Shear Stress and Pressure Distribution on a Shtp Model 
(1) the "differential methods" of Bradshaw” and Nash® ; and (2) 
the momentum integral methods of Cumpsty and Head’ , and Smith® , 
The differential methods use the Reynolds boundary layer equations 
and transport equations for the Reynolds stresses. These methods 
are numerically complex and have not yet been applied to fully three- 
dimensional flows such as over a ship hull. The momentum-integral 
methods are fairly simple extensions of two-dimendional momentum- 
integral methods, The extension is carried out in the natural setting 
of streamline coordinates. The main assumptions are: (1) skin- 
friction in the streamline direction is related to the streamwise 
boundary-layer velocity profile in exactly the same way as in a two- 
dimensional flow, (2) the crossflow velocity profile is simply 
related to the streamwise profile by an empirical formula, and (3) 
the auxilliary equation is the three-dimensional extension of the two- 
dimensional equation with exactly the same empirical auxilliary func- 
tion as in two-dimensional flow. A straight forward computation 
scheme based on these assumptions has been developed 7, 8,9 
Landweber!9 has criticized the use of momentum-integral methods 
for three-dimensional flows because of the assumptions made for the 
skin friction and crossflow velocity profile, especially when cross- 
flow occurs along streamlines which have changes in the sign of 
geodesic curvature. Fora ship of moderate block coefficient where 
the crossflow is generally small 12) the usual momentum-integral 
methods can be expected to lead to useful results. A computation 
scheme proposed by Lanweber, using a differential method or inte- 
gral-vorticity equations in principal-curvature coordinates, has yet 
to be developed. 
A few previous attempts at ship boundary layer calculations 
invariably employed momentum-integral methods. The early attempts 
of Wu!3 and Uburoi!4, consisting simply of the application of stric- 
tly two-dimensional methods along waterlines, account only for pres- 
sure gradient effects and are not reliable since the equally important 
effect of streamline convergence and divergence is neglected. Gadd!2 
used a modified form of the Cumpsty-Head-Smith method and inclu- 
ded the effect of streamline convergence and divergence, but the 
method was applied along waterlines instead of the streamlines. The 
error incurred due to departure of streamline direction from water- 
line direction is difficult to assess, but may be significant in the 
bilge area, However, Gadd makes calculations for cases for which 
he has some experimental data and obtains fair agreement. 
Webster and Huang!> made calculations similar to Gadd's. 
They used Cooke's 16 method for three-dimensional boundary layers 
and Guilloton's!”? method for the potential flow. Their calculations 
1965 
