Fundamentals of Fluid Mechanics B Questions and Answers

Question by AME536A Student I have a question about prob#1 in the assignment of 8. Can I define $\delta$ as the difference between the two symmetric inflection points of u?	05.09.21

This is not the best way of doing it because it will measure much less than the jet height. The Q&A is finished for this term: the exam is in less than 24 hours. Good luck!	05.10.21

Question by AME536B Student Dr. Parent, any idea when will you be adding the final grades to UAccess?	05.17.21

I added them already more than 1 week ago. Let me check why you can not see them.

Question by AME536B Student Will homework submissions be physical again or via D2L?	01.25.22

They have to be submitted in class on the due date, not on the D2L.

Question by AME536A Student I can't make it to office hours today but I have a question about HW3Q4. I worked through mass and momentum conservation to achieve the following equation: $$ v_\theta = -v_{\theta}ln(r) + C_1r + C_2 $$ I then used the following boundary conditions: $v_\theta=0$ at $r=R_2$ and $v_\theta = {\omega}R_1$ at $r=R_1$ After solving for $C_1$ and $C_2$ and then plugging back into the above equation and solving for $v_\theta$ I didn't get the answer given on the assignment. I'm wondering if there is something wrong with my boundary conditions or if my error is in my equation? Thank you for your time!

02.23.22

There are 2 ways to solve this problem. One which is not exact but close enough (the first answer given) and the other which is exact and does not get rid of any term (the second answer given). However, your expression for $v_\theta$ does not match any of the 2 solutions. The error is thus in the process of finding $v_\theta$.

Question by AME536B Student HW4, Problem 3A: Looking at mom-con in $y$ direction, is assuming that the body forces in the y direction are negligible a crummy assumption?	03.01.22

You should keep the gravitational effects within the $y$ momentum equation.

Question by AME536A Student Looking at problem 2 from HW5, I have some questions about order of magnitude analysis. In a previous example from class, we looked at the Stoke's Flow through a pipe with changing diameter. For this problem, we found $u_s$ and $v_s$ or the "scale velocities" in the x and y-direction. My question is, is this necessary for all order of magnitude analyses that contain more than one velocity vector?

03.19.22

In this case, I would not worry about scale velocities in $x$ and $y$ direction. This will make things more complicated then they need to be. You should rather start this by providing an order of magnitude estimate of the largest viscous terms (in any dimension) close and far from the sphere. So, the direction in which they point is not important here. Then, compare these approximate viscous terms to an approximation of the convection terms. Hint: focus on the length scales.

Question by AME536A Student I am working on problem 3 from HW5, and I'm having a hard time starting the problem. The question asks to consider both Stoke's and Oseen's solution to find the velocity of a falling droplet, but in the tables, both of these are in polar coordinates only. Can we use this relationship: $$v = -\frac{\partial\Psi}{\partial{x}}$$ like we did last semester after converting the $\Psi$ terms into x and y coordinates? As always, thanks for your time!

03.21.22

In A5Q3, there is no reason to use the streamfunction. Rather use the derived drag force on a sphere outlined in the tables.

Question by AME536A Student To clarify, we can use the drag force to find the velocity of the droplet for Stoke's and Oseen's solutions in part a of A5Q3? While trying to work this out using Newton's Law I find: $$\Sigma{F_y}=ma$$ $$F_D=mg$$ and eventually $$q_{\infty}=1.5*10^{16}m/s$$ Which I don't believe is correct. Am I greatly oversimplifying the problem?

Something is wrong. Make sure you write down your drag force correctly.

Question by AME536A Student Hi Dr. Parent, I was hoping you could give me a hint for solving Q4 on Assignment #5. When solving it originally, I found an equation that looked like: $$\frac{\mu}{r}\frac{\partial}{\partial{r}}(r\frac{\partial{v_{\theta}}}{\partial{r}}) - \mu\frac{v_{\theta}}{r^2} = 0$$ You indicated this problem was correct but I was unsure how to solve it from here. Are there any hints you can provide to help solve this differential equation? Thank you!

03.30.22

Expand the first term on the LHS in two terms. Also, you can rewrite the second term on the LHS as $$ -\mu \frac{v_\theta}{r^2} = \mu \frac{\partial}{\partial r} \left( \frac{v_\theta}{r}\right) - \frac{\mu}{r} \frac{\partial v_\theta}{\partial r} $$ This will lead to various simplifications and an expression easy to integrate.

Question by AME536B Student Would it be reasonable to ask for the LATEX document used to produce the tables to be posted to the website?	04.01.22

Download the latest version of the tables. At the bottom of the last page, there is a link that you can click to access the source files.

Question by AME536A Student I have a question for Assignment 8 Q6 part b. This question tells us to find the error using the assumption we found in part a and the "freestream flow properties". I'm not sure I know what you mean by this. Are you referring to the $u_{\infty}$, $\rho$, $\mu$, etc. terms provided in the problem statement?	04.25.22

For part (a), you need to outline a condition when this term is negligible. So, you need to compare its magnitude to the magnitude of another term in the same transport equation. In part (b), find the error simply as the ratio between this term and the other term to which it is compared to. Use order of magnitude analysis and substitute values for $u$, $\rho$, etc using the freestream properties.

Question by AME536B Student Dr. Parent, would it be possible to review some of the following questions during the final lecture tomorrow? HW2 Q1b HW5 Q1c HW8 Q6a HW9 Q2 Thank you!	05.02.22

Will look into it.

Question by AME536A Student Hi Dr. Parent, would it be possible to exclude A2Q4 from the final? This question is a long derivation that you completed entirely in class.	05.05.22

Yes, let's exclude A2Q4.

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