Charaateristias of Ship Boundary Layers 



curve of C, against longitudinal distance along the waterline undulated 

 180° out of phase with the wave profile. The most interesting feature 

 of the Cf curves for various waterlines is their large variation along 

 the waterline even at depths where the free-surface effect should be 

 negligible, in agreement with Wieghardt's results. Furthermore, the 

 variation was found to be sensitive to the shape of the bow. This again 

 indicates that one is not free to assume a simple formula for the shear 

 stress in calculating a three-dimensional boundary layer. 



The boundary layer on an ellipsoid with axis ratios 20:4:1 and 

 the incident flow in the direction of the longest axis was investigated 

 in a wind tunnel by Pavamani [ 5] . He measured the distribution of 

 both pressure and shear stress, the velocity profiles, as well as the 

 flow directions in the boundary layer. With the equipment used it was 

 not possible to probe the boundary layer in the regions of largest 

 curvature. It was found however that the shear stress in a transverse 

 section increased in the direction of increasing curvature. 



Two shear-stress formulas that are used in computing three- 

 dimensional turbulent boundary layers are one due to Young, 



C.= ii^=0.0176(^) 



-0.2 



PU' 



and another due to Ludwieg-Tillmann, 



C^= 0.246 X 10 



-0.678H/U9 



•0.268 



O 



Here To is the shear stress at the wall, p is the mass density of 

 the fluid, U is the velocity at the outer edge of the boundary layer, 

 is the boundary-layer momentum thickness computed for the 

 streamwise component of the velocity, v is the kinematic viscosity, 

 and H is the shape parameter of the boundary-layer velocity profile. 

 Although not done by Pavamani, his data can be used to compare the 

 predictions by these formulas with his shear-stress measurements 

 by Preston's method. Comparisons at two points in the miidsection, 

 one on the centerline and the other in the vicinity of the edge, and 

 given in the following table. 



COMPARISON OF MEASURED AND COMPUTED SHEAR STRESS 

 AT MIDSECTION OF 20:4:1 ELLIPSOID (R, = 10^) 



Measured Young Ludwieg-Tillmann 



at centerline 

 near the edge 



0.00330 

 0.00466 



0.00380 

 0.00444 



0.00283 

 0.00318 



455 



