d. Similitude Ratios . The model-prototype relationships for the 

 different flow characteristics (velocity, time, force, etc.) can be 

 obtained directly from the derived dimensionless ratios, equations 2-10 

 to 2-14. For example, with the Froude number the same in model and pro- 

 totype, and with gm = gp. 



from which 



r r 



and, since L = VT 



(2- 15a) 

 V, = lJ/2 (2- 15b) 



Tr = L^^ ^ (2-16) 



Since force is mass times acceleration 



Fr = M^hT = -y-i = L2p^v2 = l3^^^ (2-17a) 



r r ^rr 



Substituting the values of Vr and T^ from equations 2- 15a and 2-16 

 and considering that gm = gp, 



Fr - h^Jr . (2- 17b) 



Other ratios for the Froude-law condition, and for other types of phe- 

 nomena where the Reynolds, Weber, or Mach-Cauchy number must be adhered 

 to, can be derived in a manner similar to the above. The derived rela- 

 tionships for the conditions that occur frequently in coastal engineering 

 flow problems (i.e., where gravitational or viscous forces predominate) 

 are listed in Table 2-1. 



e. Importance of Reynolds and Froude Numbers .. The Reynolds and 

 Froude numbers are of great importance to hydraulic engineers because 

 they provide the necessary conditions, in addition to that of geometric 

 similarity, for flow similitude between model and prototype for those 

 types of flow in which the compressibility and surface-tension effects 

 can be neglected. If the Reynolds number is numerically the same in 

 model and prototype there will be dynamic similarity with respect to 

 inertia and viscous forces. The model can be used to study all problems 

 that involve the flow of liquids where viscous forces predominate, surface 

 tension is negligible, and gravity has no effect on the flow (such as the 

 flow of liquids through pressure conduits) , the motion of deeply submerged 

 bodies (when surface and internal waves do not occur) , or flow patterns 

 around objects (when the velocities are not so high as to cause cavita- 

 tion). Thus, there are few problems in coastal engineering that can be 

 studied on scale models using Reynolds number as the sole criterion for 

 similarity. For many problems in hydraulics and coastal engineering it 

 is sufficient for similitude that the Froude number be the same in model 

 and prototype; e.g., models of spillways, open-channel flow, short slucies 



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