20 



LOCAL-SKIN-FRICTION COEFFICIENTS FOR FLAT PLATES 

 AT ZERO PRESSURE GRADIENT 



Since the evaluation of the local skin friction in a pressure gradi- 

 ent depends on a knowledge of its value in zero pressure gradient, as seen in 

 Equation [40], a review of available information on the drag of flat plates 

 should now be considered. A smooth flat plate moving parallel to the direc- 

 tion of motion represents an excellent example of boundary-layer flow in a 

 zero pressure gradient. The analytic study of the drag of flat plates has 

 proceeded on a semi-empirical basis by such investigators as Prandtl and 

 von Karman. 1 ' 2 From various theoretical and empirical considerations a func- 

 tional form is assumed for the velocity profile involving both the velocity 

 and the local skin friction. Then an integration over the length of the plate 

 leads to a general expression for the drag, containing coefficients to be 

 numerically evaluated from test data. Landweber 21 has made a critical review 

 of such methods . 



For the boundary-layer relations considered in this report it is 

 necessary to express the frictional resistance of flat plates in terms of a 

 local-skin-friction coefficient as a function of a local Reynolds number or 



w 

 PU 2 



= f(R J 



[44 



where R = ~. Various investigators have developed expressions of this type 

 from drag coefficient formulas appearing in the literature. 



Tetervin 22 obtained the following local-skin-friction formula for 

 flat plates from the universal resistance law for pipes 



ptr 



i 



2.5 In 



+5-5 



[45] 



Since r /oU 2 appears also on the right hand side, it is an unwieldly equation 



w o 

 to use numerically. Furthermore, as it is based on pipe-resistance data, it 



applies only approximately to flat plates. 



Squire and Young 11 , by a combination of the von Karman asymptotic 

 formula and the Prandtl and Schlichting drag law, derived the following ex- 

 pression for the local-skin-friction coefficient 



pU 2 ~ L5--J 



log 10 (4.075 R,) 



[23] 



