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Dimensional Analysis
Published in V. Dakshina Murty, Turbomachinery, 2018
In the field of turbomachinery, the size precludes the possibility of conducting full-scale tests. For instance, the runner diameters of the Francis units at the Grand Coulee dam are 32 feet! To do performance testing on such units, it becomes necessary to use geometrically similar models, much smaller in size. In such tests, the full-scale structure is called the prototype and the replica is called the model. The performance of the prototype can be predicted by testing the model using the principle of similitude. In this context, the three types of similitude that are used in model testing are geometric similitude, kinematic similitude, and dynamic similitude. Geometric similitude implies that the ratios of all linear dimensions of the model and prototype are the same, in addition to them having similar shapes. Kinematic similitude implies that kinematic variables, such as blade velocities, relative velocities, flow speeds, and so on, should be in the same proportion for the model and prototype. This is assured when the velocity triangles for the model and prototype are similar. Finally, dynamic similitude implies that the ratios of all forces on the model and prototype are the same. This requires that all the relevant dimensionless numbers involving dynamic quantities are the same for both model and prototype.
Fluid Mechanics
Published in Raj P. Chhabra, CRC Handbook of Thermal Engineering Second Edition, 2017
Stanley A. Berger, Stuart W. Churchill, J. Paul Tullis, Blake Paul Tullis, Frank M. White, John C. Leylegian, John C. Chen, Anoop K. Gupta, Raj P. Chhabra, Thomas F. Irvine, Massimo Capobianchi
Similitude refers to the formulation of a description for physical behavior that is general and independent of the individual dimensions, physical properties, forces, etc. In this subsection, the treatment of similitude is restricted to dimensional analysis; for a more general treatment see Zlokarnik (1991, 2006). The full power and utility of dimensional analysis is often underestimated and underutilized by engineers. This technique may be applied to a complete mathematical model or to a simple listing of the variables that define the behavior. Only the latter application is described here. For a description of the application of dimensional analysis to a mathematical model see Hellums and Churchill (1964).
Laboratory Techniques for Processability Testing
Published in Nicholas P. Cheremisinoff, Polymer Mixing and Extrusion Technology, 2017
The major obstacle in material testing is the ability to scale up laboratory characterization data to full-scale processing equipment. This in fact is a formidable task that is further complicated by economic constraints of manufacturing. Manufacturing operations are manpower intensive and costly. These factors often mandate that processability tests be made simple, fast, and inexpensive, especially when they are implemented in plant operations for product quality control purposes. Unfortunately, the simpler the test, very often the less correlation it has with processability in full-scale equipment. Another serious problem that plagues even the more sophisticated processability testing labs is the scale of equipment, since geometric differences may exist between small-scale apparatuses and commercial equipment. The classical approach to scale-up makes use of the principles of dimensional analysis. The method of similitude requires two fundamental criteria in order to scale up properties or equipment: these are geometric similitude and dynamic similitude. Very often, lab-scale versions of such equipment as mixers or extruders have significantly different geometries than their commercial counterparts. In addition, to minimize experimental efforts and cost, testing is often limited to a very narrow range of conditions. When the laws of similitude are in fact ignored, efforts in laboratory-scale processability testing can be wasted and projections as to a product’s performance in a commercial operation can be misleading.
Mobile-bed similitude evaluation of hydraulic sediment response models
Published in Journal of Applied Water Engineering and Research, 2019
Muhammed T. Mustafa, Amanda L. Cox, Robert D. Davinroy, Bradley J. Krischel, Ivan H. Nguyen
Similitude, or similarity, is the existence of a relationship between a model and prototype such that hydraulic conditions in a model at a specific location and time are proportionally related to hydraulic conditions in the associated prototype at the corresponding location and time. Perfect similitude requires that the model and prototype be geometrically, kinematically, and dynamically similar. Geometric similarity is the similarity between length ratios, and kinematic similarity is the similarity between motions. Dynamic similarity is achieved when similarity between forces exist while maintaining geometric and kinematic similarity. For physical hydraulic modelling, the relevant forces include inertial, gravitational, viscous, pressure, and surface-tension forces (Heller 2011).
Determination method of scaling laws based on least square method and applied to rectangular thin plates and rotor-bearing systems
Published in Mechanics Based Design of Structures and Machines, 2020
Wen Di Zhang, Zhong Luo, Xiao Biao Ge, Yong Qiang Zhang, Si Wei Guo
To guide experimental design, reduce cost of manufacturing, and predict dynamic characteristics of practical engineering structures, the similitude theory has been widely applied in various fields of engineering. Geometrically similitude models are divided into completely and incompletely (distorted) similitude models, and most of the practical engineering structures are based on geometrically distorted models. In similitude theory, though a great deal of investigations are discussed with respect to unit structures, relative few investigations are shown for complex systems. Consequently, the dynamic scaling laws of geometrically distorted model and scaling laws of the complex system have become important investigation focus nowadays.
Seismic Performance of Frame–Shearwall Structure with Long-Span and High-Level Steel Transfer Trusses
Published in Structural Engineering International, 2021
Jingsong Liu, Xun Sun, Fengyong Lu, Cuikun Wang
The model should satisfy dynamic similitude requirements in order to ensure the model behaves in a similar manner to the prototype. The similarity of lateral force resisting members between the model and the prototype is considered firstly because this test is to study the overall seismic response of the building.14–17