APPROXIMATE MEAN-SPEED INCREMENT 



In this subsection, the method of obtaining an approximate speed 



correction formula is given, based on the potential jump discussed earlier 



12 

 by Bai. Define K as a jump in the velocity potential (J) given in 



Equation (1) between the infinite upstream and downstream directions. The 

 potential jump K is given by integrating the speed increment along a line 

 in the fluid from a point infinitely far upstream to a point infinitely 

 far downstream. Numerical solutions for practical ship forms at sub- 

 critical speeds in towing tanks and for slender bodies of revolution in 

 wind tunnels indicate that most of the potential jump occurs along the 

 body length. This finding, observed in numerical solutions, will be used 

 as the basis for obtaining the present approximate formula for the speed 

 correction. It is possible to prove this empirical finding by showing 

 that the values of the potential at the upstream and downstream stagnation 

 points are approximately equal to the corresponding asymptotic values of 

 the potential in the simple case of axisymmetric flow. However, the proof 

 will not be discussed here. Thus, the mean speed increment u due to 

 blockage is approximated by 



Au = f (7) 



In a recent simple analysis,* the expressions for the potential jump 



K in terms of the effective volume and the depth Froude number F in three 



n 



dimensions with a free surface were 



K = fr*»'/p) U (8) 



WH (1-F R ) 



*A more detailed analysis in general cases has been submitted in a 

 paper to the Journal of Fluid Mechanics (1978) . 



