Viscous Flow Questions & Answers  
If you use the same shear stress at the wall in (a) and (b), then you need to prove why it is the same (if it is!). You can start your proof by looking at the forces acting on a fluid element within the fully developed region. It's a good question, but a bit late and not so well typeset.. I'll give you 1 point bonus boost.
12.19.16
Question by Student 201227103
Well... Its really bad news..it seems unfair.. Is there anything that we could help you? Something like send an e-mail to PNU administration about our situation. If there is anything we could do please tell us. Thank you
12.27.16
I know, the PIP system in this case forces me to give you a B+ instead of a A+ and this is of course not fair. The difference between A+ and B+ is a big one.. I talked to the secretaries about it today but they seemed adamant nothing could be done. However, I'll write a very polite letter to the PNU admin tomorrow explaining the situation, and maybe they will accept making a change (the last day this can be done is January 3rd). I'll keep you posted. If this is not possible, then I can give you a higher grade in my other courses — for example, if you get B+ in my Heat Transfer class next year, I'll upgrade it to A+.
Question by Student 201527110
Professor, I wonder why didn't you make the momentum conservation equation as conservation form. For other lectures, you always keep the equations as conservation form, but for today, you didn't. Is there any special reasons for that?
09.06.17
This is a good question. The conservative form is not necessary to solve most viscous flow problems in this course, so I prefer to derive only the non-conservative form. In other courses (like Intro to CFD for instance), then we need the conservative form because it's easier to discretize.
Question by Student 201327133
Dear professor. I found few mistakes in question#4 of assignment #1. first, there is no $\partial$ in $\frac{\partial \rho v H}{ \partial y}$ of first eq. also have to change $\partial x$ for $\partial y$. Second, you have to times $\frac{\rho}{m \Delta t}$ which $δQ−δW$ to be $\frac{\rho \delta Q}{m \Delta t}− \frac{\rho\delta W}{m \Delta t}$. Please check your assignment#4. I think there is same mistake in question#3
09.14.17
I fixed the mistakes, thank you for pointing these out. It must have been quite late when I wrote this. As for Assign. 4, let's look into this again when we get there. Don't go too fast ;)
Question by Student 201327103
professor, I have a problem question #2 in assignment #1. $$ $$In this question, I need to make $$ \frac {\partial \rho v}{\partial t}+\frac {\partial \rho u v}{\partial x}+\frac {\partial \rho v^2}{\partial y}+\frac {\partial \rho wv}{\partial z} $$ from $$ m\frac{dv}{dt}$$ but i can make $$ m \frac{dv}{dt} = \triangle x \triangle y \triangle z \ \rho \frac{dv}{dt} = \triangle x \triangle y \triangle z \rho \left ( \frac{\partial v}{\partial t} + \frac{\partial x}{\partial t}\frac{\partial v}{\partial x}+\frac{\partial y}{\partial t}\frac{\partial v}{\partial y}+\frac{\partial z}{\partial t}\frac{\partial v}{\partial z} \right ) $$ $$ = \triangle x \triangle y \triangle z \, \rho \left( \frac{\partial v}{\partial t} + u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}+w\frac{\partial v}{\partial z} \right ) $$ only $$ $$ i don't know how $$ \triangle x \triangle y \triangle z \, \rho \left( \frac{\partial v}{\partial t} + u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}+w\frac{\partial v}{\partial z} \right ) $$ become $$ \triangle x \triangle y \triangle z \left( \frac {\partial \rho v}{\partial t}+\frac {\partial \rho u v}{\partial x}+\frac {\partial \rho v^2}{\partial y}+\frac {\partial \rho wv}{\partial z} \right )$$ how can i solve this problem?
09.17.17
Expand the terms $\partial \rho v/\partial t$ as $\rho \partial v/\partial t+...$ and $\partial \rho v^2/\partial y$ as $ \rho v \partial v/\partial y+...$ and so on. Then regroup terms so that the mass conservation equation appears and set those terms to zero.
Question by Student 201427564
Professor, I have a question in last Assignmet, Question #2. You asked us that we have to explain why the sign of '$ dF_{L}=- \frac {\mu r}{H} (\omega_{R} - \omega_{L})2 \pi r dr $' is minus. In the class, you explain that because ${\cal P}_{R}>{\cal P}_{L}$. But you set ${\cal P}_{R}=\frac{1}{2} {\cal P}_{L}$. How can this possible? And why $dF_{R}$ also minus?
10.24.17
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