Surge Direction 



Figure 66. Definition sketch of surge on a dry bed 

 (slope exaggerated) . 



where S is the bottom slope (negative upward), and du/dt the accelera- 

 tion term for flow under the tip of the surge. 



Substituting equations (326), (327), and (328) into equation (325) 



1,2 



F = | pgh 2 



u 2 + 1 du _ < 

 C 2 h + g dt " 



+ 1 



pu 2 h 



(329) 



If it is assumed that 



du 



(330) 



i.e., the acceleration is equal to the influence of gravity acting along 

 the slope (see Fig. 66), then b = and 



dh _ uf_ 



dz C 2 h 



h 



(331) 



or, defining u from equation (318) and assuming that the value is 

 relatively constant under the surge 



u z dh _ 4g 



C 2 h dz c 7 2 



h k 



(332) 



where C, varies with depth and is given by 



1.49 ,1/6 

 h 



(333) 



175 



