Fundamentals of Fluid Mechanics Questions and Answers  
Question by AME536A Student
For the characteristic length of blade, why do we approximate it as the diameter of windmill, not a actual flow distance on the blade, c?
You could work out the problem this way. Then, you'll have one more physical parameter and one more non-dimensional number.
Question by AME536A Student
I want to double-check my procedure for HMWK8 , Q2c. I am converting $r$ and $\theta$ to cartesian coordinates: $$ \theta = \tan^{-1}\left(\frac{y}{x}\right)$$ $$ r = \sqrt{x^2 +y^2} $$ Pluging these back into the stream function equation given on the problem statement yields: $$ \psi = Q\left(x^2+y^2\right)^{\frac{3}{2}} \sin\left(3\tan^{-1}\left(\frac{y}{x}\right)\right) $$ Does this procedure makes sense? And if so, could I use small angle approximation? $$\sin\left(\theta\right) \approx \theta$$
No you can not assume a small angle because you need to find the properties at any angle.
Question by AME536A Student
For problem $2d$ I found the flow to be rotational $(\nabla \times \vec{V} \neq 0)$. However, when we derived Poisson's equation we assumed the flow to be irrotational. Can we have stream functions in a rotational flow?
There is no mention of Poisson's equation in this question.
Question by AME536A Student
I know there is no mention of Poisson's equation but isn't the poisson's equation a requirement to have a stream function? Ergo insn't an irrotational flow a condition to find a stream function?
No not necessarily. We'll discuss this more in the next 2 classes. Just make sure you actually compute the vorticity correctly for now.
Question by AME536A Student
In general, is there any good rule of thumb to know when to use stream functions vs potential function to calculate the velocity components in a flow? Assuming a 2d flow with constant density. For instance, in prob 1 you tell us to use the stream function but the same answers could be found if we use the potential functions instead.
If you need information on where the streamlines lie (or where the surface lies), then you have to use the stream function.
Question by AME536A Student
Question for assignment 8 Question 2a:
The plurality of "stagnation points" in the question leads me to believe that there are more than one, but for the aforementioned reason, I don't think this is possible. Am I missing other stagnation points, or was the problem worded this way to make students consider the values for $\theta$ as well prior to completing their solution?
When asked to find all of the stagnation points, it's possible there is only one or none.
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