system that observations on the model may be used to accurately predict 

 the performance of the physical system. 



a. Similitude . The general theory of model design is based on the 

 fundamental principle that a functional relationship exists among all the 

 variables associated with the system. Further the number of variables 

 can be significantly reduced by forming a complete set of dimensionless 

 variables for which a new function expressing the relationship between 

 the dimensionless terms exists. If the model is designed so that each 

 of the dimensionless terms of the complete set is the same in the model 

 as in the prototype, then the nature of the unknown function is identical 

 for the model and the prototype. If all these conditions are satisfied, 

 the model is considered a "true" model which provides accurate informa- 

 tion concerning the behavior of the prototype. 



Although space limitations for the construction of the model may 

 sometimes dictate that the model be distorted, a physical model can 

 usually be operated with the same linear scale in all three dimensions 

 (i.e., an undistorted-scale model). This dictates that geometric simi- 

 larity exists, as the ratios of all homologous dimensions on the model 

 and prototype are equal. 



In addition to geometric similarity, a true undistorted-scale model 

 requires that kinematic similarity and dynamic similarity also exist. 

 Kinematic similarity exists when the ratios of all homologous velocities 

 and accelerations are equal in the model and prototype. Dynamic similar- 

 ity requires that the ratios of all homologous forces be the same in the 

 model and prototype. Since force is related to the product of mass and 

 acceleration, dynamic similarity implies the existence of kinematic simi- 

 larity which, in turn, implies the existence of geometric similarity. 



For an inlet model, the forces influencing the physical phenomena 

 include pressure, gravity, viscosity, surface tension, and Coriolis (to 

 a lesser extent). The Coriolis force has a significant effect on wind- 

 driven and tide circulations and water surface elevations in large tidal 

 estuaries, bays, and lakes; however, for a localized system such as a 

 tidal inlet, Coriolis force is truly insignificant. Elasticity is neg- 

 ligible in either case. 



Each force is related to the geometry and motion of the flow. In 

 Newton's second law of motion, the inertial force, Fj^, equivalent to 

 the product of mass and acceleration, is equal to the sum of all external 

 forces applied to a body. This inertial force can be considered as the 

 vector sum of all the others, or 



p. ziF +F +F +F r7-n 



where Fp^, Fg, Fjj, and Fst are the forces due to pressure, gravity, vis- 

 cosity, and surface tension respectively. These forces usually suffice 

 to describe hydraulic phenomena. 



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