which reduces to 



u, = u - 



b cxut + 1 



defining the velocity of the object at any time t. 



(345) 



The distance, x, traveled by the object as a function of time can 

 be determined by noting 



dx 



dt b 



(346) 



Substituting equation (345) into equation (346) and integrating give 



j o \ out + 1 ; j j out + 1 



(347) 



which gives 



ut - — in (out + 1) 



(348) 



Typical drag coefficients are given in Table 6. The coefficient of 

 added mass, C^, can be estimated for a rectangular structure by using 

 the results of Riabouchinski (1920) as given by Brater, McNown, and Stair 

 (1958) (Fig. 69). The values in Figure 69 are for irrotational flow 

 without separation, and the formation of a wake behind the structure 

 would be expected to modify these values. Individual model tests would 

 be required to obtain exact values. Example solutions of equation (348) 

 are shown in Figure 70. 



0.4 0.6 0.81.0 

 o/b 



6 8 10 



Figure 69. C^ for two-dimensional flow past rectangular 

 bodies (irrotational flow with no separation) 

 (from Uiabouchinski, 1920). 



187 



