Fundamentals of Fluid Mechanics Questions and Answers

Question by AME536A Student For A3Q3, I use my first control volume around tank 2 and obtain the following equation by applying mass conservation: \begin{equation} \dot{m}_{\rm air,2}-\dot{m}_{\rm w,out}+\dot{m}_{\rm 12}=2.995\ {\rm kg/s} \end{equation} I use a second control volume enclosing the pipes between tank 1 and tank 2 where the air is flowing and obtain the following using mass conservation: \begin{equation} \dot{m}_{\rm air,1}+\dot{m}_{\rm air,2}=0.02\ {\rm kg/s} \end{equation} and the third control volume enclosing tank 1 yields, using mass conservation and considering that the rate at which the volume of air in the tank increases is equal to the rate at which the volume of water in the tank decreases: \begin{equation} (\rho_w -\rho_{\rm air})\frac{dV_{\rm 1,water}}{dt}-\dot{m}_{\rm air,1}+\dot{m}_{\rm 12}=0 \end{equation} Thus, I end up with 5 unknowns ($\dot{m}_{\rm air,1}$, $\dot{m}_{\rm air,2}$, $\dot{m}_{\rm w,out}$, $\dot{m}_{\rm 12}$ and $\frac{dV_{\rm 1,water}}{dt}$) but only 3 equations. Can you give a hint on how I could proceed to tackle this problem?

12.09.21

Answered in the office hours.

Question by AME536A Student Hi Dr. Parent, I am working on question 1 from homework 9 and am wondering if you can help me visualize the problem a little bit more. Are we to assume that the body in the flow is a half-sphere or is it a half-cylinder? Thank you for your time!	12.10.21

Half cylinder.

Question by AME536A Student What is the length that we should use for the half cylinder? Should we relate it to the radius or theta or both?

This is a 2D problem, not a 3D problem.	12.11.21

Question by AME536A Student Hi Dr. Parent, I have a question about homework 10 question 2. For this question, we are meant to find the force on the ship. For my solution on the homework, I tried to derive the equation for the velocity of airspeed, and then perform the integral: $$\vec{F} = \int\limits_S P{n} dS$$ In your corrections, however, you mentioned that I should start with $$F_L = \rho{q}{H}\Gamma$$ I am a little bit confused about what is meant by this. I believe I still need to find the force acting on the cylinder due to the fluid motion, and then I can take a summation of forces to find the total force value, is this correct?

12.13.21

The exam is tomorrow and the final exam has been written. No more questions this semester.

Question by AME536A Student Have you assigned the first assignment yet? Will it be posted online?	08.25.22

Not yet. Each assignment's due date will be announced on the D2L. The announcement will be made at least 7 days in advance of the due date.

Question by AME536A Student Do we need to turn in the homework in class or is there also a d2l submission option?	09.05.22

The homeworks must be handed in in class.

Question by AME536A Student Where can we find the recorded lectures?	09.12.22

Go on D2L -> UA Tools -> Zoom -> Cloud Recordings.

Question by AME536A Student Most (if not all) students in your fluids class also have a math exam this upcoming Tuesday (September 27th). Would it be possible to extend the due date for the homework to provide more space to study for AME 500A and give our best on your assignment? I apologize for the last minute request, and I completely understand if it's not possible.	09.25.22

I think you should be able to manage your time to handle this situation without being given an extension. However, I'll make an exception in this case and I will give you 2 extra days to complete your assignment #4. Note that I will not give an extension to an assignment again this semester.

Question by AME536A Student I apologize if you mentioned this already, but do we need to print out the tables for the exam or will those be provided?	10.12.22

I'll bring some tables.

Question by AME536A Student For the midterm exam, is a TI-84 calculator allowable? It does not have an SD slot but I am not sure what is considered as a large screen.

No TI 84 allowed in exams. This is a programmable calculator.

Question by AME536A Student Professor Parent, Are we meant to assume that, in problem 2 of homework 3, the duct has a square cross section? The mass flow rate is a 3-dimensional quantity but we are only given the height of the duct and not the width so we may not calculate the cross sectional area. Please let me know if the width is a necessary quantity in solving this problem. Thank you.	09.17.23

The problem is 2D not 3D. Find the mass flow rate per unit depth (implied).

Question by AME536A Student For problem 2 of Assignment #4, when you say that the mass flow rate is 15kg/s is that supposed to be the flow rate at both stations 1 and 2?	09.25.23

It's a steady state problem. You can deduce it on your own starting from the mass conservation equation in CV form.

Question by AME536A Student Hello Professor, What are the necessary condition(s) we must satisfy in order to have a potential flow? Specifically in Homework 10 Problem 3 part b it must be proved that potential flow is not satisfied for r<R. Is this just a matter of finding whether or not the curl of the velocity is equal to zero (ie irrotational)? Thank you.	12.07.23

You need to show that the velocities satisfy the potential equation.

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