23 



With the exception of Palkner's equation, all the local-skin- 

 friction formulas discussed in this section are plotted together in Figure 10 

 for comparison. It is seen that there are no appreciable numerical differ- 

 ences among them. For convenient reference the flat-plate formulas are listed 

 in Table 2. 



TABLE 2 



Summary of Formulas for Local-Skin-Friction Coefficients 

 of Flat Plates 



Investigator 



Date 



Origin 



Formula for Local-Skin-Friction Coefficient 



Remarks 



Tetervin 

 Reference 22 



1944 



Universal Pipe Re- 

 sistance Law 



i^-i 1 y 



[45] 



Based on pipe re- 

 sistance data 



PU 2 1 



[2.5 In 



R, 



«,j 



2 4-#). 



Squire and 

 Young 

 Reference 11 



1937 



von Karman Asymp- 

 totic Formula and 

 Prandtl and , 

 Schlichting Drag 

 Law 



T w 

 w o / 1 



;)' 



[23] 





p0 e "15-890 iog 10 4.075 R 



Falkner 

 Reference 13 



1943 



Experimental Data 



w o 0.006534 



[25] 



Limited range of 

 Reynolds number 



Ludwieg and 

 Tillraann 

 Reference 18 



1949 



Schultz-Grunow 

 Data 



T w 0.0167 



7^~ (log^v 1 - 836 



[46] 



2x 10 3 <R s <7x 10 s 



Granville 



(This report) 



1951 



Schoenherr Formula 

 (von Karman Asymp- 

 totic Formula) 



T w 0.01466 



[57] 



7 x 1 2 < R, < 8 x 1 O 5 



W log 10 (2R„ )[^log 10 (2R, J+0.4343] 



In addition to the local-skin-friction coefficient, the variation of 

 the shape parameter of the velocity profiles H Q of flat plates with Reynolds 

 number at zero pressure gradient, is required in Equation [40] to evaluate the 

 local-skin-friction coefficient in a pressure gradient. From the measurements 

 of Schultz-Grunow, 23 and from unpublished British data, Tetervin and Lin 15 

 formulated the following empirical expression 



log H = 0.5990 - 0.1980 log 1Q R e + 0.0189 (log M R # l 



[58] 



for 1.5 x 10 3 < R e < 1 x 10 5 . Figure 11, where Equation [58] is plotted, 

 shows the decrease in H n with increasing Reynolds number R . 



