and tubes, stilling basins, and surface wave phenomena. However, every 

 effort should be made in the model design to minimize the effects of 

 viscous forces. In harbor wave action models, for instance, the bottom 

 friction effects may be appreciable in the model, whereas they are 

 negligible in nature. Thus, in wave action models, long reaches in 

 shallow water should be avoided and the wave heights in such areas should 

 be corrected by theoretical means. If it were possible to satisfy both 

 the Froude and Reynolds model laws simultaneously, most of the fluid-flow 

 phenomena that occur in hydraulic and coastal engineering problems could 

 be simulated with considerable accuracy, and without the necessity of 

 making scale-effect corrections. However, this would require that 



\ h^r 



(g,L,)l/2 



which, because g^ = 1» reduces to 



l3/2 



(2-18a) 



(2-18b) 



This relationship shows that when either the model fluid or the linear 

 scale of the model is selected, the value of the other is fixed. It can 

 also be shown that the use of a reasonable linear scale will result in a 

 required viscosity for the model fluid that does not exist. For example, 

 a linear scale of 1/10 will result in a viscosity scale of 1/30, and since 

 water is the prototype fluid in most coastal engineering problems, no such 

 model fluid can be found. For those phenomena in which forces are exerted 

 by a moving fluid on an immersed object, the forces may be evaluated by 

 the drag- force equation, 



F = Cj^ApV^ (2-19) 



where Cq = f (Rn, shape of object). For a given shape, the value of 

 Cd will vary with Rn over a certain range of Rn. Thus, when Cd is 

 constant the drag forces will be modeled accurately using the Froude model 

 law; i.e., from equation 2-17b, 



^r ^t r ^r H 'r 

 and there would be no need for a scale-effect correction. 



2. Similarity by Dimensional Analysis . 



Dimensional analysis treats the general forms of equations that 

 describe natural phenomena, and the theory of dimensional analysis is 

 an algebraic theory of dimensionally homogeneous functions. If the form 

 of an equation does not depend on the fundamental units of measurement, 

 it is considered dimensionally homogeneous. Any mathematical equation 

 of motion must be dimensionally homogeneous if it is physically correct, 

 and each term in the equation must contain identical powers of each of 



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