenomenon, or prototype, by certain constant proportions which satisfy definite mathematical conditions. These constant proportions are referred to as scales, whereas the mathematical conditions which must be satisfied by the scales are called the criteria of similarity. It follows that the design and realization of a true model of a phenomenon can only be achieved if the similarity criteria of that phenomenon are known. These can be revealed by the mathematical relationships (usually differential equations of motion) describing the physical nature of the phenomenon under investigation. However, the accuracy, and thus the reliability of the results determined by this method, depend entirely on the reliability of the mathematical relationships used, and if the phenomenon has not been formulated mathematically then its criteria of similarity simply cannot be v vi Preface determined. This is an ironic situation, for a model is of greatest use in those cases which cannot be formulated theoretically.Another, and considerably more effective way of determining the criteria of similarity is the dimensional method. Here, the criteria of similarity are supplied from dimensional study of the characteristics themselves and not from the mathematical relationships (containing the characteristics involved). In other words, the criteria of similarity are supplied by the dimensional method without the risk of misinterpretation of the physical nature of the phenomena (which might be inherent in mathematical relationships). The dimensional method has been the subject of considerable controversy and it has taken a long time for it to be accepted that it is not a 'dangerous tool which can often give erroneous results', but that it is a tool which, like every other mathematical tool, always gives correct results if correctly used and which gives erroneou...

Experimental alluvial fans: Advances in understanding of fan dynamics and processes

“…With regard to similarity, three types are important to physical model studies (French, 1987): (i) geometric similarity, where all corresponding dimensions are similar and pertain to similarity in form; (ii) kinematic similarity, where the paths of motion are geometrically similar and ratios of the velocities of the two motions are equal; and (iii) dynamic similarity, where the ratios of the masses and the ratios of the forces involved are equal. In most experimental models, geometric and kinematic similarity can be rather easily achieved; however, complete dynamic similarity is often difficult if not impossible (Yalin, 1971). This is because not all parameters from the field can be accounted and appropriately scaled for within the model; there is no practical way of scaling the forces of gravity, fluid viscosity, and temperature and these will generally be the same for the model and the prototype (detailed discussion of similarity in experimental models is provided in Paola et al, 2009).…”

Beach and dune erosion during storm surges

“…The three major dlmenslonless numbers for the interaction of natural water and quartz sand are: the Reynolds number, the denslmetrlc Froude number and the dlmenslonless fall velocity parameter (Yalin, 1971;Le Mehaute, 1970). The numbers and the corresponding scale relations are elaborated below.…”

Sediment Evacuation from Reservoirs through Intakes by Jet-Induced Flow

“…Furthermore, the density ratio between solid particles and fluid was adopted from ρ s =ρ f ¼ s ≈ 2.68 in prototypes to s ≈ 1.5 in the model. This adjustment allows also for the consideration of similarity in sediment transport when it comes to prototype applications (Yalin 1971).…”

“…The model parameters under consideration for the dimensional analysis are as follows: Underlying Buckingham's П-theorem (Buckingham 1915), the dimensionless numbers (П-groups) were determined with respect to the particles' drag. In accordance with Yalin (1971), the inverse of the Reynolds number and of the Froude number are determining nondimensional parameters in terms of dynamic similarity. Accounting for the dynamic significance of gravity as a driving force, Froude similarity is applied.…”