where 



f- = inertial force per unit length of pile 



fp = drag force per unit length of pile 



p = density of fluid (1025 kilograms per cubic meter for sea water) 



D = diameter of pile 



u = horizontal water particle velocity at the axis of the pile 

 (calculated as if the pile were not there) 



-J— = total horizontal water particle acceleration at the axis of the 

 pile, (calculated as if the pile were not there) 



Cp = hydrodynamic force coefficient, the "drag" coefficient 



Cw = hydrodynamic force coefficient, the "inertia" or "mass" coefficient 



The term f • is of the form obtained from an analysis of force on a body 

 in an accelerated flow of an ideal nonviscous fluid. The term fj^ is the 

 drag force exerted on a cylinder in a steady flow of a real viscous fluid 

 (f„ is proportional to u and acts in the direction of the velocity u ; for 

 flows that change direction this is expressed by writing u as u|u|) . 

 Although these remarks support the soundness of the formulation of the problem 

 as given by equation (7-20), it should be realized that expressing total force 

 by the terms fj and fj~, is an assumption justified only if it leads to 

 sufficiently accurate predictions of wave force. 



From the definitions of u and du/dt , given in equation (7-20) as the 

 values of these quantities at the axis of the pile, it is seen that the 

 influence of the pile on the flow field a short distance away from the pile 

 has been neglected. Based on linear wave theory, MacCamy and Fuchs (1954) 

 analyzed theoretically the problem of waves passing a circular 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 (7-20) to apply, the restriction is 

 obtained that 



f- < 0.05 (7-21) 



Figure 7-68 shows the relative wavelength ^a^^o ^"^^ pressure factor K 

 versus d/gT for the Airy wave theory. 



*************** EXAMPLE PROBLEM 16************** 



GIVEN ; A wave with a period of T = 5 s , and a pile with a diameter D = 0.3 

 m (1 ft) in 1.5 m (4.9 ft ) of water. 



7-103 



