Hi there! How does one choose the repeating variables? What defines a repeating variable? I seem to follow the rest of the operation well but I've looked in many places and have not been able to understand how the repeating variables are identified and chosen. Thank you!
You have to be able to cover the all the dimensions found in the dimensionless number. Also, since we can alter these in experiments, it helps to use ones we can typically control. There is another video on this topic, with additional helpful comments: ua-cam.com/video/aN9rC65byCk/v-deo.html
You choose the repeating variable in terms of that when you combine those repeating variables it does not make a dimensionless number as long as it does not for a dimensionless number you can choose which ever combination you want , once you make the pi term now it should be dimensionless
That makes sense, but I get stuck as to how do I now use these Pi terms to my benefit? How do I end up plotting? Which values were used in the plot as these Pi terms still include a number of variables.
why not choose viscosity? you said we had to choose a number equal to the number of dimension types, but you also defined the number of dimension types using the chosen dimensions, right?
As stated, step 1 is rather confusing. Were the variables chosen arbitrarily? Why were those variables chosen? Why not take others into consideration for instance the pressure or acceleration of the sphere? Wouldn't those affect the drag coefficient?
The variables weren't chosen arbitrarily, you need to use your intuition. The reason we could rule-out pressure is because we already included density, which is proportional to pressure in a compressible fluid. Therefore, the density term will account for a lot of the effects pressure has. I think we can rule out acceleration because we have included velocity, which is the integral of acceleration. The current velocity of the sphere is related to the past acceleration of the sphere, so velocity somewhat accounts for this. You should know that this is a low-order analysis, so it won't give an exact answer, but will get close. In reality, it might turn out that pressure and acceleration affect the drag force independently from the density & velocity. However, the low-order formula is simple to derive and probably does a good-enough job. I think the process of refining a model by adding higher-order corrections is the basis for perturbation theory, which is very applicable in fluid dynamics.
Can someone explain whats significance of pi theorem? its just doesnt makes sense to me at all.We forcing terms to cancel each other and become dimensionless thats it.What does it give us mathematically what type of data and importance it have ? Why we able to multiply or divide extract.. PI terms without changing them or their significance ? Im looking for more intuitive explanation cause it looks nonsense to me...
Everything seemed good, until there was no explanation for the primes. Why is one inverted, but the other is some projected area? Why bother changing it? Why not leave it where it is?
You have to manipulate them to get a term that exists, in this case it must be equal to the Reynolds number and coefficient drag. This is done so you can compare real terms.
Once you have the dimensionless number of pi, you can manipulate it to become a term of greater interest. In the first case, the reciprocal of the initial pi is the Reynold's number. In the second case, we merely replaced the diameter squared with area. Since we are only interested in the units and not the actual number, we are able to substitute a 1/2 for the 4/3.14, thus giving us the coefficient of drag.
![Buckingham Pi theorem [Fluid Mechanics #6]](http://i.ytimg.com/vi/eRBEPV8NCHI/mqdefault.jpg)
Probably the 20th clip I've watched on B-pi Theorem and the only one that has made sense to me
I've been in college for over 3 years and this is the best professor i've ever had. Thank you for the past 8 minutes of my life.
I just want to thank you from the bottom of my heart for this clear explanation!Thank you.
thank you so much for this video. literally searched everywhere for an explanation for this theorem and this is the only video that has helped me
qpaqw
Your video is really clear. I have seen lot of videos about this topic, but most of them are confusing. Congrats for your method.
You choose the same number as reference dimensions (i.e. length, time, mass).
You are correct that we are plotting Re on the x-axis and we defined this earlier as Pi1'.
Hi there! How does one choose the repeating variables? What defines a repeating variable? I seem to follow the rest of the operation well but I've looked in many places and have not been able to understand how the repeating variables are identified and chosen. Thank you!
You have to be able to cover the all the dimensions found in the dimensionless number. Also, since we can alter these in experiments, it helps to use ones we can typically control.
There is another video on this topic, with additional helpful comments: ua-cam.com/video/aN9rC65byCk/v-deo.html
Ok, thank you very much!
It's good to use geometric, kinematic, and dynamic variables as repeating variables
Why isnt pi 2 prime the inverse of pi 2, like pi 1 prime?
How do you know what to choose as your repeating variables?
