Fundamentals of Fluid Mechanics B Questions and Answers

Question by AME536B Student Is it possible to give us a hint on how to find the wake height on question 4?	05.02.20

Well I think I gave you many examples of what not to do in class. This is sufficient. You need to formulate the definition of the wake height in a way that is fool proof, that will work equally well in the near or the far field.

Question by AME536B Student Per university policy, I am not sure if a homework applies Under, Policy Memo: Final Examination Regulations and Information 4. It is Faculty Senate policy that all forms of exams (quizzes, take homes, etc.) are prohibited on any scheduled class or reading day during the calendar week in which regularly scheduled final exams begin. Specific exceptions for certain courses may be made with approval from the appropriate academic unit head and academic dean. Students shall be informed of any such exceptions in the class syllabus. https://www.registrar.arizona.edu/cours ... pring-2020

05.04.20

Assignment 10 definitely does not qualify as an exam. You won't receive a grade for it and it doesn't count towards the final score. The purpose of the assignments in this course is to help you learn the material and give you feedback. The material for the final exam includes the last lecture hence the need for assignment 10. The submission of the assignment 10 can take place anytime between Wednesday 6 pm and Sunday 11 am. If you don't submit it, you don't lose any point. If you do, I'll give you feedback. It's up to you.

Question by AME536A Student I have a problem with question 3. As we did in class, I found the velocity $u$ from the streamfunction through: $$u=\frac{\partial \Psi}{\partial y}$$ Then I integrated u over y in the limits from 0 to $x^{\frac{2}{3}}$. The second x-term cancels out, but I still end up with an expression that contains $\frac{1}{x}$, which I think should not be the case. Is there something wrong with this approach?

This is possible. Then if this happens, you need to explain what this entails. Answer the other parts of the Q3 carefully. You need to think about this.

Question by AME536A Student I believe you mentioned this in class, but I wanted to double check — Is the final exam open note? If not, will we be expected to do proofs of equations for the final exam? Are there any that might be excluded from being on the exam?	05.07.20

Yes it's open notes, and the exam will be designed in consequence. I could ask you part of a proof that I didn't finish in class. No assignment problem is excluded. You should make sure you understand and remember the proofs and other problems in the assignments. I may ask you the same problem as in the assignment or a very similar problem that builds upon the assignment problem. Thus, I expect you to have finished all your assignment problems correctly. I recommend not to open your notes during the exam — most likely this will end up being detrimental. You should have all the theory and assignments well understood and inside your brains.

Question by AME536B Student Could you provide a hint on Q1 from HW 8? Should I start with the continuity eq. and assume that $u=u(x,y)$ instead of assuming that $u=u(y)$ ?	05.09.20

Yes, that's how this problem should be started.	05.10.20

Question by AME536A Student Should we be able to derive the general solution of the streamfunctions we found for Stokes and Oseen's solution?

Well, it's open book, so you can always consult your notes for this matter if you don't remember how the Stokes streamfunction was derived. But I won't ask you the part of the derivation that I didn't do in class or that I didn't ask you to do in the assignments.

Question by AME536B Student Is assignment 10 included on what we have to study for the exams?

Of course. This was mentioned in class.

Question by AME536A Student Could you give us a hint on HW 7, Q2? Should the explanation about the difference of the Reynolds solution and the exact solution be a verbal explanation, focusing on the difference in the equations we solved?

Yes, the explanation of the differences between Reynolds and Blasius can be “verbal”. That is, you can simply put down in written form the verbal explanation you would give to others as to why there is a large discrepancy. You can include some math expressions if this makes your explanation easier to follow. Note that both are exact solutions.

Question by AME536A Student Regarding the last question. I've been focusing my explanation on the difference in the equations we're solving and the assumptions that are involved. I'm not sure if pointing out these differences is explanation enough. If not, could you give a hint on what I have to think about?

You need to explain why there are discrepancies between the solutions obtained despite the latter all originating from the Navier-Stokes and despite Reynolds and Blasius being both exact solutions to the boundary layer phenomenon. How is this possible? Explain things in simple terms so that they are readily understandable to someone with basic knowledge in fluid mechanics.

Question by AME536B Student In HW9, Q4b and 4c, I am not sure if $(a)$ or $(b)$ are the right assumptions or if both o them are wrong. Could you provide a hint please? $$(a)\;\;\;\frac{u_w}{U_{\infty}} = constant $$ $$(b)\;\;\; \frac{u_w}{v} = constant$$ if $\;(b)$ is used, $v$ will be calculated from the continuity eq.	05.11.20

See my answers above for similar questions. You need to make sure that the way you define the height works well equally when $u_w$ is much less than $u_\infty$ and when $u_w$ everywhere in the profile is more than 0.99999999$u_\infty$. I mentioned in class specifically that (a) is improper. Why are you writing this here? As for (b), I see many problems with a $v$ on the denominator.. Ask yourself this question: where is $v$ approaching 0? This will occur at several locations..

Question by AME536A Student In HW 8 Q1, I'm using the mass conservation equation and integrate over y to get an expression for v, so that I can finally find the vorticity vector component $\omega_z$. The expression I end up with contains terms $ -y^4$ and $ y^2$. Is that correct?

Yes, the logic seems correct.

Question by AME536B Student Would it be possible to get our finals back? It will help preparing for the qualifying exam. Thanks!	05.16.20

Will do.

Question by AME536A Student Question about Homework 2 Problem 4: The problem asks us to start from the Navier-stokes equation and prove that it corresponds to a slightly modified Navier-stokes equation. From the tables, the Navier-Stokes equation is: $\rho(\frac{\partial v}{\partial t}+u \frac{\partial v}{\partial x}+ v\frac{\partial v}{\partial y}+w\frac{\partial v}{\partial z})=-\frac{\partial P}{\partial y}+\mu \frac{\partial^2 v}{\partial x^2}+\mu \frac{\partial^2 v}{\partial y^2}+\mu \frac{\partial^2 v}{\partial z^2}+B_y$ The endpoint for our derivation was given to be: $\rho(\frac{\partial v}{\partial t}+u \frac{\partial v}{\partial x}+ v\frac{\partial v}{\partial y}+w\frac{\partial v}{\partial z})=-\frac{\partial P}{\partial y}+\frac{a}{2} \frac{\partial^2 v}{\partial x^2}+\frac{a}{2} \frac{\partial^2 v}{\partial y^2}+\frac{a}{2} \frac{\partial^2 v}{\partial z^2}$ Comparing the two, the only differences is the Body Force was deemed negligible in the derived equation, and $\mu$ was substituted with $\frac{a}{2}$. I understand you don't want us to just say that "a" is an arbitrary constant used in place for $\mu$, (especially after the derivation made in class from mechanical pressure to that equation), but I am having a hard time seeing where you want us to go with this derivation. Can you please provide guidance?

02.09.21

You should start from the non-constant-density and non-constant-viscosity Navier-Stokes equations. I clarified the question.

Previous   1 ,  2 ,  3 ,  4  ...  7    Next  •  PDF 1✕1 2✕1 2✕2  •  New Question