Figure 7-72, for shallow-water waves with H 

 consequently the total force may be written 



= Hfo , gives KDm = 0.96 « 1.0; 



F^ = C 



m 



V2^^^ Hb 



(7-63) 



From Figure 7-74, the corresponding lever arm is ^h^Dm " ^b (I'H) ^^^ the 

 moment about the mud line becomes 



Mm= ^m (1-11 ^h) 



(7-64) 



Small-scale experiments (R^ « 5 x 10 by Hall, 1958) indicate that 



F « 1.5 pg D h; 



(7-65) 



and 



M « F H, 



m mo 



(7-66) 



Comparison of equation (7-63) with equation (7-65) shows that the two 

 equations are identical if C^p = 3.0 . This value of Cjj is 2.5 times the 

 value obtained from Figure 7-85 (Cp = 1.2 for Rg " 5 x 10^). From Chapter 2, 

 Section VI, since Hj, generally is smaller than (1.11) d^ , it is con- 

 servative to assume the breaker height approximately equal to the lever arm, 

 1.11 d-L . Thus, fhe proseduve outlined in Section III,l,b of this chapter may 

 also be used for breaking waves in shallow water. However, Cd should be the 

 value obtained from Figure 7-85 and multiplied by 2.5, 



Since the Reynolds number generally will be in the supercritical region, 



where according to Figure 7-85 , 

 breaking wave forces using 



Cp = 0.7 



it is recommended to calculate 



(S) 



breaking 



= 2.5 (0.7) = 1.75 



(7-67) 



The above recommendation is based on limited information; however, large- 

 scale experiments by Ross (1959) partially support its validity. 



For shallow-water waves near breaking, the velocity near the crest 

 approaches the celerity of wave propagation. Thus, as a first approximation 

 the horizontal velocity near the breaker crest is 



""avest " yf^" V^^fc" 



(7-68) 



where Hj, is taken approximately equal to d^ , the depth at breaking. Using 



7-158 



