Fluid Mechanics: Dimensional Analysis: Buckingham Pi Theorem

[@rashikanjum]

The video offers the same level of information and teaching expertise as a private tutor I pay monthly for, yet here I am receiving it for free. Thank you very much for this valuable video.

[@aerodynamico6427]

Your "sir"s are useless.

[@Jon_]

Really appreciate the video, an actually intuitive explanation of the Buckingham Pi Theorem unlike the incomprehensible mess that is the lecture notes by my mechanics professor👍

[@CaptainChicco]

😂Better they give you notes, mine just leaves us hanging to dry (die, I mean)🤣🤣

[@StudyfromHomewithUs]

Glad to know it helps.

[@ryderphillips241]

truth

[@Astro-gy3nh]

Actually made this once incomprehensible topic very understandable to me. Amazing job.

[@StudyfromHomewithUs]

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[@asimi.c]

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[@DrAidFawzal]

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[@StudyfromHomewithUs]

Alhamdulillah boleh membantu. Aamiinn...

[@45rampradeeps65]

Thanku ser, what an explanation May God bless you and your family 🙏❤️ You are an extraordinary talent My favourite teacher 💓🤪

[@vaisakht6724]

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[@yadhu1884]

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[@StudyfromHomewithUs]

Thank you. Wish you all good luck.

[@1q84-u6f]

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[@StudyfromHomewithUs]

You are welcome

[@CluckYou21]

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[@StudyfromHomewithUs]

Glad it was helpful!

[@MATHSdotPHYSICS]

Greatest lecture i have ever watched. Thanks

[@StudyfromHomewithUs]

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[@Harshavardhan-es5xt]

Very clear and crisp Wonderful help!!!

[@StudyfromHomewithUs]

Thank you. Glad to help.

[@CM-dx6xu]

thank you so much, i was able to understand this in 10 mins thanks to your video! Bless you

[@StudyfromHomewithUs]

Glad it helped!

[@Dylan-mn1qv]

At the end would it not be a function of Re^-1? Why is it f(Re) when Pi 2 is the inverse of Re and not Re^-1? Or are they the same? Great video, much better than my professor!

[@axuwu6939]

My reply is probably too late, but it’s the same! Think about any function of x. 2x is a function of x, x^-1 is a function of x, x+5 is a function of x, and so on. You don’t say f(x^-1), you just say f(x). It’s the same case here! You’re not writing the specific function Re^-1, you’re just saying that it’s any function of Re.

[@charlschnetler]

Excellent! Thank you very much for posting this.

[@李佳芸-o3u]

the best explanation about this topic！very clear！！

[@StudyfromHomewithUs]

Glad to hear that!

[@redalreemphasis4907]

Thank you soo much i really grasp the topic!!! Love it!!!

[@StudyfromHomewithUs]

Glad to know that.

[@edokamichael1218]

God bless you sir. You have done a great job

[@StudyfromHomewithUs]

Thanks for the nice compliment.

[@mukhtarabdi4443]

Thank you so much for sharing us this lesson.

[@StudyfromHomewithUs]

My pleasure!

[@9wyn]

Thank you very much for presenting a concise explanation. 🙏🏽

[@StudyfromHomewithUs]

You are welcome.

[@nabaaali8961]

Thank you very much, may God bless you all

[@StudyfromHomewithUs]

Welcome. God bless you too.

[@sergeydukman5832]

Why PI1 is the functtion of Re: PI1=f(Re)? Shouldn't it be PI1=f(Re^-1)? Thanks a lot for the video.

[@StudyfromHomewithUs]

Both correct. If you have an equation y = 1/x, you will say y is a function of x, or y = f(x). Of course, you can also say, y is a function of 1/x, or y = f(1/x). And 1/x is a function of x. Analogically: if A = f(B), and B = f(C), then A = f(C).

[@sergeydukman5832]

@@StudyfromHomewithUs Thanks for clarification. I understand now.

