Fundamentals of Fluid Mechanics Questions and Answers  
Question by AME536A Student
I have a question for Assignment #7 Question #2 Part b. After manipulation of the energy equation I arrive at $\frac{DH}{Dt}=\frac{1}{\rho} \frac{\partial P}{\partial t}$. After applying the chain rule $\frac{\partial P}{\partial t}=\frac{\partial P}{\partial s}\frac{\partial s}{\partial t}=q\frac{\partial P}{\partial s}$ where q is the velocity magnitude and s the stream line coordinates the equation becomes $\frac{DH}{Dt}=q\frac{1}{\rho} \frac{\partial P}{\partial s}$. If we want the total enthalpy to be conserved, we should have zero pressure gradient along the streampath. Is this correct?
11.03.19
You can't apply the chain rule here. You can only apply the chain rule when converting a total derivative, not a partial derivative.
Question by AME536A Student
I have a question on homework #10, question #1. From the problem statement, we know that the flow around the circular part of the body follows potential flow theory, meaning we can find velocity components using potential theory definitions. I'm confused on how to include the blunt edge into a pressure coefficient drawing. Using the bernoulli equation, we can derive Cp as the following: $$ C^{}_{p} = 1 - \frac{u^{2}_{}}{u^{2}_{\infty}} = \frac{P-P^{}_{\infty}}{\frac{1}{2}\rho u^{2}_{\infty}} $$ If we can find the flow velocity, we should be able to find the Cp. The flow at the top and bottom of the circular body should be purely horizontal (and from potential flow theory we find the velocity), but I'm not sure what the velocity does after those points. We can't assume that the top and bottom of the circular body with a blunt edge are stagnation points, correct? I am stuck on how to figure out what happens to the flow velocity in the blunt region of the body ( $\theta = \frac{3\pi}{2}$ to $\frac{\pi}{2}$).
11.24.19
I guess that “blunt edge” here means the right side of the half cylinder. No, the top and the bottom of the half cylinder are not stagnation points. Hint: for the air to flow horizontally at the top and bottom edges, and to continue in that direction, the net force along $y$ on the flow at those locations must be zero. Think about what this means with respect to the pressure on the right side of the object.
Question by AME536A Student
We are having trouble on Homework #10, Question #2 part B. We originally found the max velocity to be at the top of the bump with $r = 2R$ and $\theta = \frac{\pi}{2}$. We are stuck on how to find the max velocity, if it's not at this point. We are trying to use the streamline function to find velocity components, but can't find them because we don't know the radius on the bump at any point other than the top. We can't assume that the bump is a cylinder and so there isn't any information on how to find the radius at at given theta on the bump. What is the best way to look at this problem?
11.25.19
You can find $q$ as a function of $\theta$ on the bump by setting $\psi$ to a constant which is determined from $r=\infty,y=h$.
Question by AME536A Student
Hi Professor, would it be possible to get an extension on homework 10?
Hm, OK. It will be due Tuesday after the Thanksgiving. Note that you will have two homeworks due on that week.
Question by AME536A Student
In Assignment #10, problem #3, part (b): I am struggling to prove that $\int_S \rho \vec{v} (\vec{v}\cdot\vec{n}) dS = \frac{3}{2}\rho Q U \vec{i}$. I tried to find the integral and use the Momentum equation without any result. Is there any hint to proceed in this problem ?
12.03.19
But, can you prove that the force has no component in $\vec{j}$? This is easier to do and will guide you towards the right solution to find the component along $\vec{i}$.
Question by AME536A Student
On assignment #12 on question #1, I think there is a mistake on the equation for the supersonic potential flow.
12.08.19
That's right. It has been corrected.
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