Shear Stress and Pressure Distrtbutton on a Shtp Model 
by the method of Cumpsty and Head? and Smith® with the addition- 
al assumption of small crossflow. A complete description of the 
method is given in References (7) and (8) anda description of its 
application to ship hulls in Reference (18). We will only reproduce 
the final formulas here. 
In the following we have non-dimensionalized with the follow- 
ing units : half the sae length, L/2, for length, the ship speed, V, 
for velocity, and PU ies for stress, where U isthe (dimensional) 
inviscid velocity at the edge of the boundary layer. Let @ 4 and 6 i> 
be the momentum and displacement thickness of the streamline com- 
ponent of the boundary layer flow, where 
N is the coordinate normal to the body, U, is the inviscid velocity 
at the edge of the boundary layer, u is the boundary-layer time- 
averaged velocity component in the streamline direction and 6 is the 
nominal boundary layer thickness, The relationship between 6,,, 67 , 
and Cy, = 75, /0U“/2) where 7, is the wall shear stress in the 
streamline direction is determined by assuming small crossflow and 
integrating the approximate momentum-integral equation 
d 6 
gt 16 HU 
6 Bee G = 
se eaareliahi ld alana iA legidantliioe Vga de oe 
Ss) de 
and the auxilliary rate-of-entrainment equation 
d( 6 G) 1 dU 
6 a = 
it + wha s ee F (G) (3) 
da S de 
along the streamlines, where a is the arc length parameter along the 
streamlines, In equations (2) and (3) K, is the geodesic curvature 
of the equipotential line, H = 6 11/67 is the shape factor and G 
is the parameter ( 6 - 6*)/@,and F is the empirical rate- of- 
entrainment function, The empirical correlation of F to G to H is 
given by Standen 23as 
1967 