[@m.s.sakib2205]

The best video on the topic ❤️

[@yahyeabdi1681]

WOW. easily explained in 10 min.. Thank you

[@StudyfromHomewithUs]

Glad you liked it

[@CharlesXavier-po6tm]

way more better than my university's teacher😊

[@StudyfromHomewithUs]

Glad it helps

[@Adarsh_mviit]

Sir maja aa gya ... Nice lecture 👌

[@StudyfromHomewithUs]

Thanks

[@mhhhcheese]

wow what an amazing explanation

[@AndSooOn]

Really great Video Sir🙏It helped me a lot

[@IbrahimAli-nn5yh]

Thank you so much this is really well explained

[@StudyfromHomewithUs]

Thank you.

[@reabetsweseisho5325]

This was very helpful. Thank you

[@StudyfromHomewithUs]

Happy to help.

[@arpitashilpuja5999]

Why have we took Density for mass ? Can we not take Viscosity and drag force as mass is already related to them in case of repeating variables?

[@axuwu6939]

This is super late, but I’m case anyone else has the same question, I think you can choose anything. The point of doing this is so that you can create a simplified function to solve for whatever variable you need. So, there’s no real rules as to which ones you take, because you’re taking whatever it is that you need for your function to be useful, or whatever is most convenient for you to solve. To quote from my textbook: “Clearly there is ambiguity in these choices, something that often vexes the beginning experimenter. But the ambiguity is deliberate. Its purpose is to show a particular effect, and the choice is yours. The followings are two guidelines for selecting scaling variables: 1. Do not select output variables for your scaling variables. In Eq. (5.1), certainly do not select the dependent variable F, which you wish to isolate for your plot. Nor was μ selected, for we wished to plot force versus viscosity. 2. If convenient, select simple and popular, not obscure, scaling variables because they will appear in all of your dimensionless groups. Select density, not surface tension. Select body length, not volume. Select stream velocity, not speed of sound.”

[@kkb2687]

@@axuwu6939 thanks for the info. really needed it

[@PhemeloMatlhoko]

THIS WAS REALLY HELPFUL THANK YOU😘❤

[@MyMemesAreTerrible]

Woah that was so clear! Thanks a ton!

[@StudyfromHomewithUs]

Glad to know it helps.

[@danielgilder8672]

you earned your self a subscriber todoay my friend

[@StudyfromHomewithUs]

Great! Thank you

[@whacq]

Great video definitely gonna sub!! My only question is why do we choose primary variables as density, diameter, and velocity? I know it says it is advantageous to choose mass, geometry and kinematics but I still find it confusing. Would you be able to choose any variables as your repeating one’s and still get the correct answer?

[@KedharSrinivas]

Greatly helpful .. Thank you

[@enestlv01]

Sir the last part is it true? I think (Fd/p.V^2.D^2) = f(Re^-1) must be like this.

[@StudyfromHomewithUs]

Please see my answer to a similar question above. Thank you.

[@cerinsebastian6784]

I understood the method well thank you

[@StudyfromHomewithUs]

Glad to know it helps.

[@np7015]

Thanks. Can you please shed some light on the application of these equations in the pharmaceutical scale up?

[@StudyfromHomewithUs]

I am sorry, I am not familiar with pharmaceutical cases. But I am sure that it can also be applied to the cases where you need to conduct experiments with different scales than the actual situation.

[@sethwilliams3683]

From where are we defining these parameters? Force the drag force equation? I don't know how I am suppose to realize viscosity is part of this equation. The only way I see that you would POSSIBLY know that viscosity is part of this equation would be if you realized that drag coefficient is viscosity based. Well presented video, I'm just struggling with this concept and the generic math jargon that accompanies it.

