Yamazaki 



To calculate these viscous velocity components we must require full knowledge 

 of the three-dimensional tvurbulent boundary layer and turbulent wake, but we 

 will not further refer to the problems in this paper. Moreover, if both the ve- 

 locity induced by and the viscous velocity are small compared with the ship 

 speed V, these velocities should approximately be superposed on each other. 



For convenience, defining the nondimensional quantities 



^ = '■/•"o ' ^A=V''o' ^F=''f/'"o' ^b(^i) = yb(''i)/''o' ^d(^i) = yd(''i)/'^o' 



^o(^i'^i) = ^oC'^i-yiV'-Q- ^B='-b/'-o' ©(^) = aC'^V'-o' ^(^) = h(x)/ro , 



4(^'V) = ''b('^'V)/ro' ^m(^)=^m(0. ^(^)=^(r). t*(^,v) = t(r,v)/ro , 



S^ = 277(k- i)/N - nt, T^, = yyr„, -n.^y./r^, ^m(^i) = '^MCyiVro' 



U^i)= x(y^)/ro, z* (77^,u) = ZR(y^,u)/ro, tJ(T7j,u)= t^{y^,u)/T^, 



^0 = V/Cfir^), m*(^^,77^,s) = m^Cx^ , y, , t )/(nr „) , gk(^.v,s) = 7^{v ,v ,t)/{^v ^) , 



gR(T?j,u,s) = 7R(yj,u,t)/(nro2), 0* = 4^/{^r^), 4^^ = ^h/C^^o')' ^P = <PWi^^^)^ 



0* = <^R/("r„2 ) , w* = wy(Qr„) , w; = w/(fir„), w* = w^Cfir^) , w* = ^ ,/ {^v ^) , 



-tr= Vi,/(nr„), V*, = v,,/(nr„), (15) 



we obtain from Eqs. (2), (3), (12), and (13) 



^ = ^1 - v^s, r] = r]^ - ^ cos 6, z* = z* = ^ sin 6' , 

 w* = w* cos 6* + w* sin (9 , w* = -w* sin + w* cos d , 

 ^ir = ^ly <^°S ^ + ^*z ^i" ^' ^*e = ~^% ^i" ^ + ^*z COS (9 . (16) 



The surface Sjj of the ship hull is expressed from Eq. (4) as 



(,= ^,-v^s, v=rj^, z* = z*= (-ir-^zla^,r,^), (17) 



where 



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