entrapment, the ventilated type of shock pressure occurs. Although some 

 scale effects are involved because the acoustical velocity E^^/p^ was 

 assumed infinite (actually a function of the concentration of bubbles in 

 the water), the primary forces in the ventilated shock phenomenon are in- 

 ertial and gravitational. Thus, the impulses and the pressures can be 

 transferred from the model to the prototype with enough accuracy on the 

 basis of Froude's law. 



(2) Compression Shock . If the wave front approaching the wall 



is concave in shape, the crest part of the front can reach the wall first, 

 trapping an air pocket and producing a compression shock. This phenomenon 

 involves a very complicated process and only the impulses can be trans- 

 ferred from model-to-prototype on the basis of Froude's law. Lundgren 

 (1969) recommends the use of an equation derived by Mitsuyasu (1966), who 

 used the water-piston model of Bagnold (1939), as a "compression model 

 law" for the interpretation of model-test results when the compression 

 type of pressure curve with respect to time is obtained. This equation 

 is 



-^^^ + 0.4 M^ -\A = K-^ (6-7) 



Pat / V Pat / Pat 



where p is the maximum pressure developed on the vertical wall by 

 the compression shock phenomenon, and K is a dimensionless constant 

 equal in model and prototype. A convenient method of using equation 

 (6-7) in the interpretation of model results, as recommended by Lundgren, 

 is to: 



(a) Plot a curve calculated from equation (6-7) with values 



of (Pjj^x " Pat^/Pat °" °"® ^-^^^ ^^^ values of P^gH/Pat* ^ dimen- 

 sionless wave height, on the other axis; 



(b) use the model test data, enter the curve with the 

 value of (Pmax^m ^'^'^ determine the corresponding value of 

 the model dimensionless wave height (H(jj^nj),^; 



(c) multiply (Hdini)jn by Lp/Lj„ to obtain the dimension- 

 less value of the prototype wave (^(iini)^; and 



(d) enter the curve with the value of (H(iiin)p ^^'^ deter- 

 mine the corresponding value of the prototype pressures 



[(Pmax - Pat^/Patlp' ^^°^ ^^^^^ CPmax)p i^ calculated. 



(3) Hammer Shock . In the discussion of compression shock pres- 

 sure, the phenomenon was such that the maximum pressures which are possi- 

 ble to obtain when a plane wave front impinges on a plane breakwater 

 surface could not be generated because of the cushioning effects of the 

 trapped air pocket. However, in rare instances the wave front may be so 

 plain that a real water hammer occurs. In this case, the theoretical 

 maximum pressure that occurs is a function of the elasticity of the 



324 



