the downstream stagnation point x = L/2. The slope of each straight line 



is equal to the speed correction defined by Equation (7) . Owing to the 



skew symmetry of the potential with respect to x = 0, the result for the 



upstream half-body can be obtained from the downstream potential shown in 



Figure 3. The velocity potential increases monotonically from a value 



slightly lower than - K/2 at the upstream stagnation point to a value 



slightly higher than K/2 at the downstream stagnation point on the body 



surface. However, the potentials at R = 1.25b approach monotonically the 



asymptotic values at both ends for R /b = 1.25 and R /b = 1.5. 

 J o o 



In Table 6 the approximate mean speed correction given by Equation 

 (10) is compared with the exact mean-speed correction computed from 

 Equation (6) . Table 6 also gives the speed correction obtained by the 



Q 



Lock and Johansen formula, which is given in Pope as 



f* = 2.391 (|V 



When R /b < 3, our approximate results show better agreement with the exact 



numerical results than with those of Lock and Johansen. 



In Figure 4 computed values of the added mass coefficient and the 



mean speed correction Au/U are shown as a function of b/R . In Figure 4, 



note that for b/R > 0.765, the contribution of the added mass to the 

 o 



speed correction in Equation (10) is more dominant than the contribution 

 of the displaced volume, i.e., m = m'/p^ > 1. This finding indicates that 

 a crude blockage correction, based on only the local cross sectional area 

 of the body using one-dimensional theory, cannot always give a good 

 approximation of the mean-speed correction when the added mass coefficient 

 is not small. 



CONCLUSIONS 

 In the present study a new mean-speed formula for corrections caused 

 by blockage is proposed. The approximate formula is tested by comparing 



17 



