Dr Bart's world of chemical engineering
Dr Bart's world of chemical engineering
  • Видео 214
  • Просмотров 209 456
UW-Madison polymer processing (EPD650): lesson 1, part 1.
This introductory video serves two purposes. Firstly, it introduces the course, its learning outcomes, syllabus and assessment. It also describes the two text books that will accompany the course. The second purpose is to give a motivation for the subject. This is done by giving a brief history of some of the key moments in the development of polymer engineering before moving on to identifying the environmental challenges faced by the industry today.
Просмотров: 347

Видео

Take a break from the math and relax :)
Просмотров 1496 месяцев назад
Vexed by vector calculus? Confused by convection? Despairing with differentiation or indifferent to your integrals? Take five and relax with the adventures of Bertie the cat 😻
UW-Madison polymer processing (EPD650): lesson 7, part 6.
Просмотров 806 месяцев назад
The final part of lesson 7 examines how to derive the fully-developed temperature profile for the effect of viscous dissipation in the Poiseuille flow in a slot. The momentum equation is solved initially to yield the velocity profile in the flow, and then the energy transport equation is solved to calculate the effect that viscous dissipation has on the temperature profile within the fluid flow...
UW-Madison polymer processing (EPD650): lesson 7, part 5.
Просмотров 776 месяцев назад
The penultimate part of lesson 7 examines the phenomenon of viscous dissipation, or the internal friction that can be present in the flows of viscous liquids. The basic phenomena is discussed, and then its inclusion in the energy transport equation as a heat source term highlighted.
UW-Madison polymer processing (EPD650): lesson 7, part 4.
Просмотров 566 месяцев назад
This part of lesson 7 takes a look at Heisler charts. Proposed in 1947, and used for many decades to gain insight into heat transfer problems, they may not receive the attention they deserve today. Not only can they still be used to get the "feel" of a heat transport problem very quickly, but they are also an invaluable source of validation data for numerical simulations.
UW-Madison polymer processing (EPD650): lesson 7, part 3.
Просмотров 516 месяцев назад
The third part of lesson 7 examines the cooling of an injection moulded slab of polymer: an example of two dimensional, transient, heat transfer. As before the four-step workflow is followed, the problem understood, the energy transport equation simplified and then the resulting equations solved using Mathematica. Validation is carried out by means of comparing the numerical solution to data ex...
UW-Madison polymer processing (EPD650): lesson 7, part 2.
Просмотров 516 месяцев назад
Part 2 of lesson 7 examines a two dimensional heat transfer case. The problem is examined carefully, the energy transport equation simplified to describe the problem and then the resulting equations solved using Mathematica. The answer is then validated against the analytical solution for one dimensional heat transfer.
UW-Madison polymer processing (EPD650): lesson 7, part 1.
Просмотров 486 месяцев назад
The introduction to lesson 7 examines the use of twin screw extrusion in applications other than processing of synthetic polymers. Extrusion cooking and food production are alluded to and a case study of flavour burst chewing gum given. Video on twin screw extrusion: ruclips.net/video/N1QSToN7T_E/видео.html
UW-Madison polymer processing (EPD650): lesson 6, part 7.
Просмотров 407 месяцев назад
The final part of lesson 6 examines how to solve a radiative heat transfer problem using Mathematica. It also addresses the importance of validating the numerical solution!
UW-Madison polymer processing (EPD650): lesson 6, part 6.
Просмотров 447 месяцев назад
The penultimate part of lesson 6 has a very brief look at radiative heat transfer. The basic principles are outlined, along with how to incorporate radiative heat transfer either as flux-based energy transport or as a volumetric heat source term. The concept of effective emissivity is also introduced and discussed for systems that have a view factor of unity.
