7.312 Vertical Cylindrical Piles and Nonbreaking Waves - (Basic Concepts) . 

 By analogy to the mechanism by which fluid forces on bodies occur in uni- 

 directional flows, Morison et al. (1950) suggested that the horizontal 

 force per unit length of a vertical cylindrical pile may be expressed as, 

 (See Figure 7-39 for definitions.) 



ttD^ du 1 



where, 



f. = inertial force per unit length of pile, 



f^ = drag force per unit length of pile, 



p = density of fluid (2 slugs/ft^ 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) 



du 



— = total horizontal water particle acceleration at the axis of 



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



C^j = hydrodynamic force coefficient, the "Drag" coefficient, 



and 



^M ~ 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 fp 

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

 fluid (fr^ 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 that given by Equation 7-13, it should be realized that 

 expressing total force by the terms f^ and fp is an assumption justi- 

 fied only if it leads to sufficiently accurate predictions of wave force. 



From the definitions of u and du/dt, given in Equation 7-13 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 



7-66 



