26 



It is not possible to calculate § from [4] without detailed knowledge of the 



variation of r' . r , and 6 over the entire model. The usual approximation 



mm 

 must be employed, viz., that the integral of the shear forces over the hull is 



equal to the drag of a flat plate of the same wetted surface towed at the same 

 Reynolds number. Since only the ratio of the integrals is desired this approx- 

 imation to the exact ratio should be good. Therefore £ m may be approximated 

 by the decrement for a flat plate £, that is 



Ij T ' - T ) " S 15) 



f l* ( " ! r'ds 



I 



where t' and r are the shearing stresses for a flat plate in turbulent and 

 laminar flow respectively. 



Equation [5] will be expressed later in terms of the Schoenherr 

 frictional-resistgnce coefficient but at first it is desirable to obtain £ as 

 a simpler function of the Reynolds number, inasmuch as the Schoenherr coef- 

 ficient cannot be written in explicit form. To obtain an elementary form for 

 I, the law of Blasius for the laminar shearing stress and the Prandtl-von 

 Karma'n formulation 11 for turbulent shearing stress are assumed: 



r= 0.352Vy^- (for laminar flow) [6] 



and 



,1/5 



t' = 0.02^6pU 2 (-~-^ (for turbulent flow)* [7] 



where n is the absolute or dynamic viscosity of the fluid, 

 p is the mass density of the fluid, 

 U is the speed, 



X is the distance from the leading edge, and 

 v is the kinematic viscosity of the fluid. 



Substituting Equations [6] and [7] into [5] and integrating gives 



' # .X»r ^ " 18R ^ [81 



♦It will be noted that the numerical coefficient in the expression for t 1 is given in Reference 11 

 as 0.0288. Schlichting 5 has recommended the slightly larger coefficient to give better agreement with 

 experimental data. 