UW-Madison polymer processing (EPD650): lesson 6, part 5.
Просмотров 577 месяцев назад
Part 5 of lesson 6 examines correlations that can be used to estimate the convective heat transfer coefficient for various geometries that are relevant to polymer processing. Both forced and natural convection correlations are discussed.
UW-Madison polymer processing (EPD650): lesson 6, part 4.
Просмотров 577 месяцев назад
Erratum: at 27'45", the first term in the Peclet number should be V/A (not A/V!) as it's a representative length scale for the problem. This part of lesson 6 solves the energy transport equation for a simple film casting process. Three different heat transfer scenarios are examined that involve combinations of conduction, convection and advection. The resulting temperature profiles are discusse...
UW-Madison polymer processing (EPD650): lesson 6, part 3.
Просмотров 417 месяцев назад
The second part of lesson 6 examines some key non-dimensional groups that allow us to gain insight into the dominant modes of heat transfer within a problem. The Biot number, Nusselt number, Reynolds & Prandtl numbers are all discussed along with the Peclet number.
UW-Madison polymer processing (EPD650): lesson 6, part 2.
Просмотров 677 месяцев назад
Polymer processes often involve changes of temperature and the transfer of heat. This part of lesson 6 introduces the energy transport equation and discusses each of the terms it contains. Underpinning principles: Scalars and vectors: ruclips.net/video/VbcFLEG5aH0/видео.html Vector calculus: ruclips.net/video/8JZvZpr2ZXc/видео.html
UW-Madison polymer processing (EPD650): lesson 6, part 1.
Просмотров 417 месяцев назад
The introduction to lesson 6 features the multi-layer film extrusion process. This is discussed both in the light of multiple functional layers (for example, protective packaging for perishable foods) and a die design that splits and recombines multilayer film to increase the number of layers. A video of multilayer film extrusion can be found here: ruclips.net/video/atdksIv-xWk/видео.html
UW-Madison polymer processing (EPD650): lesson 5, part 5.
Просмотров 917 месяцев назад
UW-Madison polymer processing (EPD650): lesson 5, part 5.
UW-Madison polymer processing (EPD650): lesson 5, part 4.
Просмотров 547 месяцев назад
UW-Madison polymer processing (EPD650): lesson 5, part 4.
UW-Madison polymer processing (EPD650): lesson 5, part 3.
Просмотров 627 месяцев назад
UW-Madison polymer processing (EPD650): lesson 5, part 3.
UW-Madison polymer processing (EPD650): lesson 5, part 2.
Просмотров 777 месяцев назад
UW-Madison polymer processing (EPD650): lesson 5, part 2.
UW-Madison polymer processing (EPD650): lesson 5, part 1.
Просмотров 717 месяцев назад
UW-Madison polymer processing (EPD650): lesson 5, part 1.
UW-Madison polymer processing (EPD650): lesson 4, part 5.
Просмотров 1587 месяцев назад
UW-Madison polymer processing (EPD650): lesson 4, part 5.
UW-Madison polymer processing (EPD650): lesson 4, part 4.
Просмотров 737 месяцев назад
UW-Madison polymer processing (EPD650): lesson 4, part 4.
UW-Madison polymer processing (EPD650): lesson 4, part 3.
Просмотров 827 месяцев назад
UW-Madison polymer processing (EPD650): lesson 4, part 3.
UW-Madison polymer processing (EPD650): lesson 4, part 2.
Просмотров 1047 месяцев назад
UW-Madison polymer processing (EPD650): lesson 4, part 2.
UW-Madison polymer processing (EPD650): lesson 4, part 1.
Просмотров 697 месяцев назад
UW-Madison polymer processing (EPD650): lesson 4, part 1.
UW-Madison polymer processing (EPD650): lesson 3, part 6.
Просмотров 837 месяцев назад
UW-Madison polymer processing (EPD650): lesson 3, part 6.
UW-Madison polymer processing (EPD650): lesson 3, part 5.
Просмотров 597 месяцев назад
UW-Madison polymer processing (EPD650): lesson 3, part 5.
UW-Madison polymer processing (EPD650): lesson 3, part 4.
Просмотров 657 месяцев назад
UW-Madison polymer processing (EPD650): lesson 3, part 4.
UW-Madison polymer processing (EPD650): lesson 3, part 3.
Просмотров 607 месяцев назад
UW-Madison polymer processing (EPD650): lesson 3, part 3.
UW-Madison polymer processing (EPD650): lesson 3, part 2.
Просмотров 897 месяцев назад
UW-Madison polymer processing (EPD650): lesson 3, part 2.

