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.
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