in equations (4-34a) , (4-34b), (4-36a), and (4-36b) is equal to unity. 

 The methods of Le MeHaute and Keulegan for the determination of K have 

 been compared in Table 4-5 for common values of Pp, (AL)p, Dp, dp, Tp, 

 and (Hx)p, a distortion factor of 4, a vertical scale of 1:100, and a 

 kinematic viscosity corresponding to a temperature of 21° Celsius (70° 

 Fahrenheit). The values of (AL)p and dp were 45 and 30 feet, respec- 

 tively. Values of pp. Dp, Tp, and (Hi)p were 0.40 foot; 0.25, 0.50, and 

 0.75 foot; 60, 120, and 180 seconds; and 1.0 and 2.0 feet; respectively. 

 It was assumed that P™ = Pp- 



Table 4-5. Values of K according to Le Mehaute and Keulegan for distorted-scale models.* 



dp 



Tp 



Hp 



Dp 



Kl^ 



Kk^ 



Kl 



(ft) 



(s) 



(ft) 



(ft) 







Kk 



30 



60 



1.0 



0.25 



17.0 



6.6 



2.58 



30 



120 



1.0 



0.25 



17.0 



6.6 



2.58 



30 



180 



1.0 



0.25 



17.0 



6.6 



2.58 



30 



60 



1.0 



0.50 



12.0 



4.9 



2.45 



30 



120 



1.0 



0.50 



12.0 



4.9 



2.45 



30 



180 



1.0 



0.50 



12.0 



4.9 



2.45 



30 



60 



1.0 



0.75 



9.5 



4.2 



2.26 



30 



120 



1.0 



0.75 



9.5 



4.2 



2.26 



30 



180 



1.0 



0.75 



9.5 



4.2 



2.26 



30 



60 



2.0 



0.25 



14.8 



6.3 



2.35 



30 



120 



2.0 



0.25 



14.8 



6.3 



2.35 



30 



180 



2.0 



0.25 



14.8 



6.3 



2.35 



30 



60 



2.0 



0.50 



10.5 



4.7 



2.24 



30 



120 



2.0 



0.50 



10.5 



4.7 



2.24 



30 



180 



2.0 



0.50 



10.5 



4.7 



2.24 



30 



60 



2.0 



0.75 



8.5 



3.9 



2.18 



.30 



120 



2.0 



0.75 



8.5 



3.9 



2.18 



30 



180 



2.0 



0.75 



8.5 



3.9 



2.18 



'fh)r =1=400; (L,)^^ 1:100. 



^Subscripts L and K refer to Le Mehaute and Keulegan, respectively. 



As in the case of short -period waves and geometrically similar models, 

 the problems of obtaining dynamic similarity for wave transmission in 

 distorted-scale models should be further investigated; meanwhile, the 

 results of investigations by Le Mehaute (1965) and Keulegan (1973) can 

 be used to minimize the scale effects to the extent that satisfactory 

 results can be obtained for most practical problems. Because of the 

 difference in the results of the two methods, and because it is not 

 known which of the two methods is the most accurate, the values of K 

 used in design of model structures are again recommended to be the aver- 

 age of those calculated by the two methods in accordance with equation 

 (4-40). 



234 



