Similarly, for area, volume, discharge, and pressure. 



and 



Pr 





(4-6) 

 (4-7) 

 (4-8) 



(4-9) 



Essentially, g^ = 1 and this should be considered when referring to the 

 model scales (derived above) in Table 4-2. The similarity relations for 

 undistorted wave models, derived by the method of differential equations, 

 are also presented in Section 11,3. 



Table 4-2. Derived model scales. 



Characteristic 



Dimension 



Model-to-prototype scale 



Length 



L 



Lr 



Area 



l2 



\ = L? 



Volume 



l3 



V. - L? 



Time 



T 



T. = Ll/2 



Velocity 



L/T 



V. = l;/2 



Discharge 



L^/T 



Q, = L5/2 



Force 



F 



Fr = ^hr 



Weight 



F 



Wr = L^T, 



Pressure 



F/l2 



Pr - L^7, 



Energy 



FL 



Er = ^hr 



b. Geometrically Dissimilar (Distorted-Scale) Models . Linear-scale 

 distortion (where the horizontal length scale is not the same as the 

 scale of vertical lengths) is used in hydraulic models of harbor wave 

 action problems when the wave periods, and also wavelengths, are of a 

 magnitude that requires the use of excessively large models, and when 

 the water depths in the prototype are such that the use of an undistort- 

 ed scale would result in depths in the model so small that the friction 

 effects would be excessive. The use of distorted-scale models also pro- 

 vides easier measurement of wave heights, especially for long-period. 



208 