Комментарии

  • @ahmetkelleci5938
    @ahmetkelleci5938 2 дня назад

    Mr. Hallmark in case of suspended sediment transportation at vortex flow which parameter should be more impotant than others?(Richardson-Zaki or Turbulent Diffusion or Molecular Diffusion or Entrainment rate) Thank you very much again:)

  • @ahmetkelleci5938
    @ahmetkelleci5938 2 дня назад

    Mr. Hallmark in case of suspended sediment transportation at vortex flow which parameter should be more impotant than others?(Richardson-Zaki or Turbulent Diffusion or Molecular Diffusion or Entrainment rate) Thank you very much again:)

  • @ahmetkelleci5938
    @ahmetkelleci5938 2 дня назад

    Mr. Hallmark in case of suspended sediment transportation at vortex flow which parameter should be more impotant than others?(Richardson-Zaki or Turbulent Diffusion or Molecular Diffusion or Entrainment rate) Thank you very much again:)

  • @rafilelyas9312
    @rafilelyas9312 27 дней назад

    Came for a DWC referesher, left with the urge to listen to Rancid (then watched some of your videos and discovered Dragster). Thank you.

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 26 дней назад

      @@rafilelyas9312 a pleasure! East Bay punk is still great and relevant!

  • @mediwise2474
    @mediwise2474 Месяц назад

    professor can i have your email or contact number wattsapp no

  • @sumadoolpeep7171
    @sumadoolpeep7171 Месяц назад

    When you are comparing between the full size against the model at the end of the video, where do you get the values for pi1, pi2 and pi4?

  • @wxzhenn7588
    @wxzhenn7588 Месяц назад

    LoL

  • @bassemhanafy
    @bassemhanafy Месяц назад

    More than perfect, this has been a big issue for me in fluid mechanics until now, thank you very much wishing all the best

    • @drbartsworldofchemeng
      @drbartsworldofchemeng Месяц назад

      @@bassemhanafy thank you for your kind feedback and glad to be able to help!

  • @Ribena499
    @Ribena499 2 месяца назад

    Hi thank you, you have saved me

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 2 месяца назад

      @@Ribena499 I'm very glad you've found this useful! Thank you for your kind feedback.

  • @thanoselefth1303
    @thanoselefth1303 2 месяца назад

    Κανείς για το ΤΟΜ εδώ;

  • @UmairKhan-r4q3o
    @UmairKhan-r4q3o 2 месяца назад

    Can you give me book name?

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 2 месяца назад

      @@UmairKhan-r4q3o certainly - it's "polymer processing: principles and design" by Baird and Collias.

  • @kaitoonzx
    @kaitoonzx 2 месяца назад

    Is it possible to predict long-term stress relaxation of multilayer thermoform polymers (unknown polymer) from short-term data at only three different temperatures?

  • @andreichelaru3021
    @andreichelaru3021 2 месяца назад

    Hey tnx for your lectures, i was wondering in what program were the drawings made?(i need to work in my chem E license and i need a program)

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 2 месяца назад

      @andreichelaru3021 thank you for the kind words - very glad the material is useful. I used MS Visio - which is now part of Office. Because careful to ensure that the version you use ships with the process engineering templates and stencils though!

    • @andreichelaru3021
      @andreichelaru3021 2 месяца назад

      @@drbartsworldofchemeng thanks

  • @lamineabassi3238
    @lamineabassi3238 3 месяца назад

    Dr Bart's lecture videos are an amazing, and I have benefited greatly from them.I hope you could also offer lectures on CFD using the finite volume method.Thank you very much

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 3 месяца назад

      @lamineabassi3238 thank you for your kind comments! I'm so glad that you find them useful! I have no plans at the moment to record any more CFD material, but if I do I'll keep finite volumes in mind! Have you looked at my existing CFD playlist?

    • @lamineabassi3238
      @lamineabassi3238 3 месяца назад

      @@drbartsworldofchemeng 💚

  • @gamingniche8620
    @gamingniche8620 4 месяца назад

    which software did you use to create the Plot layout , PFD & P&ID

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 4 месяца назад

      I used Visio with the process engineering symbol sets. Very useful.

  • @cakefactoryy
    @cakefactoryy 4 месяца назад

    Absolutely amazing video! Really helped me alot! Thank you!

  • @aliauid7449
    @aliauid7449 5 месяцев назад

    dr. your lectures are great, thank you so much

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 5 месяцев назад

      @@aliauid7449 thank you very much for your kind comment and I'm glad that the content is useful for you

  • @Knowledgeispowerofqazi
    @Knowledgeispowerofqazi 6 месяцев назад

    awesome work sir.

