Lesson 1 - The Reynolds Transport Theorem

Online lesson for EME 303 at Penn State Hazleton.
This lesson follows the derivation of the Reynolds Transport Theorem. We will apply this theorem in several subsequent lessons.
License: CC-BY-SA 4.0 (creativecommons.org/licenses/...)

[@jiangye7693]

I have seen many versions of the explanation of Reynolds Transport Theorem, yours is the best one. Thanks!

[@abhiaerospace]

here is love and gratitude all the way from INDIA...u just made my day....thanks a lot.....incredible explanation

[@ariid4662]

Loads of love from India!!

[@user-wh2gy9lk6m]

the best explaination ive seen till date for Reynolds Transport Theorem.

[@srikanthprasad9208]

This is the best explanation of RTT I have ever seen! Thanks a ton!!!

[@manandepala3673]

The best explanation for reynolds transport theorem so far! Loved it!!!

[@fan7016]

I loved it!! Finally I could understand this theorem...... Thanks a lot!!!

[@marcuscesar1343]

Great way to derivate this important theorem. Many thanks for sharing!

[@vkiran7847]

Whole one day preparation covered in 15 mints superb thanks allot for explaining this complex concepts in such a neat way

[@TonnyPodiyan]

Word wont be enough to express my gratitude. Thanks very much

[@debayan7]

Greetings from India. Was racking my brain on RTD for the last one hour. Ur video made it very simple.

[@jordancrowell6441]

So well explained and was easy to understand! Thank you so much for making this video!

[@elnica0941]

Hi there, I really like the way you relate and explain everything. Very clear. From now on, I will study my Fluid Mechanic class just watching your videos.

[@andreafassbender5728]

Thank you! Really great explanation, I have everything clear know. Hope to see new videos! - Universidad Técnica Federico Santa Maria, Valparaiso, Chile.-

[@anoojafaustine2480]

Finally I understood what is this.... thanks for this wonderful explanation of yours ... really helpful 💯

[@karll1715]

You are the best teacher for me! Thank you a lot.

[@urbananime5484]

Amazing stuff!! So clear!

[@abhishekkumarjaiswal7397]

Thank you so much. It's really helpful. Soon I will be uploading a little more visualization based explanation of RTT based on what I learnt through your video. Thanks again.

[@ndbharti]

loved it... really this lecture is too much helpful for understanding the RTT.

[@junaidnisar6457]

Superb..we need teachers like you

[@pradyumnaks7621]

Wow! I finally understood it! Thank You Joe Ranalli.

[@akshaykumarpatil3908]

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[@mdabdullahalmamun5067]

Best 16.11 mins in my life as gas dynamics students....

[@AbdoRyudamon]

Thank you very much, I wish professors at my school can explain the material like you do.

[@JoeyDiCienzo]

best explanation yet... simple and effective! thanks

[@tovichallenger7469]

you kind sir, just saved my life.

[@SUMITKUMAR-tm4ht]

Superb video...even guy without mechanical or civil background can understand

[@bernadettebouchard415]

This is total common sense. Phrased lovingly.

[@_IntroMe]

Finally I found the best one. Thank you so much ❤

[@sadasivan1988]

That was wonderful..... Thank U Dr. Joe

[@divyanshraka2974]

Really great explanation. Thank you sir.

[@naveenraj6277]

Thanks, man .u just cleared my years of doubt

[@dsbupadrasta2385]

Thanks a lot man.. U really helped for understanding the basics of my research

[@mariafernandaguerrero5987]

This video is amazing, thank you so much it was really helpful

[@vaidyanathanr9970]

What about that application of RTT in the nozzle and cylindrical pipe? Didn't get what that means. Could you be more specific like the other explanations you gave?

[@kushakjafry1329]

one of the best explanation.... thanks

[@7luckyforme]

Joe "the Man"! Thanks for making this common sense.

[@beatrizreis9087]

MASSIVE thanks for this

[@odeforodds]

Thanks a lot for this video! This really helps me from stucking at the derivation lol.

[@DasCayman]

Best explanation. Thank you

[@yangli3932]

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[@jayeshmahajan6764]

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[@priyagupta7662]

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[@amaljith007aj]

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[@sajagpoudel3559]

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[@tabdude8391]

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[@cenasingh1010]

Thanks for the help! - Student from Georgia Institute of Technology

[@fizzybubblyify]

Awesome! Thanks from Ireland

[@baslielabraham7152]

This explains it all. Thank you!

[@crismathews4354]

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[@davidmunoz6606]

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[@henrigernaey7113]

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[@BIGgymnast10]

Saving my life. Thank you.

[@jensburgert838]

amazing explanation! Thanks a lot!!

[@qiulanable]

great and clear explanation!!!

[@erfanvatanpour865]

Awesome! cheers Dr.

[@timurkoktas6841]

Very helpful, thank you!

[@andrewbubb1249]

Good Clear Explination

[@leeheebeom5504]

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[@tymofei8586]

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[@lapchauhung2605]

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[@Noob00035]

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[@ahmedalqutaini8553]

I go to cu Boulder !! and our our department is one of the best in the nation !! yet, none of the professors could explain this !!! better

[@augustye3489]

Than you so so so much. My native language is not English, so I find it trouble to understand what my prof said cause he spoke at a high speed. Now I understand!!!

