Understanding Aerodynamic Drag

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  • เผยแพร่เมื่อ 21 ธ.ค. 2024

ความคิดเห็น • 527

  • @tmmyvrctt11
    @tmmyvrctt11 3 ปีที่แล้ว +1164

    This video is more useful than whole semester fluid course

    • @naveenkondeti5494
      @naveenkondeti5494 3 ปีที่แล้ว +21

      True 😂😂👍.
      It's the conclusion of our complete semester

    • @og805kanker
      @og805kanker 3 ปีที่แล้ว +18

      That’s very unlikely 😂 what school do you go to

    • @a_s_3.o
      @a_s_3.o 3 ปีที่แล้ว +3

      Exactly yAr..itne knowledge ke liye daily class,uske bad bhi concept clear nhi ho pata

    • @arkitkabir6950
      @arkitkabir6950 3 ปีที่แล้ว +13

      @@a_s_3.o try prof Suman chakrobarty videos for fluid ( available in TH-cam). I have watched all of them. Really good to build elementary level concept.

    • @xinlulin6463
      @xinlulin6463 3 ปีที่แล้ว +1

      Thanks,I love this vedio

  • @rashedabuamoud7794
    @rashedabuamoud7794 3 ปีที่แล้ว +356

    Just finished my fluid mechanics course, this video sums everything up so elegantly. Love your videos!!!

    • @FormulaJuan75
      @FormulaJuan75 3 ปีที่แล้ว +1

      69 likes. Perfection 👌

    • @dantheman3022
      @dantheman3022 3 ปีที่แล้ว +1

      I failed that course 2 times in eng school 😂😂😂

  • @mallikarjunv5
    @mallikarjunv5 3 ปีที่แล้ว +125

    0:00 - 0:30. Introduction to Drag (What is drag ?)
    0:50 - 1:05. Why is drag an unwanted force ?
    1:30 - 2: 18 How is drag generated ? and formula for calculation of drag
    2:19 - 2:31 Components of Drag force (Pressure drag and Friction drag )
    2:32 - 3:19 Pressure drag in detail
    3:20 - 4:47 Flow separation in detail
    4:48 - 5:00 Why do golf balls have dimples?
    ( Dimples increase turbulence and hence reduce flow separation. Reduced flow separation means less "pressure drag" and so the ball travels large distance).
    5:01 - 7:15 Turbulence and its effects on Pressure drag and friction drag
    7:17 : 8:05 Ridges on shark skin as bio inspired solution to reduce friction drag.
    8:07 - 9:31 Effect of geometry and the orientation on Total drag.
    9:32 : 9 :51 Quantification of drag force through integral approach.
    9:52 Simplified formula for drag force.
    9:53 - 10:11 The drag coefficient and how it's calculated.
    10:22 - 10:36 The reference area (Emphasis on the selection of Area.)
    10:37-12 :25 Re Vs Cd and arriving at stokes law.
    12:26 -13:26 Arriving at terminal velocity of a sphere.
    13:29-13:53 Constructing a Viscometer (In breif).
    13:57-14:22 Components of drag forces of particular interest in aviation

    • @IAMDOGGGGG
      @IAMDOGGGGG 2 ปีที่แล้ว +2

      Thank you :D

  • @muhammadabdullah3467
    @muhammadabdullah3467 2 ปีที่แล้ว +37

    This video is essentially a summary of chap 9 in the fluid mechanics book by Munson. I love how this channel explains these important topics with such simplicity. Keep up the good work.

    • @Insomnia_tic
      @Insomnia_tic 10 หลายเดือนก่อน

      ….simplicity? 😨 high school physics student here haha

    • @muhammadabdullah3467
      @muhammadabdullah3467 9 หลายเดือนก่อน

      You'll eventually get it bro. Everything happens on its time.@@Insomnia_tic

  • @titorotod
    @titorotod 3 ปีที่แล้ว +37

    I got so excited to see this on the feed, I was long waiting for a video about this. I started working on computational fluid dynamics half a year ago and it took me a lot of time to learn the theory behind it. You make everything look so easy to understand, you truly are a gifted teacher. Cheers!

  • @TheEfficientEngineer
    @TheEfficientEngineer  3 ปีที่แล้ว +110

    I hope you enjoyed this look at aerodynamic drag! I'll be covering lift in the next video.
    ✈️
    You can get access to extended versions of this and other videos on Nebula - nebula.tv/videos/the-efficient-engineer-understanding-aerodynamic-drag-extended-version

    • @rohi7597
      @rohi7597 3 ปีที่แล้ว +1

      Hi sir, what software applications used for animation

    • @urp8916
      @urp8916 3 ปีที่แล้ว

      Thank you

    • @Bel...QWERTY1
      @Bel...QWERTY1 3 ปีที่แล้ว

      please ....why hydrostatic forces exist in fluids and even in gases???