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 6 месяцев назад

      @MolanaTariqJameel-dn4sm thank you very much! Much appreciated!

  • @andrewmountianou2697
    @andrewmountianou2697 6 месяцев назад

    Thanks again for the very nice video. The N1 estimation is just PP geometry I 'd guess?

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 6 месяцев назад

      @andrewmountianou2697 thank you! Yes, I think so! I'm away at the moment so can't quite check!

  • @andrewmountianou2697
    @andrewmountianou2697 6 месяцев назад

    Awesome video once again! Is there an easy explanation how Trouton viscosity for LDPE is lower? I would assume it's higher due to potential entanglements from the branches.

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 6 месяцев назад

      @andrewmountianou2697 thank you very much! Yes, it's all about branching an the subsequent entanglements that result! More entanglement results so higher strain hardening!

    • @andrewmountianou2697
      @andrewmountianou2697 6 месяцев назад

      @@drbartsworldofchemeng Thanks but why Trouton predicts a lower viscosity for low density?

    • @andrewmountianou2697
      @andrewmountianou2697 6 месяцев назад

      I got it, these where shear viscosities multiplied by a constant the T ration, not a real prediction.

  • @andrewmountianou2697
    @andrewmountianou2697 6 месяцев назад

    Very nice lecture. Very good to know practically what you showed in the previous course. 1)About swelling, in a filled polymer: will the filler follow the polymer to the swelled edges? (around 15) 2) In your nice reference, I assume the Wagner is not the onw that Wagner's function is called by right? (around 19:00

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 6 месяцев назад

      @andrewmountianou2697 thank you very much! So, I don't think that there would be any physical basis for relative movement between filler and polymer, so yes I would have thought that swelling shouldn't introduce any inhomogeneity. I'm not aware of Wagners function being called anything, but I could be wrong

    • @andrewmountianou2697
      @andrewmountianou2697 6 месяцев назад

      @@drbartsworldofchemeng thank you for all your kind replies!

  • @andrewmountianou2697
    @andrewmountianou2697 6 месяцев назад

    Thanks for the nice explanation! Can we have the video you are promoting in a comment or the descriptions to see how this process is done? (I already checked but would be convenient for future viewers)

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 6 месяцев назад

      @andrewmountianou2697 thank you! That link is meant to be there so will remedy...

  • @ANKITSHARMA-iq5zy
    @ANKITSHARMA-iq5zy 6 месяцев назад

    Very nice lecture

  • @docd7779
    @docd7779 6 месяцев назад

    Dr. Bart's Lecture videos are an amazing contribution to those working or studying fluid mechanics - thanks so much

  • @nicksgarage8295
    @nicksgarage8295 6 месяцев назад

    how does the dredger device make sure it does not scoop up electroylte as well, and if so is that an issue. Also the molten sodium does it appear as little sporadic things randomly so wouldnt the dredger need to be moved around so it collects the sodium balls as the appear and disappear in the bath.

    • @dimaminiailo3723
      @dimaminiailo3723 5 месяцев назад

      sodium has much greater surface tension than molten NaOH, so it might've had small holes in its spoons (or whatever those scooping things are called), which captured sodium blobs whilst left NaOH behind

  • @thomasmuntzer1004
    @thomasmuntzer1004 6 месяцев назад

    You are my fucking hero. Thanks

  • @andrewmountianou2697
    @andrewmountianou2697 6 месяцев назад

    This video should be moved as the first video of your EPD650 playlist (it's last). Thanks for making this course available for everyone!

  • @andrewmountianou2697
    @andrewmountianou2697 6 месяцев назад

    Very nice lecture huge! This was the best video regarding TTS i've seen today while searching but it was very hard to find. I highly suggest adding titles of each lecture so people that search similar titles find your videos.

  • @andrewmountianou2697
    @andrewmountianou2697 6 месяцев назад

    Very nice lecture as usual! If I may ask, it seemed like the solvent's viscosity did not play a role in the fingerprint. I am actually surprised with that as you almost reached 1mPa s in the steady shear part.

  • @andrewmountianou2697
    @andrewmountianou2697 6 месяцев назад

    Once again a very nice lecture! Are these equations the same if we use oscillatory rheometry? Thanks in advance!

