where, F = total drag force on object, lb 

 Cq = drag coefficient 

 A = cross-sectional area of object, ft^ 

 p = fluid mass density, slug/ft-^ 

 U = flow velocity, ft/sec 



The drag coefficient depends on the shape and surface roughness of the 

 object, the angle of attack of the flow and the Reynolds number R = DU/v, 

 where D is the characteristic length of the object in ft. and v the 

 kinematic viscosity of the fluid in ft^/sec. The value of Cq can be 

 obtained analytically only when in the region of low Reynolds number i.e. 

 when the flow is laminar. For large objects and/or high flow velocities, 

 the flow becomes turbulent and values of Cq are best obtained by conducting 

 scale model tests in Laboratory flumes or wind tunnels. Many such tests 

 have been made in the past and curves of C^ vs R have been established 

 from the test data for many basic geometric shapes in the Reynolds number 

 range from near zero to 10 . 



Therefore, Equation (1) has been used widely to estimate drag forces 

 with empirical values of Cq. Drag forces caused by surface wind or 

 underwater currents can be calculated from Equation (1) using a mean wind 

 or current velocity. 



This classical drag formula is useful but is limited to constant 

 velocity flow only. For oscillatory flow or flow in the surface wave zone, 

 the Morison equation for piles is widely used.-^ It has an additional term 

 to account for the inertia component of the total wave induced drag 



P = Cd D -y- + Cx -^ pa ^^^ 



where, P = local wave force per unit length, lb/ft 

 D = diameter of pile, ft. 



V = horizontal component of water particle velocity, ft/sec 

 a = horizontal component of water particle acceleration, ft/sec 

 Cj = inertia coefficient 



The second term at the righthand side of Equation (2) is the inertia force 

 which is directly proportional to the local particle acceleration and to 

 the square of the pile diameter. The inertia coefficient, C j , is not as 

 well-established as the drag coefficient, Cq, and it is also more difficult 

 to measure than the drag coefficient. Since the velocity and the acceleration 

 are 90° out of phase in sinusoidal flow, the drag term and the inertia 

 term are also 90° out of phase. The total wave force is really a vectorial 

 sum of the two components. Therefore, the magnitude of the total force 

 will be approximately equal to the larger component when the larger component 

 is about 2.5 times the smaller component-^. In cases where the drag force 

 dominates the wave force. Equation (1) is valid. 