    • @naveenkondeti5494
      @naveenkondeti5494 3 ปีที่แล้ว

      @@Bel...QWERTY1 due to the body force components ( eg :- due to gravity)
      Once go through the hydrostatic law in fluid mechanics for better clarity

    • @Bel...QWERTY1
      @Bel...QWERTY1 3 ปีที่แล้ว

      @@naveenkondeti5494 If it is due to gravity why or how it exists on vertical surfaces..??..i find it really hard to be understood im sorry

  • @shauryagupta4990
    @shauryagupta4990 3 ปีที่แล้ว +22

    Atlast ...... A video on drag, the way you explain concepts is really amazing..... Please keep uploading more and also more frequently

  • @aliptera
    @aliptera 3 ปีที่แล้ว +2

    The most intuitive and real physical explanation of all aerodynamic forces I can think of - is modification of static atmospheric pressure around an object due to air movement. Atmospheric pressure is defined by random bombardment of air molecules as per the kinetic theory of gases; this randomness is changed by the macroscopic air movement. As a result the pressure is modified around the object creating forces that we're labelling as drag and lift.

  • @berkdogu8150
    @berkdogu8150 3 ปีที่แล้ว +7

    The Efficient Engineer has actually encouraged us to prepare such videos because all videos in this channel are very descriptive and informative.

  • @stefanguiton
    @stefanguiton 3 ปีที่แล้ว +27

    another gem of a video, keep up the great work you do!

  • @Megadanne98
    @Megadanne98 3 ปีที่แล้ว +27

    This is not the first time you've managed to time your content with the same subjects I'm studying at the time , great video!

  • @NikitaKaminskyy
    @NikitaKaminskyy 3 ปีที่แล้ว +17

    As I said it many times, I wish someone explained me these concepts as well as you do back in the days!

  • @LJ7v
    @LJ7v 3 ปีที่แล้ว +9

    Clear, concise, straight to the point, great illustrations, please keep doing those ! Hi from France !

  • @alexanderunguez9633
    @alexanderunguez9633 3 ปีที่แล้ว +5

    I really enjoyed that you pointed out that pressure drag becomes more significant for blunt objects and friction drag becomes more significant for thin structures(and pipes I should add). This is something that isn't specifically mentioned in a lot of literature, but is an important intuition.

  • @mazenelgabalawy3966
    @mazenelgabalawy3966 3 ปีที่แล้ว +1

    These types of videos and people like you sir are the reason I still have hope I can truly understand what university professors poorly teach.

  • @magarinoskevin2063
    @magarinoskevin2063 3 ปีที่แล้ว +3

    Somehow you manage to cover the topics I'm coursing right now at Uni
    Truly a gem of a channel

  • @naveenkondeti5494
    @naveenkondeti5494 3 ปีที่แล้ว +10

    Wahh...!
    Solved many of my doubts regarding fluid mechanics in a single video. The best of best 👏👍.
    Engineers of our generation are blessed to have such sources.
    Thanks for providing such content and keep doing it.

  • @mosayed4792
    @mosayed4792 3 ปีที่แล้ว +5

    I was thinking about you from a while, I said to myself why didnt he uploaded something till the moment and here you are❤

  • @mohammedfawaaz693
    @mohammedfawaaz693 3 ปีที่แล้ว +1

    Mannnnn......why the hell do you explain so much gooooood.....you really explain clearly and hats off proud to the animation.....you the best

  • @ivansandoval946
    @ivansandoval946 3 ปีที่แล้ว +3

    Thanks mate, glad there're people like you making this kind of content! I really appreciate it!

  • @mlfb01ag
    @mlfb01ag 3 ปีที่แล้ว +1

    7:18 Shark skin
    8:05 Shape of body and angle of attack, plate
    9:08 Friction, pressure, and total drag on graph
    11:45 Stoke's Law

  • @kariossyr6018
    @kariossyr6018 3 ปีที่แล้ว +2

    Really great! It's so rare to find such simple analysis while being thoroughly! Keep it up. I really enjoyed your comprehensive language.

