calculation problem in terms of the momentum- integral entrainment method. 

 The third section describes the surface coordinate system and the potential 

 flow calculation method. The fourth section describes the numerical method 

 for integrating the momentum- integral equations. The fifth section 

 describes and discusses some sample computational results and the sixth 

 section gives some concluding remarks on further developments of this 

 three-dimensional ship boundary layer calculation method. An appendix at 

 the end of the report gives some detailed formulas that are used in the 

 computational algorithm. 



THE BOUNDARY LAYER MOMENTUM INTEGRAL EQUATIONS 

 It is assumed that the ship surface is hydraulically smooth and has 

 no abrupt changes in principal curvature anywhere on the hull. Also assumed 

 is that the boundary layer thickness is small compared to the principal 

 curvatures everywhere on the hull. Only the turbulent boundary layer 

 development is considered. The length scale used is half the length, L, 

 between the perpendiculars of the hull. The velocity scale is the steady 

 ship speed U . Henceforth, all physical quantities that are discussed will 

 be dimensionless with respect to these scales. There is an orthogonal 

 surface coordinate system on the hull, which has lines of constant 6 running 

 generally lengthwise along the ship and lines of constant (f) running nearly 

 parallel to the cross-sections of the ship. This system will be described 

 in detail in Section 3. The coordinate perpendicular to the hull surface 

 can be described in terms of its arc length parameter A. 



At an arbitrary point on the hull surface the potential flow velocity 

 vector U is given by 



y = U^ e^ + Ug eg (1) 



where e, and e, are unit tangent vectors in the direction of the (j) and 6 



coordinates, respectively, and U = | |u| | is the magnitude of the velocity 



vector U. The angle that the velocity vector U makes with the <^ coordinate 

 line is denoted by 



