breakwater material and the compressibility of the water. In this theory 

 the effects of the air that is usually trapped are ignored. According to 

 Kamel (1968b) the maximum shock pressure that can occur is given by the 



relation 



where 



^v/ w '^bm bm 



p = theoretical maximum pressure 



Pbm ^"'^ Pw ~ mass densities of the breakwater material and the 

 water (respectively) 



C^jj, and C^^ = acoustical velocities of the shock front in the 

 material and the water (respectively) 



V^ = velocity of the water (wave front) impinging on 

 the structure 



Kamel performed special tests where plates of different types of metal 

 were dropped on both glassy and disturbed water surfaces, and the result- 

 ing pressures were recorded electrically. His results showed that, be- 

 cause all the air could not be evacuated from the area between the plate 

 and the water surface at the instant of impact, the recorded pressures 

 were never more than about 50 percent of the theoretical. Considering 

 that a prototype breakwater surface will never be as smooth and regular 

 as the test plates, that a storm wave front will never be as plane as the 

 glassy water surface used in the tests, and that a prototype wave at the 

 instant of breaking will contain large amounts of trapped air in the form 

 of bubbles, pressures more than 0.5p|- are believed unlikely to occur 

 for a full-scale structure. Therefore, model studies for determining the 

 maximum shock pressures on breakwaters are considered unnecessary. How- 

 ever, such tests, designed and operated by Froude's law, can give valuable 

 information as to the relative magnitude of water-hammer shock pressures 

 for different geometric shapes of the breakwater. 



(4) Shape of Pressure Curves and Model Design . The above dis- 

 cussions showed that the method of model design and interpreting the re- 

 sults varied with the type of phenomena causing the wave pressures (ven- 

 tilated shock, compression shock, and hammer shock). The type of phe- 

 nomena involved in a particular model study can be determined by observ- 

 ing the shapes of the recorded pressure curves. The pressure curves for 

 the ventilated and compression shock are similar in shape, varying in the 

 rate of pressure rise and the maximum pressure. The water-hammer shock 

 curve has a very fast rising front and a very high maximum pressure com- 

 pared with the ventilated and compression shocks. Figure 6-2 shows the 

 shapes of the compression- and hammer-shock pressure curves as recorded 

 in wave-flume tests by Hayashi and Hattori (1958). 



325 



