Fundamentals of Fluid Mechanics B Questions and Answers
 Question by AME536B Student Can you please omit question 2 of homework 6? In the exam, it would be time consuming to rederive these equations to determine the different assumptions and approaches to boundary layer theory each solution uses.
 05.05.21
I don't see why this question should be omitted. You should remember what assumptions were made in the derivation of each equation and what they entail. This is important to know for a fluid dynamicist.
 Question by AME536A Student Can you please omit Question #2 of Homework #8? It is a proof that tests less our understanding of fluids and instead is more of a time-heavy mathematical manipulation using Reynold's Transport Theorem.
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.
 Question by AME536B Student For Homework 9, Question 2, I am having trouble determining the velocity in the y-direction in the boundary layer. After integration I get: $$v(x,y)=...+C$$ where $C$ is the constant of integration. However, from our aforementioned boundary conditions, we will run into issues as there is no value for $C$ that will satisfy both boundary conditions at the wall and at the boundary layer edge. Can you please provide a recommendation on where I might have made my mistake?
 05.07.21
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.
 Question by AME536A Student I have a question about prob#2 (a) in the assignment of 7. If the fluid density is not uniform, will the three order polynomial fit, $\frac{u}{u_\infty}$, obtained from what is the uniform density become different?
 05.08.21
If the density is not uniform, then you can not use the polynomial fit expression for $u$ given in the tables.
 Question by AME536A Student If you don`t mind, could you please give me a hint how to solve the problem?
Follow the steps shown in class for the displacement thickness and submit revisions to your assignment to get feedback.
Question by AME536B Student

For Hw8 Question 6 Part A, you asked to find the condition where $\mu \frac{\partial ^2 u}{\partial x^2}$ is negligible. In my attached Hw I gave the condition $L>>\delta$ , is this sufficient or is a more thorough explanation necessary?
Thank you
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.
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