User Tools

Site Tools


parasitedrag

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision
Previous revision
parasitedrag [2018/05/03 15:30]
jgravett Minor changes
parasitedrag [2019/07/08 08:10] (current)
admin created
Line 108: Line 108:
  
 ===== Coefficient of Friction Equations ===== ===== Coefficient of Friction Equations =====
 +
 +Unfortunately,​ there is substantial opportunity for confusion around the equations for the skin friction coefficient. ​ The primary source of confusion is inconsistent nomenclature in the literature around two related quantities -- the local skin friction coefficient vs. the flat plate average skin coefficient. ​ Different references use inconsistent nomenclature to differentiate these quantities. ​ A reader must be pedantic to verify that they understand the notation for any given publication. ​ Often, the nomenclature is defined far away from where the equations are presented.
 +
 +^  Local    ^  Average ​ ^  Reference ​            ^
 +|  $C_f$    |  $C_D$    | White (3)              |
 +|  $C_{\tau}$ ​ |  $C_f$    | Hoerner (1)            |
 +|  ${c_f}'​$ ​  ​| ​ $c_f$    | Schlicting (6)         |
 +|  $c_f$    |  $C_f$    | Anderson (5)           |
 +|  $C_f$    |  $C_D$    | White & Christoph (2)  |
 +
 +This analysis is only concerned with the flat plate average skin friction coefficient,​ which will be denoted $C_f$ herein.  ​
 +
 +
 $ x \equiv \mbox{distance along chord} $\\  $ x \equiv \mbox{distance along chord} $\\ 
 $ k \equiv \mbox{roughness height} $\\  $ k \equiv \mbox{roughness height} $\\ 
Line 126: Line 139:
  
 == Blasius (25) == == Blasius (25) ==
-$$ C_f = \frac{1.32824}{Re^{1/2}}\ $$+$$ C_f = \frac{1.32824}{\sqrt{Re}}\ $$
  
 ==== Turbulent ====  ==== Turbulent ==== 
Line 134: Line 147:
  
 == Explicit Fit of Spalding and Chi (2) ==  == Explicit Fit of Spalding and Chi (2) == 
-$$ C_f = \frac{0.225}{\log(Re)^{2.32}}\ $$+$$ C_f = \frac{0.430}{\log(Re)^{2.32}}\ $$
  
 == Explicit Fit of Schoenherr (1) == == Explicit Fit of Schoenherr (1) ==
Line 141: Line 154:
 == Implicit Schoenherr (1) ==  == Implicit Schoenherr (1) == 
 $$ \log\left(Re\ C_f\right) = \frac{0.242}{\sqrt{C_f}}\ $$ $$ \log\left(Re\ C_f\right) = \frac{0.242}{\sqrt{C_f}}\ $$
- 
-== Implicit Karman (2) ==  
-$$ \frac{1}{\sqrt{C_f}}\ = 4.15\log\left(Re\ C_f\right) + 1.70 $$ 
  
 == Implicit Karman-Schoenherr (4) ==  ​ == Implicit Karman-Schoenherr (4) ==  ​
Line 149: Line 159:
  
 == Power Law Blasius (2) ==  == Power Law Blasius (2) == 
-$$ C_f = \frac{0.0592}{Re^{1/​5}}\ $$+$$ C_f = \frac{0.072}{Re^{1/​5}}\ $$
  
 == Power Law Prandtl Low Re (5) ==  == Power Law Prandtl Low Re (5) == 
Line 155: Line 165:
  
 == Power Law Prandtl Medium Re (3) ==  == Power Law Prandtl Medium Re (3) == 
-$$ C_f = \frac{0.027}{Re^{1/​7}}\ $$+$$ C_f = \frac{0.0315}{Re^{1/​7}}\ $$
  
 == Power Law Prandtl High Re (3) ==  == Power Law Prandtl High Re (3) == 
-$$ C_f = \frac{0.058}{Re^{1/​5}}\ $$+$$ C_f = \frac{0.0725}{Re^{1/​5}}\ $$
  
 == Schlichting Compressible (6) ==  == Schlichting Compressible (6) == 
 $$ C_f = \frac{0.455}{\log\left(Re\right)^{2.58}}\ $$ $$ C_f = \frac{0.455}{\log\left(Re\right)^{2.58}}\ $$
- 
-== Schlichting Incompressible (7) ==  ​ 
-$$ C_f = \frac{0.472}{\log\left(Re\right)^{2.5}}\ $$ 
- 
-== Schlichting-Prandtl (2) ==  
-$$ C_f = \frac{1}{\left(2\ \log\left(Re\right) - 0.65\right)^{2.3}}\ $$ 
- 
-== Schultz-Grunow High Re (2) ==  
-$$ C_f = \frac{0.370}{\log\left(Re\right)^{2.584}}\ $$ 
  
 == Schlutz-Grunow Estimate of Schoenherr (1) ==  == Schlutz-Grunow Estimate of Schoenherr (1) == 
 $$ C_f = \frac{0.427}{\left(\log\left(Re\right) - 0.407\right)^{2.64}}\ $$ $$ C_f = \frac{0.427}{\left(\log\left(Re\right) - 0.407\right)^{2.64}}\ $$
    
-== White-Christoph Compressible (2) ==  +{{ :parasitefrictioncoefficientsfixed.png?850 |}}
-$$ C_f = \frac{0.42}{\ln^2\left(0.056\ Re\right)}\ $$ +
- +
-{{ :parasitefrictioncoefficients.png?850 |}}+
  
 === Roughness === === Roughness ===
Line 184: Line 182:
 == Schlichting Avg (6) == == Schlichting Avg (6) ==
 $$ C_f = \left(1.89 + 1.62\ \log\left(\frac{l}{k}\right)\right)^{-2.5} $$ $$ C_f = \left(1.89 + 1.62\ \log\left(\frac{l}{k}\right)\right)^{-2.5} $$
- 
-== Schlichting Local (6) ==  ​ 
-$$ C_f = \left(2.87 + 1.58\ \log\left(\frac{x}{k}\right)\right)^{-2.5} $$ 
- 
-== White (3) ==  
-$$ C_f = \left(1.4 + 3.7\ \log\left(\frac{x}{k}\right)\right)^{-2} $$ 
  
 == Schlichting Avg Compressible (7) ==  == Schlichting Avg Compressible (7) == 
parasitedrag.1525386606.txt.gz · Last modified: 2018/05/03 15:30 by jgravett