is squared. For a quick estimate of the variation of the two force 



components relative to their respective maxima, the curve labeled 



K = l/cosh[2iTd/L] in Figure 7-40 may be used. The ratio of the force 



at the bottom to the force at the surface is equal to K for the inertia 



forces, and to K^ for the drag forces. 



The design wave will usually be too high for Airy theory to provide 

 an accurate description of the flow field. Nonlinear theories in Chapter 

 2 showed that wavelength and elevation of wave crest above Stillwater 

 level depend on wave steepness and the wave height - water depth ratio. 

 The influence of steepness on crest elevation n and wavelength is 

 presented graphically in Figures 7-41 and 7-42. The use of these figures 

 is illustrated* by the following examples. 



************** EXAMPLE PROBLEM *************** 



GIVEN : Depth d = 15 ft., wave height H = 10 ft., and wave 

 period T = 10 sec. 



FIND : Crest elevation above Stillwater level, wavelength, and 

 relative variation of force components along the pile. 



SOLUTION : Calculate, 



d 15 



gT^ 32.2 (10)^ 

 H 10 



= 0.0047 



= 0.0031 



gT2 32.2 (10)2 

 From Figure 7-40, 



L^ = 0.41 L^ = (0.41) (5.12)7^ = 210 ft. 



K = 0.9 . 

 From Figure 7-41, 



Vc = 0.845 H = 8.45 ft. 



From Figure 7-42, 



and 



L = 1.165 L^ = 245 ft. 



^1 (z = -d) 

 K = -p = 0.9, 



S(2 = 0) 



^D (z = -d) 

 K^ = —^ -= 0.81 . 



*D (z = 0) 



7-70 



