satisfied simultaneously. This requirement can only be met by choosing 

 a special model fluid. Since water is the only practical model fluid, 

 an approximate similarity requirement may be used, based on empirical 

 relationships which include the major effects of frictional forces (such 

 as Manning's equation). This approach is used in studying inlet prob- 

 lems. Another approach is to attempt to correct both model and proto- 

 type measurements for the forces due to friction during operation of the 

 model by Froude law. 



Since fairly high Reynolds numbers are usually associated with tidal 

 flow through an inlet, the shear stresses are primarily determined by 

 form drag. When Manning's formula is used in an undistorted-scale model, 

 and assuming similarity for velocity. 



l}" 



= t1/6 



V, - -^— and n, = Li'» , (7-4) 



where n is Manning's roughness coefficient. 



The use of Manning's formula as a similarity criterion requires that 

 the flow be fully rough turbulence in both the model and the prototype. 

 When a bulk Reynolds number defined as Vd/v is greater than about 1,400 

 (where d is the depth of flow and v is the kinematic viscosity), fully 

 rough turbulence will normally exist. 



A surface gravity wave is essentially a gravitational phenomenon; 

 therefore, the controlling criterion of similitude is the Froude number, 

 and waves may be represented correctly in undistorted-scale models. 



Based on the Froude criterion of scaling, and considering an 

 undistorted-scale, fixed-bed model, the geometric, kinematic, and dy- 

 namic scaling ratios may be expressed in terms of the model-prototype 

 length ratio used for scaling, L^., when the same fluid is used in the 

 model and the prototype (see Table 7-2). 



There are several physical interpretations that may be given the 

 Froude number, but fundamentally it is the ratio of inertial to gravita- 

 tional forces acting on a particle of fluid. It can be shown that this 

 ratio reduces to V/(gL)^''^, where V is a characteristic velocity, 

 and L is a representative length. Here the velocity is taken to be a 

 horizontal length divided by the time parameter. However, any represen- 

 tative velocity and any representative length can be used in the Froude 

 number as long as dynamic similarity is maintained and corresponding 

 regions are considered in the model and prototype. For an undistorted- 

 scale model, the scaling ratios in Table 7-2 are appropriate; here the 

 time and velocity ratios are equal to the square root of the linear scale 

 ratios, where the horizontal and vertical linear scale ratios are identi- 

 cal. The Froude number, defined as V/(gd)^/2, is related to the 



465 



