Ogilvie 



r = rQ(x, 9) X in A, 



where r = (y + z )' , and is an angle variable measured about 

 the X axis. It will be assumed that r = 0(e). In this section, I 

 take the most conventional definition of 6, namely, that it be 

 measured in a right-handed sense from the y axis. (In ship prob- 

 lems, it is more convenient to measure the angle from the negative 

 vertical axis.) A is the part of the x axis which coincides with 

 the longitudinal extent of the body; typically, one might take it to be 

 the interval, - L/2 < x < L/2, but I shall not insist that the origin 

 be located at the mid-length section. Figure 2-3 shows a typical 

 cross section. 



r=T^ {x,e) 



Fig. (2-3), Cross Section of the Slender Body 



As usual, assume that there exists a velocity potential, 

 ^(x,y,z), which satisfies the Laplace equation. There is an incident 

 stream which, in the absence of the body, is a uniform flow in the 

 positive X direction, with the velocity potential Ux. It will be 

 convenient to use cylindrical coordinates, (x,r,9), in which case 

 the Laplace equation takes the form: 



Vr+ 7 



+ ^^^= 0, for r > rQ(x,e). 



(2-57) 



The kinematic boundary condition on the body can be written: 



VOx - <^r + -^ Vofl = ^ °^ "■ = ro(x,e). (2-58) 



With respect to the physical arguments presented at the 



712 