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 6 месяцев назад

      Thanks again for your positive feedback! No, they won't be - in the same way that complex viscosity and shear viscosity at only the same by coincidence (look up the Cox-Merz rule and Laun's relationship for more insight!)

  • @andrewmountianou2697
    @andrewmountianou2697 6 месяцев назад

    Very nice lesson! If you re not on vacations, allow me to ask: Why we care so much about having the solvent term. n(0) is basically n(polymer) especially in a real example (unless you really work with polymers with n= 50 Pa s. Same for all the terms extracted i.e. λ2 is basically near 0. I understand that we use Giesekus just to get a nice model for our "theoretical" melt/make Maxwell work but does the Giesekus equation really work to model real model real melts (apart from oligomers perhaps?) If yes what do we add experimentally in the solvent term? Thanks again! Really cool lesson!

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 6 месяцев назад

      Hi Andrew! Thank you for the positive comments! It's appreciated! So, originally, the Giesekus equation was developed for polymer solutions - hence the inclusion of solvent terms. It does, however, apply nicely to some melts so then we can neglect solvent terms as they don't make physical sense.

  • @johnfakes1298
    @johnfakes1298 7 месяцев назад

    Dr. Bart we never ran into eachother at the CEB but i enjoy your RUclips lectures and I hope your time in the states is going well. Cheers

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 7 месяцев назад

      That's very kind of you! Thank you! I hope you're enjoying ceb!

  • @thebrownprofile1352
    @thebrownprofile1352 7 месяцев назад

    Hi Dr. Bart, thank you for this video - the derivation is easy to absorb. I had a question regarding 8:02 of the video - why are we introducing stress imbalances in the opposite faces of the unit volume? I understood why an imbalance was introduced in your mass continuity derivation video due to mass accumulation in the unit volume or small mass amounts escaping through the other unit volume faces, but since the Cauchy stress tensor is symmetric, how can there be an imbalance?

  • @andrewmountianou2697
    @andrewmountianou2697 7 месяцев назад

    Great lecture! So this is why for all the previous videos you were writing -(t-t') instead of just t'-t? For the relaxation modulus and the memory function?

  • @andrewmountianou2697
    @andrewmountianou2697 7 месяцев назад

    Very nice discussion! However, at 8:15 the function exp[ (t-t0/λ ] is not a decaying function for positive t0 and λ. I think it should be t0-t?

  • @andrewmountianou2697
    @andrewmountianou2697 7 месяцев назад

    Awesome lecture! Some questions in regards to Bagley correction: I guess a is a material property. Any info we could get from that? Can't we have an easier correction without a if we just remove the pressure contribution for L/R=0?. Simply said: ΔP(true)= ΔP(apparent)-ΔP(intercept). I guess there must be something wrong with this as we would not have to repeat for different Qs and it's "too" easy. Once again thanks in advance!

  • @andrewmountianou2697
    @andrewmountianou2697 7 месяцев назад

    Great lecture! the nice expression at 2:48 is derived from a future lecture (7 part 2) not a previous. Based on that there is a minus missing.

  • @andrewmountianou2697
    @andrewmountianou2697 7 месяцев назад

    Once again a very nice lecture!~ At 7:30 I think the right part of the u(rc) should also be divided by μΒ?

  • @andrewmountianou2697
    @andrewmountianou2697 7 месяцев назад

    Thanks for the very nice lecture! For Carreau model don;t we always have λγ>>1 in the power law region of the graph so we can safely assume it? Shouldn't p=n-1/2 in that case? or -p=1=n/2? Thanks in advance!

  • @andrewmountianou2697
    @andrewmountianou2697 7 месяцев назад

    Great video! Γ at 2:00 should have minus in front just as at 2:56 (the blue)

  • @andrewmountianou2697
    @andrewmountianou2697 7 месяцев назад

    That is an amazing idea! very clever! thanks for sharing! Can you share the link of the end suggested video for people's convenience? Thanks in advance

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 7 месяцев назад

      No worries - I've updated the description! It's cool isn't it?

  • @marcinstaszkiewicz1574
    @marcinstaszkiewicz1574 7 месяцев назад

    Dear Professor, can we expect to receive the first part of the lesson? I am absolutely ecstatic about all the lectures and courses you share with us. Best regards and thank you for your work!