[@mojtabakarimtabar4407]

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[@wiskifrac]

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[@scien-tít-daily]

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[@kumar-jatin-2000]

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[@nikhilagrawal2423]

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[@JayTheMachine]

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[@mohabmetwally5749]

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[@itswhoppertime]

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[@shubhamkshirsagar6429]

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[@mariamfonseca2668]

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[@1234SLUR]

really wish you have videos for those problems at the end

[@abhishektiwari2101]

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[@juanmanuelortega3765]

great exposition, clear, simple, within the range of konwledge of an averaged physic student: i see, you´ve got six videos in a row about CFD, are you going to add new videos ?? thanks

[@richardaversa7128]

6:42 "And you can probably see that we're going to get into calculus here". Bruh I can't even see a "d" in a word without thinking I'm about to be calcced

[@Defenseaffairs814]

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[@jheadley635]

Good video, thanks! I imagined Badger from Breaking Bad teaching me fluid mechanics.

[@kamranshirazi3030]

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[@jensburgert838]

Thank you very much for the great video! I still have same issues understanding the lagrangian idea. If we would talk about a solid material or one particle, I would totally understand it. But how is it possible for fluids, that the particles, that are considered at time t in the system volume are the same particles at time t +dt and are not mixed up with other particles. So basically the question is, how is it possible to follow a package of mass as it could could comprise of other particles a little time later?

[@eng.andre.fialho]

One year later but I hope I can help. That's because of continuum hypothesis. The volume we have is big enough to keep particles inside it and small enough to measure the same quantities in every point. Besides of that, there's no mass crossing a system (or a volume of fluid) , so it can be deformed and its shape can be changed but it will still have the same particles. And because it can be deformed, in Fluid Mechanics it's much more useful to work with control volumes, which is completely defined by you in the sense of geometry, size and so on.

[@tumul1474]

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[@andrejsternin7879]

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[@vikasmahey1523]

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[@ofeyee]

Best lesson on youtube I guess

[@user-wb8gg9ee8h]

Good good !!!!thank you

[@kevinyapri6941]

I'm still confused about the derivative parts. Why do we use material derivative for the B_sys? What I've learnt is this: For B_sys, it only got derived by time, not with position, so it can't be written as material derivative right? Why don't we use partial derivative notation here?

[@sabyasachisen8767]

Hi Kevin, you have a valid point. The material derivative is not applicable to B_sys. The operator D/Dt can be applied only to field variables (like velocity, temperature, density etc) and not to variables associated with identifiable entities of mass. Hence, it is appropriate to use the operator d/dt for B_sys where B_sys = integral of (rho*b*dV) over the material volume. Also, please note that the volume integral corresponding to B_sys at 3:20 is an integral over a material volume whereas the volume integral corresponding to B_cv = integral of (rho*b*dV) is an integral over a volume which is a geometric entity (not associated with matter).

[@alielhajj79]

perfect!

[@timnguyen1329]

6:00 is that the Bcv(t+dt) = Bcv(t) ? since they have same region. thanks!

[@EME303HN]

Tim Nguyen Not totally sure what you mean, but Bcv(t+dt) does not equal Bcv(t). We say the system and the control volume are equivalent only at the beginning instant (t) because they occupy the same space. The second equation is where we account for the changes over the interval dt.

[@matiasrabbia4480]

excellent

[@swetaindian9726]

Sir at 13:26 in the rtt integration of cv dont have velocity only it has pbdA ?????

[@EME303HN]

No it does not. That term represents the amount of b inside the CV, and so velocity doesn't enter into it. Remember though that in the case of momentum, b represents the velocity.

[@kevinbelza67]

Hello professor. Im a bit confused of the illustration of the control volume which is the red part. At time t and t+dt is cv is still the same? Thank you. And if yes, can we just cancel out the those cv in the further equations? Thank you sir! :)

[@EME303HN]

The idea is that when we allow dt to become very very small (as the limit approaches zero in calculus language), the two parts of the sketch become the same region in space. That doesn't mean we can cancel them out though.

[@sourabhpandey2410]

If control volume analysis focuses on a FIXED region in space then how it is allowed to change its size?

[@EME303HN]

It really just means that you're fixed to something that's independent of the flow. So perhaps the control volume is "all the water in a bath tub." The size of that control volume will increase and decrease along with the water level but the physical thing it represents remains fixed. In Into Thermo we would describe the difference most basically as: a system follows the same mass while a control volume allows mass to enter and leave to accommodate representation of some convenient device.

[@sourabhpandey2410]

@@EME303HN ok. By now I have never encountered any case where the size of control volume changes. In fact I have seen some well known people in fluid mechanics area saying that the volume of a control volume region doesn't change ( that is why I asked about size and not shape). Thank you😊.

[@MonsieurLeBoucher]

Great! Why do you write d∀ instead of dV? I have never seen this notation

[@EME303HN]

I use Vbar to represent volume and V to represent velocities. It's the same notation used by the Munson Fundamentals of Fluid Mechanics book.

[@michaelchantonese]

Hi Joe, excellent explanation. Actually understood what was happening for once! Just a question, 11:18 was this supposed to be "Flow rate of B(out) of the CV, and not system? Thanks!

[@EME303HN]

Yep that's right! Guess I was being a little careless with choice of words.

[@michaelchantonese]

@@EME303HN Awesome. Thanks for clarifying :)

[@sonniechan2636]

anyone care to explain the negative sign in B in=-pA1V1b1?

[@EME303HN]

+Sonnie Chan It's due to the dot product in the (V dot n_hat). On an inlet, the surface normal (n_hat) points outward from the surface, which is opposite the direction of the velocity. So there's 180° between the velocity and surface normal vectors, which produces a -1 when the dot product is computed.

[@CDinkle]

11:43 A cat meows off in the distance

[@antonissexywisdom]

You are a living legend. What is that nice font you used?

[@EME303HN]

It was a custom handwriting font I made