Fundamentals of Fluid Mechanics Questions and Answers  
Question by AME536A Student
I have a question about Prob #1 in the assignment 7. In order to find the wind speed of the flow going toward the prototype windmill, I have used another nondimensional number other than Re and $C_{D}$. The common parameters used to make the new nondimensional number are $\rho$, D, W(angular velocity of blade). A extra parameter used is $q_{\infty}$. As a result, I got another nondimensional number $q_{\infty}$/ W. My logic used to get the wind speed is $q_{\infty proto}$/ $W_{proto}$ = $q_{\infty model}$/$W_{model}$ and I got the $q_{\infty proto}$, but the answer is incorrect. I was wondering if I choose wrong common parameters and extra parameter.
This sounds more or less correct. But what units does the angular velocity of the blade have? Radians per second?
Question by AME536A Student
Yes. I use the unit of rad/s for the angular velocity. 240 rpm= 240 round/min * 2$\pi$ rad/round * min/ 60s= 25.13m/s, 30 rpm= 30 round/min * 2$\pi$ rad/round * min/ 60s= 3.14m/s Therefore, I got 5m/s / 25.13m/s = $q_{\infty proto }$ /3.14m/s. $q_{\infty proto }$ = 0.62m/s, but the correct answer is 12.5m/s.
Well in that case one of your dimensional numbers is wrong because it has dimensions.
Question by AME536A Student
I don`t understand your comment. Do you mean that I select wrong common parameter and extra parameter? If you don`t mind, could you explain in detail?
I gave you a big enough hint. Now, think about this and find your bug.
Question by AME536A Student
Hello, In class, you mentioned that we shouldn't worry about Temperature as one of the common parameters in Buckingham Pi theorem. For Assignment 7 Question 2, do we have to consider Temperature as the fourth common parameter? thanks
No, I did not say not to worry about temperature. I mentioned there are 4 independent dimensions in classical physics, but in fluid dynamics we generally only use 3 (excluding electric charge). Temperature can definitely be a physical parameter of interest in this course (either common or extra parameter).
Question by AME536A Student
Clarifying question about problem 2 for assignment 7:
For part A, do you only want 2 non-dimensional numbers and for us to show their connection to $Re_D$ and $C_D$? Or do you want us to determine all of the $\Pi$'s of the system?
You should first identify all independent parameters of importance, and build as many $\Pi$s as necessary.
Question by AME536A Student
I have a question about the characteristic length of blade explained in the nondimensional class. My understanding is that the ratio of c (actual flow travel distance) to the diameter of blade is fixed. In order for the above statement to become true, is the geometric similarity be satisfied between prototype and model?
Yes, when designing the small scale experiment, you need to make sure that the ratio between the chord $c$ and the radius $R$ remains the same.
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