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 7 месяцев назад

      Thank you for your kind words and I'm glad you are finding the material useful! There will be a lot of material appearing on the channel in the coming weeks!

  • @RichardWilliamLawson
    @RichardWilliamLawson 7 месяцев назад

    Neat topic for a regular human who uses these products erryday of our lives! I’m gonna go watch ur first episode, and please keep up these

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 7 месяцев назад

      Thank you!! I hope you enjoy and there's a lot more coming in the next few weeks

  • @busythato8577
    @busythato8577 7 месяцев назад

    I have seen videos of this derivation before nothing come close to this, simplified to the core. thank you, Dr. Bart,

  • @michaeltamajong2988
    @michaeltamajong2988 7 месяцев назад

    Great lectures.

  • @andrewmountianou2697
    @andrewmountianou2697 7 месяцев назад

    Great lesson! coming back to this video, I wanted to comment that it's very strange that the velocity on the wall is 0 but the shear rate on the wall is positive! What is the meaning of the shear rate on the wall if the fluid is "not moving" there?

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 7 месяцев назад

      Thank you for your feedback! Ah - now don't forget that velocity and the rate at which it changes are two different things! Consider, for a moment, where the velocity is maximum (for example in the centre of a pipe). The rate at which at which the velocity changes with position is exactly zero on that centreline. Now consider where the velocity falls to zero: the rate at which velocity has to change with respect to position to attain this is significant! Therefore, the shear rate at the wall is very much non-zero, as the shear rate is a measure of the *rate of change* of velocity, not the velocity itself. Remember too that (for a Newtonian fluid), the stress due to fluid motion is the viscosity * shear rate: it is the non-zero shear rate at the wall that gives rise to the stresses that are responsible for pressure drop!

    • @andrewmountianou2697
      @andrewmountianou2697 7 месяцев назад

      @@drbartsworldofchemeng thanks a lot for the detailed answer!

  • @andrewmountianou2697
    @andrewmountianou2697 7 месяцев назад

    very nice explanation as usual! This lesson is below part 5 in the playlist (I guess you want it above)

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 7 месяцев назад

      Many thanks for your positive feedback. It's appreciated :) And I'll alter that playlist - thank you for noticing :)

  • @andrewmountianou2697
    @andrewmountianou2697 7 месяцев назад

    Thanks for the very great lesson. Do you know by any chance where the ρθ part of the stress/shear rate can be found analytically? It's quite hard to prove it for me.

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 7 месяцев назад

      Hi Andrew - thank you for the feedback, it's appreciated. I don't quite understand your question though - which bit of the proof would you like a bit more insight on?

    • @andrewmountianou2697
      @andrewmountianou2697 7 месяцев назад

      @@drbartsworldofchemeng thanks a lot for the willingness to help! At 5:33 you present the rθ position of the shear rate tensor in cylindrical co-ordinates. Correctly (imo), you say that as an engineer you do not need to derive the term analytically but can look it up. I would like to know how it's derived because I could not get it using the divergence of the velocity + its transient. I looked up for 3 rheology/polymer processing books and all just use the same formula as you did from one of their appendices. None derived the term. My curiosity costed several hours of research, so if you have a source that derives the term I would be very fulfilled. Thanks in advance!

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 7 месяцев назад

      @@andrewmountianou2697 Sure - let me look out some resources. I'll get back to you in a day or two - if I don't, please remind me.

  • @andrewmountianou2697
    @andrewmountianou2697 8 месяцев назад

    Very helpful. I did the homework and it was impossible unless, I add an extra minus on the ΔP/L, but need to justify physically.

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 8 месяцев назад

      Yes, that's right. \partial p / \partial z = -\Delta P/ L. If you think about it, a positive \partial p / \partial z increases from left to right as that's the sign convention. But for the flow to be from left to right, the pressure needs to decrease from left to right!

  • @andrewmountianou2697
    @andrewmountianou2697 8 месяцев назад

    Very useful! Thanks a lot! Any chance you can share the mentioned notes with your YT viewers? Thanks in advance!

    • @drbartsworldofchemeng
      @drbartsworldofchemeng 8 месяцев назад

      A pleasure - and thank you for the feedback. I'm afraid I can't really share those notes as they're for a live uni course that folk subscribe to.