You choose the repeating variable in terms of that when you combine those repeating variables it does not make a dimensionless number as long as it does not for a dimensionless number you can choose which ever combination you want , once you make the pi term now it should be dimensionless
really helping for my final exam fluid
you are the bestt brooooo -utm-
Extremly interesting and good explained!
Even as a somebody who doesnt speak English as native Language I got it all!
Really helped with my first biotransport exam!!!
How would you explain why we choose a variable as a repeating variable ? Like give a reason why d,v and density are chosen
Best tutorial for dimensional analysis out there! Thanks!
mechanical engineering student here
it was brilliant!
Why didn't you choose dynamic viscosity as a repeating variable? and why did you choose the other three?
This helped refresh me on the material for an exam. Thank you!
How is force the dependent variable
That makes sense, but I get stuck as to how do I now use these Pi terms to my benefit? How do I end up plotting? Which values were used in the plot as these Pi terms still include a number of variables.
why not choose viscosity? you said we had to choose a number equal to the number of dimension types, but you also defined the number of dimension types using the chosen dimensions, right?
As stated, step 1 is rather confusing. Were the variables chosen arbitrarily? Why were those variables chosen? Why not take others into consideration for instance the pressure or acceleration of the sphere? Wouldn't those affect the drag coefficient?
The variables weren't chosen arbitrarily, you need to use your intuition. The reason we could rule-out pressure is because we already included density, which is proportional to pressure in a compressible fluid. Therefore, the density term will account for a lot of the effects pressure has. I think we can rule out acceleration because we have included velocity, which is the integral of acceleration. The current velocity of the sphere is related to the past acceleration of the sphere, so velocity somewhat accounts for this. You should know that this is a low-order analysis, so it won't give an exact answer, but will get close. In reality, it might turn out that pressure and acceleration affect the drag force independently from the density & velocity. However, the low-order formula is simple to derive and probably does a good-enough job. I think the process of refining a model by adding higher-order corrections is the basis for perturbation theory, which is very applicable in fluid dynamics.
how do we choose the repeating variables???
You have to use your intuition
What does "repeating" mean?
An extremely well rounded explanation
pi 1 is the reciprocal of the Reynolds number, right? feel like that should be pi 1 prime at the end, but i may be wrong
I don't think you explained step 2 well enough? just choose any random variables doesnt matter what? I can just choose the diamater and be good?
How did you chose to take exactly three repeating variables?
How to choose core variables? Thanks
I'm not even english but this is saving my chem semester
How did 4/pi become 1/2
plz tell me how to select vescocity & density while both r fluid property
For the last graph, I thought you had defined the Reynolds number to be Pi1' not Pi1.
Could you explain this?
Can someone explain whats significance of pi theorem? its just doesnt makes sense to me at all.We forcing terms to cancel each other and become dimensionless thats it.What does it give us mathematically what type of data and importance it have ? Why we able to multiply or divide extract.. PI terms without changing them or their significance ? Im looking for more intuitive explanation cause it looks nonsense to me...
where did A=(pi/4)d^2 come from?
That is just the equation for area. Area = pi*r^2. r = D/2, so A = (pi/4)D^2.
are you always supposed to just choose 3 repeating variables?
NEpatsfan93 You choose the same number as reference dimensions (i.e. length, time, mass).
Everything seemed good, until there was no explanation for the primes. Why is one inverted, but the other is some projected area? Why bother changing it? Why not leave it where it is?
You have to manipulate them to get a term that exists, in this case it must be equal to the Reynolds number and coefficient drag. This is done so you can compare real terms.
Very good explanation thank you!
He's using The Force, especially on 6:16.
is this the only american youtuber who works in si units?
Thanks Knutsen :D
:)
How did u calculate pi prime?
Once you have the dimensionless number of pi, you can manipulate it to become a term of greater interest. In the first case, the reciprocal of the initial pi is the Reynold's number. In the second case, we merely replaced the diameter squared with area. Since we are only interested in the units and not the actual number, we are able to substitute a 1/2 for the 4/3.14, thus giving us the coefficient of drag.
So much better than my teacher
So helpful ❤
thank you you legend
mindblowing
very useful video
hey dady
THANK U
Thank you :)
Useful.....
Noice!
how do I choose which variables are for repeating variables?