Quantities for the Blasius Boundary Layer Solution.

For the Blasius similarity solution for a two-dimensional boundary layer given by equation (3.47), we can compute the the quantities defined above:

• Displacement thickness $\delta_{1}$:

  
  

  $$\begin{split} \delta_{1} & = \left(\frac{2\nu x}{U}\right)^{1... ...)^{1/2}\lim_{\eta \rightarrow \infty}(\eta-f(\eta)) \end{split}$$ (84)

  
  

• Momentum thickness $\delta_{2}$:

  
  

  $$\begin{split} \delta_{2} & = \left(\frac{2\nu x}{U}\right)^{1... ...nfty}_{0}+\int_{0}^{\infty}ff''d\eta\right\} \end{split}\notag$$

  
  
  and taking into account the boundary conditions (3.49) to (3.51), we obtain that

  
  

  $$\delta_{2} = \left(\frac{2\nu x}{U}\right)^{1/2}\int_{0}^{\infty}ff''d\eta$$ (85)

  
  

• Energy thickness $\delta_{3}$:

  
  

  $$\begin{split} \delta_{3} & = \left(\frac{2\nu x}{U}\right)^{1... ...}_{0}+2\int_{0}^{\infty}ff'f''d\eta\right\} \end{split} \notag$$

  
  
  and taking into account the boundary conditions (3.49) to (3.51), we obtain that

  
  

  $$\delta_{3} = \left(\frac{2\nu x}{U}\right)^{1/2}2\int_{0}^{\infty}ff'f''d\eta$$ (86)

  
  

• Skin friction $\tau_{\omega}$:

  
  

  $$\tau_{\omega} = \mu\left(\frac{U^{3}}{2\nu x}\right)^{1/2}f''(\eta)\vert _{\eta = 0}, \notag$$

  
  
  and according to the initial condition f''(0) = 1, we have that

  
  

  $$\tau_{\omega} = \mu\left(\frac{U^{3}}{2\nu x}\right)^{1/2}$$ (87)

  
  

• Dissipation integral D:

  
  

  $$D = \mu\left(\frac{U^{3}}{2\nu x}\right)\int_{0}^{\infty}f''(eta)^{2}d\eta$$ (88)