Sometimes I hate videos like this because I already focused in on computer engineering and I'm super jealous I don't get to use techniques like this. Immaculate video. You've probably made someone decide their major with this. I dream of having the kind of education ability you have.

I like how approachable this explanation is. It introduced me to a method that was left out in my secondary / post secondary STEM courses.

Oh Lord I haven't been so engaged by an explainer video in *ages* I cannot wait for the next one and thank you for making this one!

i love how your videos help in clarifying the topics that I learned "raw" because I couldn't wrap my head around them

Amazing ... The easiest explanation I could ever ask for !

Outstanding video! I was sure this would have 100k+ views when I finished. The motivation was clear and the example was the perfect length.

Great video. I learned something new and it was motivated and explained nicely!

Brilliant explanation. This is something super relevant and useful that I had basically never heard of. Awesome.

There's a long-standing meme (at least in Russian academia) that French kids can tell that 2 + 3 = 3 + 2, but don't know how to get to the result.

@DontYouDareToCallMePolisz

9 ай бұрын

I don't get it

Nice. I wasn't exposed to this method in college. I came across it on my own in later years, and have the impression that it was given more emphasis in earlier decades. I think this should be in every engineer's toolbox.

Awesome video!

great video! keep up the good work

Very useful approach, well done :)

They always ask "Who's Albert Hung?", but never "Is Albert hung?"

awesome video, thanks

This is good stuff.

In grad school, I grappled with what was regarded as the most comprehensive and difficult treatment of dimensional analysis for engineers: the book "Similarity and Dimensional Methods in Mechanics" by Russian physicist L. I. Sedov. Dimensional analysis is SO RUSSIAN, I can only think the professor meant that "your" approach to scaling laws is very French. For all Oppenheimer fans, the blast wave generated by an atomic bomb is a super-famous dimensional analysis problem. The more approachable, yet rigorous description of what happens when the bomb explodes is in the book by another distinguished Russian physicist Y. B. Zeldovich: "Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena".

this is pretty good

Hi, the value of the Boltzmann constant (k_B) seems to be the same as that of the vacuum permittivity (\varepsilon_0) A minor typo, i assume?

I don't know if you read the comments frequenlty, but I wanted to ask you -yeah, I know it has nothing to do with the video- which career did you study, because I'm starting my engineering bachelor and am deciding between electronics, mechanics and chemistry, and I like materials science but I don't know how much I would like the job as materials engineer. So I wanted to ask you too what do you do normally in your job - do you choose materials, design them, choose optimized shapes for the materials, ... ? Thanks for reading me! Love your videos!

Was first introduced to dimensional analysis way back in pharmacy school: through answering flow rate problems for IV drugs. I was amazed about its application, especially in engineering through this old video: kzread.info/dash/bejne/ZZussNScj6irfps.html Still, I thought it was trivial piece of information that dimensions have to cancel if the equation work BUT I GOT MY MIND BLOWN NOW THAT I KNOW THERE'S ACTUAL MATHEMATICAL RIGOR TO THE METHOD HAHA the yt algorithm has blessed me, kudos to the vid creator!

Note that in hindsight, it is easy to just assume that the drag in fluid flow scales with the Reynolds number. But you don't know that is the case until you actually do the tests, regardless of how some units might cancel out somewhere on a piece of paper.

Love buckingham pi

What if the number of variables = the number of dimensions?

@Ender240sxS13

9 ай бұрын

Then you're missing something, likely there are important variables that you haven't considered.

Like negative the noise & add it to the original signal ❤

Can anyone simplify the explanation? I'm still lost in the sauce.

10:23 well, looking at it as a matrix means you can just invert it in general: A you got a relationship like M a + µ = 0 so a = M^-1 µ and for that matrix you get as inverse 3 1 1 0 0 -1 1 0 0 which solves your problem for all choices of µ in one go: a = 3 µ1 + µ2 + µ3 b = - µ3 c = µ1 You can do that exercise with a bunch of fundamental constants: Speed of light c: Length / Time Planck constant h: Mass Length² / Time Gravitational Constant G: Length³ / Mass Time² Boltzmann constant kb: Mass Length² / Temperature Time² So you get the matrix: | c h G kb | (Powers of) ------------------------------------------- | 1 2 3 2 | Length | -1 -1 -2 -2 | Time | 0 1 -1 1 | Mass | 0 0 0 -1 | Temperature and its inverse: | len time mas tem (powers of) ----------------------------------------------- | -3/2 -5/2 1/2 5/2 | Speed of light | 1/2 1/2 1/2 1/2 | Planck constant | 1/2 1/2 -1/2 -1/2 | Gravitational Constant | 0 0 0 -1 | Boltzmann Constant So to get any combination of powers of length, time, mass, and temperature, you can also use any combination of the speed of light, Planck constant, Gravitational Constant, and Boltzmann constant using that matrix. A volume can be given in terms of (multiplying the vector (3,0,0,0)) c^(-9/2) h^(3/2) G^(3/2) This works out to 6.65 *10^-104 m³ or 16 Planck Volumes. (I think it's not just 1 Planck Volume because that chose a different parametrization of the Planck Constant and/or the Gravitational Constant. (Both of those often get modified by some factor of pi and could be chosen just as well for this task) Force works out to be 1.21*10^44 Newton (using c^4 / G) etc. This is what the Natural Units basically come from. I wonder if there is something interesting to be said about those matrices in terms of their eigenvalues and eigenvectors... They have -1 as one of the eigenvalues and the corresponding eigenvector for the inverse matrix is (6, -1, -4, 1) but the three eigenvalues/eigenvectors are more complicated.

