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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
:
![\begin{displaymath}\begin{split}
\delta_{1} & = \left(\frac{2\nu x}{U}\right)^{1...
...)^{1/2}\lim_{\eta \rightarrow \infty}(\eta-f(\eta)) \end{split}\end{displaymath}](img111.gif) |
(84) |
- Momentum thickness
:
and taking into account the boundary conditions (3.49) to (3.51), we obtain that
![\begin{displaymath}\delta_{2} = \left(\frac{2\nu x}{U}\right)^{1/2}\int_{0}^{\infty}ff''d\eta
\end{displaymath}](img113.gif) |
(85) |
- Energy thickness
:
and taking into account the boundary conditions (3.49) to (3.51), we obtain that
![\begin{displaymath}\delta_{3} = \left(\frac{2\nu x}{U}\right)^{1/2}2\int_{0}^{\infty}ff'f''d\eta
\end{displaymath}](img115.gif) |
(86) |
- Skin friction
:
and according to the initial condition
f''(0) = 1, we have that
![\begin{displaymath}\tau_{\omega} = \mu\left(\frac{U^{3}}{2\nu x}\right)^{1/2}
\end{displaymath}](img117.gif) |
(87) |
- Dissipation integral D:
![\begin{displaymath}D = \mu\left(\frac{U^{3}}{2\nu x}\right)\int_{0}^{\infty}f''(eta)^{2}d\eta
\end{displaymath}](img118.gif) |
(88) |
Next: Momentum and Energy Equations.
Up: Boundary-layer Thickness, Skin friction,
Previous: Boundary-layer Thickness, Skin friction,
Karl P Burr
2003-03-12