21 



The Prandtl and Schlichting drag law has been criticized for its use of pipe 

 velocity profiles in its derivation. 3 



Falkner, 13 by a study of various test data for flat plates, proposed 

 the following simple power-law formula 



T w = 0.006334 [25] 



/>U* R e 1/6 



Like all power-law formulas, this equation is valid only for a limited range 

 of Reynolds numbers. 



Ludwieg and Tillmann 18 derived the following equation from the test 



data of Schultz-Grunow 23 



°= 0-O l6 7 [46] 



pit (iog 10 RJ 



1.838 



for 2 x 10 3 <R e <7x 10 s . 



A local-skin-frictTion formula will now be derived from the well- 

 known Schoenherr (Karman-Schoenherr ) frictional-resistance formula for flat 

 plates. Prom an extensive collection of test data for the frictional resist- 

 ance of flat plates covering a wide range of Reynolds numbers, Schoenherr 24 

 supplied numerical values to the coefficients of the von Karman asymptotic 

 drag-law formula. The Schoenherr formula has become the basis of frictional- 

 resistance calculations for the prediction of full-scale horsepower from tests 

 on models of ships. The Schoenherr formula is 



^r= 4.13 log 10 (R x C f ) [47 



where R = ^. Here 



C f = j^j- [48] 



where D is the drag and S is the total surface area. Hence for a flat plate 

 of width W and length x the drag of one side is 



D = C f jpU 2 x W [49] 



