cylinder. Their analysis assumes an ideal nonviscous fluid, and leads 

 therefore to a force having the form of f^. Their result, however, is 

 valid for all ratios of pile diameter to wavelength, D/L^, and shows 



the force to be about proportional to the acceleration du/dt for small 

 values of D/L^ (L^ is the Airy approximation of wavelength). Taking 

 their result as indicative of how small the pile should be for Equation 

 7-13 to apply, the restriction is obtained that 



D 

 — < 0.05. (7-14) 



Figure 7-40 shows the relative wavelength L^/L^ and pressure factor K 

 versus d/gT^ for the Airy wave theory. 



************** 



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



GIVEN : A wave with a period of T = 5 sec, and a pile with a diameter 

 D = 1 ft. in 5 ft. of water. 



FIND : Can Equation 7-13 be used to find the forces? 



SOLUTION : 



L^ = 5.12 T^ = 5.12(25) = 128 ft., 



A e, 



= 0.0062 , 



gT^ 32.2 (5)2 

 which, using Figure 7-40, gives 



^A 



- 0.47 



L 



L^ = 0.47 L^ = 0.47(128) = 60 ft. 

 = 0.017 < 0.05 . 



D _ 1 



L, ~ 60 



Since D/L^j satisfies Equation 7-14, force calculations may be based 

 on Equation 7-13. 



************************************* 



The result of the example problem indicates that the restriction 

 expressed by Equation 7-14 will seldom be violated for pile force calcula- 

 tions. However, this restriction is important when calculating forces on 

 dolphins, caissons, and similar large structures that may be considered 

 special cases of piles. 



7-67 