[@StudyfromHomewithUs]

Good question. Listing the parameters is the first step in the dimensional analysis. This is the brainstorming part of the process which is based on our physical knowledge. You may refer to another video: Fluid Mechanics: "Why do we need to do dimensional analysis?" (kzbin.info/www/bejne/gHa9c2ePgb-efMk). You may find the answer in this video. On the other hand, you may also just add any parameter that you feel related to the case, let's say "temperature, T". During the analysis of the dimension of all parameters, you will obtain the power of parameter T is zero, which means it is eliminated by itself. Or, you may want to add the rotation speed of the sphere, as you think that it may influence the drag force. In the end, you may find different expression than the one in this video. It is still OK, it is correct, it shows the dependence of the drag force to all parameters that you listed. Later, when you do the experiment, you will know what to vary. Hope it enlightens a little bit.

[@abhishekkash3440]

sweet explanation thank you

[@StudyfromHomewithUs]

You are welcome

[@Adarsh_mviit]

बहुत सुंदर

[@isaaccottrell8172]

Great video thank you!

[@icontrolthespice]

Brilliant video

[@StudyfromHomewithUs]

Thanks

[@icontrolthespice]

@@StudyfromHomewithUs I just had a fluid mechanic question today where 12% of the marks were on pi theory. You gained me all those marks with you brilliant and clear explanation. Thank you.

[@StudyfromHomewithUs]

Happy to hear that.

[@m.s.d.prasad8880]

Clear cut explanation 👌. Sir could you prepare an video on Rayleigh method also🤗..., Because I like the way of explanation 🤩

[@StudyfromHomewithUs]

Will do the Rayleigh method. Thanks for the suggestion.

[@m.s.d.prasad8880]

@@StudyfromHomewithUs waiting for that video 🤩

[@StudyfromHomewithUs]

@@m.s.d.prasad8880 Rayleigh method is there (kzbin.info/www/bejne/eZmZeqSlnJ6ao5o)

[@yusfsami2189]

thank u , really nice describe and vedio edit

[@StudyfromHomewithUs]

Thanks for the compliment.

[@judeolivermaquiran8622]

Why is it at the end of the solution, the Reynolds number did not carry the raise of negative 1

[@StudyfromHomewithUs]

If you have an equation, for example y = 1/x, you will say y is a function of x (or y depends on x), or y = f(x). Even though it is not wrong to say y is a function of 1/x.

[@ibnumahmmoud4365]

thankssss sir nice explanation really appreciate it

[@StudyfromHomewithUs]

Most welcome

[@fabriciocollado9377]

Thanks, is a good video. 👍🙂

[@amizahir2195]

You literally saved my life thank you so much

[@StudyfromHomewithUs]

Happy to help👍

[@muhammadizzuddinbinhafizi6183]

Good explanation

[@StudyfromHomewithUs]

Thank you

[@bobbob-lw5ve]

Please help! So ive done loads of examples of this type of question, and the method is almost the same as yours. However in all my tutorial solutions, when constructing the dimensionless groups, if viscosity is one of the remaining variables, it is made to the power of -1. It is the only variable they do this to. So the answer is almost the same as what you got for pi2, but the answer is inverted. Your way makes more sense to me, i dont know why they do this. Its only for viscosity. Please help!

[@StudyfromHomewithUs]

If you obtain the power -1, it is also correct. For example: if you have an equation y = 1/x, you can write y = f(1/x) (we say: y is a function of 1/x). But if you write y = f(x) (we say: y is a function of x), it is also correct, as the only variable that y depends on is x. Hope it answers your question.

[@Quazify12]

god bless your soul!

[@abdallahabdulkarim7279]

What if the repeating variables are diameter, velocity then density instead of density, diameter then velocity? Obviously the pie terms would change. So how to order them correctly?

[@StudyfromHomewithUs]

The sequence of the repeating variables has no importance as they have commutative property for multiplication. They can be swapped from their position without making any difference to the answer. The pie terms will not change.

[@m.albert482]

I struggle to understand how to use the final result. F/(rho*V^2*D^2) = function(Re). But what is the function, is it cos(Re), or exp(Re^2/2). The function can be anything. I'm not sure how the final result is helpful if you don't know what the function is.

[@StudyfromHomewithUs]

Would you mind watching this video: kzbin.info/www/bejne/gHa9c2ePgb-efMk ? You might find the answer to your question there. Please let me know if you get the answer after watching the video or if you still have questions.

