It is therefore likely to be pertinent to cases of isolated objects of moderate 

 size around which the flood water can establish a regime of flow. In the 

 case of large objects such as continuous breakwaters, sea walls, blocks 

 of buildings, and other objects with large frontages which are liable to 

 deter a cascading bore and obstruct the flow, the effect of both hydrostatic 

 and dynamic pressure and of the destruction or deflection of momentum 

 must be taken into account. This leads to the definition of the force F 

 per unit length of wall, in the form 



F = ^ yogd^ + C„ pdv^ (D-24) 



2'^°w F'^ts 



where d is the depth of water formed at the wall, d the depth of 

 w t 



water at the toe of the wall before deflection of the stream, u the surge 



s '^ 



velocity appropriate to the height d of the surge (Fig. D-1), P the mass 



density of sea water and C„ a dimensionless force coefficient. 



This formula is well known in the hydraulics of river and canal flow 



(cf. , for example, Francis, 1958), although usually without the inclusion 



of the coefficient C„ . Cross (1966, 1967), who introduces the equation 

 r 



to the study of tsunami surges has evaluated the coefficient C„ on the 



basis of theoretical work by Cumberbatch (I960), in which the impingement 



of a water-wedge normal to a plane wall was analyzed. Cross finds a 



nonlinear dependence of C„ on the slope of the water surface of the wedge 



or the angle (6 (Fig. D-1) such that for (6=0, C = 1.0; and (6 = 60 , 



C„ - 3. 0. 

 F 



In his experiments on tsunaiTii surges, Cross found that a peak force 

 developed on the experimental wall after the initial build-up of force, 



D-10 