Does anything interesting happen when Reynolds number is 1? A lot of the time there is an interesting property when a dimensionless number is 1. I can't think of anything though, I mean sure it means the fluid has viscosity, but I don't see anything special.

hey super video and all that but really 4:40 the SI unit for mass is KILO gram, not gram 😭

Yeah the first big thing we teach undergrads in fluid mechanics is the Buckingham pi theorem.

SoME3 "memorability"... I've come back 4 times already. ummm... it's good.

Why would you use a capital m for mass? **cries in Moles** And why capital V for volu... I mean speed? (and then later at 14:45 actually for volume)

This might be accurate, but it is not explained in an easily assimilated way. I suggest devising something simple.

@Ender240sxS13

9 ай бұрын

This is probably the simplest explanation for dimensional analysis you're going to find. If you aren't understanding it you need to do some studying and actually work some problems to increase your understanding.

Nice video. The Buckingham PI theorem does remind me of the Sparse Identification of Nonlinear Dynamics technique. It's basically a technique to describe the relationship of polynomial combinations of observed variables to the state dynamics of a dynamical systems. They're quite similar in the sense that you don't necessarily need to analyse the effect of each variable and parameter individually...

**d**

All proportionality gives ridiculous results, for example, Cd coefficient depends from velocity. 11:55 Cd=1.5 how dimensionless parameter can be higher than 1 it implies that in wind can move faster than wind velocity it so stupid that you even not need explain that is violation of all logic. Maximum velocity let say sail of ship can only move with velocity of wind that is idealized limit. That is not worst, in world are many wind tunnels facilities and biggest problem as one expert say computer simulation of fluid dynamics never agrees with experimental, humanity really can save money and men hours on wind tunnels which are very expensive to built but more expensive to operate. If theory is based not on fundamental laws of geometry and proportionality constants for sine, cosine and exponent, but on dimensionless numbers Re, Pr, Nu. I found heat transfer for heat exchanger has 72 different dimensionless equations for heat transfer variations even with extra d dimensionless parameters that is monstrosity that not works but billion dollars wasted through chimney stack because Re, Nu, Pr, Fr dimensionless parameters are adapted for one experiment you change experiment geometry or flow parameters and equation becomes useless. Is heat convection equation is heat conduction (Fourier law) and is Bernoulli laws of hydrodynamics no laminar no turbulence factor matters, always complain theory never matches experiment when all fundamentals law are discarded and only dimensionless parameters are used in calculations we get infinity many equations for various geometry and flow regimes.

@Ender240sxS13

9 ай бұрын

What on earth are you talking about. You've demonstrated you did not understand how dimensional analysis works. Nothing about Cd being higher than 1 implies anything about "moving faster than wind". Cd is a dimensionless force, it relates the force on an object to the flow velocity that object is subject to. We've been successfully employing dimensional analysis for decades, it is used in the design of literally everything from cars to satellites.

@phyarth8082

9 ай бұрын

@@Ender240sxS13 Implies. Wind force at arbitrary cross-section are A is equal F=ro*A*w^2/2, object in what wind can stop wind velocity to stand still w=0, Cd=1, not to violate energy conservation law condition. Or ultralight object m=0 in wind can reach maximum velocity v=w. That is from I-Newton law of motion.

@angelmendez-rivera351

7 ай бұрын

@@phyarth8082You done eating your word salad?

@phyarth8082

7 ай бұрын

@@angelmendez-rivera351 Is hard to disprove video in comment section. I spend 20 years reading and following methodology of Buckingham PI, Kirpichev extended Buckingham PI theory, and Newton methods. They work only in simulation of fluid visualization. Newton methods in non-steady heat and fluid dynamics. I know to much and is hard to disprove. But video disregards other laws of energy conservation condition, III-Newton law. Video has nothing to do with reality, to solve fluid dynamics or heat transfer problems. And that is bad you cannot create efficient heat exchanger or energy turbine without these fundamentals.