Charaoteristios of Ship Boundary Layers 



equation in the streamwise direction becomes a differential equation 

 for momentum thickness after assuming a power law of variation for 

 the streamwise velocity profile and a semi-empirical relation from 

 two-dimensional boundary-layer theory between the shear-stress 

 coefficient and the momentum-thickness Reynolds number. An 

 additional assumption, that the cross-flow angle varies as the square 

 of the distance from the outer border of the boundary layer, .is intro- 

 duced to determine the cross-flow. Finally a new auxiliary relation 

 between the shape parameter and the momentum thickness is derived 

 by combining the streamwise momentum and energy integral equations 

 and introducing one more assumption, another semi-empirical rela- 

 tion between the dissipation coefficient and the momentum thickness 

 Reynolds number, also borrowed fronni two-dimensional theory. 



Each of the five assumptions of the method used by Lin and 

 Hall is of doubtful validity for a ship boundary layer. Boundary- 

 layer data on ship forms, which are discussed in subsequent sections, 

 indicate that the cross -flow is not everywhere small, that the two- 

 dimensional relations are not generally valid in a three-dimensional 

 boundary layer, that a power law is not a good approximation for the 

 streamwise velocity profiles, and that the cross -flow angle cannot 

 obey a quadratic relation. 



Finally, a paper due to Gadd [ 16] , which the author has not 

 yet seen, should be mentioned. He determines the outer potential 

 flow, taking wavemaking into account, and applies this to calculate 

 the boundary layer on an equivalent body of revolution, neglecting 

 cross-flow. In referring to this paper. Shearer and Steel [ 17] remark 

 that "Gadd has recently applied a three-dimensional boundary-layer 

 theory to the pressure distributions obtained using the Hess and Smith 

 method, taking account of the free surface, to give friction distribu- 

 tions which agree very well with measured values. Comparison of 

 this theory with some of the experimental values detailed herein (in 

 [17]) are given in ..." (in [ 1 6] ) . 



IV. BOUNDARY-LAYER DATA FOR SHIP FORMS 



It has been indicated that the relations for the shear stress 

 used in calculating two-dimensional boundary layers may not be valid 

 for a three-dimensional boundary layer. In order to investigate the 

 applicability to ship forms of these and other empirical relations that 

 have been proposed, it would be desirable to have a set of data, in- 

 cluding pressure distributions, mean velocity profiles for both the 

 streamwise and cross-flow directions, and shear stresses, for some 

 shiplike forms. 



Full scale boundary-layer measurements on a 210-foot ship, 

 the USS Timmerman, have been reported by Sayre and Duerr [ 18] . 

 Mean velocity profiles are given for four points along the hull, at 

 speeds of 5, 10, 15 and 20 knots. The nieasured boundary-layer 



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