Yamazaki 



V (i) ~ (face pitch at 0.7 r^)/2Tj or an appropriate constant. (31) 



It is found from Eqs. (29) that the quantity 7T0(<f) represents the pitch ratio of the 

 zero lift line of the blade section at ^. 



Then we consider the boundary conditions satisfied on the hull surface Sjj 

 the mean surface Sp of the kth blade of the propeller, and the mean surface Sp, 

 of the rudder (8). Since the thickness of the boundary layer on the hull is con- 

 sidered to be very thin compared with the breadth of the hull, the viscous veloc- 

 ity may be neglected on the surface S^. Thus we obtain the boundary condition 

 on S„ as 



H 





'(SH) " ""o B^j 



KJ,.„. = -0 —^r • (32) 



where the symbol [ ],sh) indicates the quantity in the brackets at point (l,,r],z*) 

 on the surface S^ are expressed by Eqs. (17). The viscous velocity, however, 

 cannot be generally neglected in the wake behind the hull , so that the boundary 



conditions on the mean surfaces Sp and Sp are 



K + <J(sp) --^^[W*+ V*J(3p) - |[0m(O + ^(Ovj 



+ e 



d^ 



' (^p) ~e(^)dv ° (33) 



d^M(^i) d^(77j) 



dr] 



L ' 



^4(^i-")lr . , * 1 ^4(^1-") 



i(Vi)^u r ^ ^^^(SR) ° !(77j)Bu (34) 



The nondimensional viscous velocity components v*^, v*y, v*^, v*^., and 

 v*g are mainly produced by the hull, so that they can be assumed to be functions 

 of ^1, T?, and 2* and explicitly independent of s. And their vorticities are as- 

 sumed to be very small. We denote the density of water, the water pressure, and 

 the ambient pressure due to only the viscous velocity by p, p, and p^ respec- 

 tively and define the nondimensional pressures p* and p* as 



p* = p/(pn2r„2) , p* , p^/(^Q2r^2) . (35) 



We shall assume in this paper that the pressure p* at any point at any time is 

 given by the approximate equation 



26 



