Fundamentals of Fluid Mechanics B Questions and Answers  




No, this question will remain because it is a very important problem in fluid dynamics. A fluid dynamicist should know how to derive the integral form from the differential form.




Keep in mind our polynomial for $u$ is not exact. If it would be exact, $u$ would never reach free stream and $v$ would never become zero even infinitely far from the plate (although $u$ would become very close to freestream and $v$ very close to zero, they would never reach these values). Thus, find the integration constant by specifying $v=0$ at the surface and don't worry about whether $v=0$ at the boundary layer edge.




If the density is not uniform, then you can not use the polynomial fit expression for $u$ given in the tables.




Follow the steps shown in class for the displacement thickness and submit revisions to your assignment to get feedback.




There are a few problems here. The first is that your answer “$\partial_x^2 u \ll \partial_y^2 u$” is not a proper answer to what is asked in the question. If what you meant is that this would occur when $L \gg \delta$, then this should be the answer highlighted. But this is also not what is sought here. You should find a condition based on the freestream flow properties. Another issue is that the length scale you use to approximate the derivative along $x$ is not in practice the length of the plate: it may be much less. Redo this problem so you get rid of these concerns. I gave a hint in class on how to approach this. See the recorded lectures.



$\pi$ 