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.
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?
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?
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
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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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