27 



where R is the x-Reynolds number, 



x is the linear extent of the laminar region on the flat plate taken 

 to be the arc length along the half-draft water line to the boundary 

 of the laminar region on the ship model,* and 



R is the model Reynolds number. 



For a flat plate without disturbances arising from the lower edge or from the 

 water surface we may assume that tl 

 stant. From this it follows that: 



water surface we may assume that the transition Reynolds number R is a con- 



S L R x 



[9: 



So that Equation [8] becomes 



,..(£) : (i-isV) no] 



)del 

 tion [10] reduces to 



Since on this ship model transition occurs, on the average, at R = TO 6 Equa- 



£' = 4.52 x 10 4 R~ ' 8 [11 ] 



Thus for the hypothetical case of the flat plate the decrement of 

 frictional resistance in percent of the total turbulent frictlonal resistance 

 decreases almost hyperbolically with Reynolds number. 



However, the Reynolds number of transition R , and hence S L is from 

 a consideration of theory and experience, a function of the pressure gradients, 

 disturbances arising at the water surface, and the characteristics of the free- 

 stream turbulence . Roughness of the model surface would also greatly affect 

 the location of transition. However, only hydraulically-smooth surfaces are 

 considered in the foregoing derivations. 



Since S T /S and R have been determined from the hot-wire surveys on 



Jj x 



the tanker model at various values of R, I for the model computed from Equa- 

 tion [8] may be compared with £' for the flat plate, computed from Equation 

 [11]. These values are plotted as functions of model Reynolds number in 

 Figure 20. Included in the same figure is the decrement in terms of the 

 Schoenherr frictional resistance coefficients as defined by the following 

 equation: 



♦Although this definition is arbitrary it is believed to give an average value for the linear extent 

 of the laminar region which is sufficiently accurate for the approximate calculations made in this 

 report . 