[@thatsound7057]

Can we say , in this way formulas are created and then experiments are doing to check correctness?

[@StudyfromHomewithUs]

We formed the relationship between the dimensionless groups to reduce the number of experiments that we need to do. Please check this video (kzbin.info/www/bejne/gHa9c2ePgb-efMk) for the explanation as to why we need to do dimensional analysis.

[@usmanahmad2115]

Great professor

[@StudyfromHomewithUs]

Thank you

[@Khawsh]

this video is very helpful

[@StudyfromHomewithUs]

Glad to know that.

[@monversity]

Thank you👍

[@StudyfromHomewithUs]

You're welcome

[@alimozaffar6884]

Thanks 🙏🙏

[@StudyfromHomewithUs]

You are welcome

[@swastiktiadi6473]

Nice explanation

[@StudyfromHomewithUs]

Thanks for the compliment.

[@0xbinarylol]

but what expression relate F/rhovd=f(Re)

[@StudyfromHomewithUs]

Do you mean the mathematical expression? If necessary, it can be derived later after we plot the curve from the experiment. For experimental purpose, what we need is the dependency between the variables, so that we can measure the variable that we need by varying the other variables. This dimensional analysis is to find that dependency.

[@0xbinarylol]

@@StudyfromHomewithUs Yes I get it in your other videos of Bucking Humm Pi Theorem

[@bakrhani4960]

thank you so much

[@StudyfromHomewithUs]

You're welcome

[@robertolson7304]

Reminds me of pie. You can find any shape in pie. Its just a circumference. Area is also fluid. Its area. Not a shape. Fluidness comes in a form like this. LxW= area. 2x2=4 . That is 2D or binary. 2 lines of 2. What if i added 1 line or 1D. It would be absorbed evenly. Like 1 line of 2. The 2 would be split apart into 1 and 1. Then put into line L of 2 and line W of 2. 3x3=6.. not 2x2x2=8 in cube form. circumference are always 2D. Its a surface.. congrats🎉 you know know why pie is infinate..

[@StudyfromHomewithUs]

Oups!

[@sukranochani5764]

Nice

[@StudyfromHomewithUs]

Thank you.

[@yashtupekar2872]

Thank u sir

[@StudyfromHomewithUs]

You are welcome.

[@kuba2466]

good video

[@StudyfromHomewithUs]

Thank you

[@ibnuabdullah99]

sangat2 membantu.

[@StudyfromHomewithUs]

Alhamdulillah...

[@Right_Place_To_learn]

sir which software are u using

[@StudyfromHomewithUs]

I am using PowerPoint.

[@davidyang9902]

@@StudyfromHomewithUs very impressive mastery of PP, i thought i knew how to use PP but this is on another level! well done

[@StudyfromHomewithUs]

@@davidyang9902 Thank you

[@davidyang9902]

@@StudyfromHomewithUs I watched this video 30 minutes before my midterm today. You saved me! Thank you very much

[@StudyfromHomewithUs]

Glad to hear that. You are welcome.

[@rashmikakrishnan4475]

💯👌

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👌

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❤

[@StudyfromHomewithUs]

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[@12thninja]

👌👌

[@niralnaik16]

Good sir

[@StudyfromHomewithUs]

Thank you

[@williamcase426]

Is this video narrated by a robot

[@StudyfromHomewithUs]

Yes

[@bernardlubis8007]

sorry mas, can u speak javanese. Because i don't speak English.

[@suleymantnr6749]

great video but I need a more example

[@StudyfromHomewithUs]

You may refer to examples and exercises in some textbooks.

[@zhenccc]

thank you so much...

[@StudyfromHomewithUs]

You're most welcome

[@cruzyt4020]

❤

[@bernardlubis8007]

sorry mas, can u speak javanese. Because i don't speak English.

[@youssefstudent7485]

thank you so much

[@anuragnaidu7517]

thank you so much