  • @gzizou_seif
    @gzizou_seif 3 ปีที่แล้ว +1

    This video is out just in time for my fluid mechanics course , thanx

    • @kytddjj
      @kytddjj 3 ปีที่แล้ว

      Hi :)

  • @abdelrahmanelnabawy7434
    @abdelrahmanelnabawy7434 3 ปีที่แล้ว +1

    bro your videos is significant worth the time

  • @elena6516
    @elena6516 3 ปีที่แล้ว +1

    One if the better explanations on this topic. Excellent work. Keep it up please!

  • @LeoLanzi
    @LeoLanzi 3 ปีที่แล้ว

    I study high school with mechanical technical in Brazil and my teacher shared your video to my class. Your videos are really good, keep doing that!!! Sorry if i made a mistake in english, i'm still learning. Peace!

  • @chankokkeong802
    @chankokkeong802 3 ปีที่แล้ว +9

    Fluid Mechanics
    All I learned from my previous study were solving maths problems only, my lecturer didn't explain the real examples such as golf ball, aeroplane wings, shark skin, etc
    and they are still getting high paid, Respect!!!
    That is why my country always poor, because they fail to educate and the cycle goes on.

    • @dougball328
      @dougball328 ปีที่แล้ว

      A fun application of the terminal velocity is using a ping pong ball to determine altitude. To see whose rocket goes the highest, you eject a ping pong ball and time how long it takes to get to the ground.

  • @qolbola_bilimuz4424
    @qolbola_bilimuz4424 3 ปีที่แล้ว

    brother, just watching the tutorial and thinking wow you put a good background music at such a level that helps the listener to concentrate many make it too loud to hear the speaker, great job.

  • @de0509
    @de0509 2 ปีที่แล้ว

    Studying engineering and then watching this video = mind blown
    Theres always that missing piece of a puzzle. And for the study of fluid dynamics, I have no idea if humanity will keep unlocking all the secrets of the universe regarding this. I remember from a professor that told that a lot of these constants are found experimentally. I wonder if someday humanity can fully understand how these things are to a point where experimentation wont even be needed

  • @michaelbabatunde3915
    @michaelbabatunde3915 3 ปีที่แล้ว

    I am short of words to thank you for clarity of your explanations.
    Thanks sir

  • @sohanherath4610
    @sohanherath4610 3 ปีที่แล้ว +8

    Brilliant just brilliant!

  • @LazieKat
    @LazieKat 3 ปีที่แล้ว

    We did a viscometer experiment in a fluid dynamics course, we understood, but this explanation makes more intuitive and harder to forget

  • @engineeringarts4509
    @engineeringarts4509 3 ปีที่แล้ว

    This video is very excellent - clearly highlighting all the key issues about drag, e.g. how adverse pressure gradient causes flow separation, how dimples on golf ball change boundary transition to delay flow separation and in turn reduce drag, etc. These are very important concepts!!!!

  • @andreasgrover8444
    @andreasgrover8444 3 ปีที่แล้ว +1

    This helped me and my science partner a LOT Thank You!

  • @AJ-et3vf
    @AJ-et3vf 3 ปีที่แล้ว +2

    Awesome, informative, and engaging video! Videos and channels like these will revolutionize education and learning for future engineers ❤️

  • @monishreddy1797
    @monishreddy1797 3 ปีที่แล้ว

    I watched this video more than five times completely, and each time I watch it, i understood this video better
    When i first watched it I had doubts like why turbulent flow delays boundary layer separation..why does flow separation cause dictate drag force..and how majestic is the graph at 11:44 I believe when I come back later, I would understand this video better.

  • @DigitalvideotoolsOrg
    @DigitalvideotoolsOrg 3 ปีที่แล้ว +1

    I am an aeronautical engineer. This video is spot on.

  • @chrisdalg89
    @chrisdalg89 3 ปีที่แล้ว +2

    Incredible way to explain so complicated concepts in a clear an intuitive way. Really good job!!! Subscribed for more content!!!!

  • @ratfor19
    @ratfor19 3 ปีที่แล้ว

    Never seen or found a video with this level of detail! It's so well explained, just amazing!! Congrats!!

  • @fateenahmed659
    @fateenahmed659 3 ปีที่แล้ว +2

    This video is so amazingly great. For anyone looking to dig deeper, a very good book is "Introduction to Flight - John Anderson". It explains the math as elegantly as this video does and covers a whole whole lot more.

    • @TheEfficientEngineer
      @TheEfficientEngineer  3 ปีที่แล้ว

      Thanks Fateen! I agree - Introduction to Flight is a great resource.

  • @amaarquadri
    @amaarquadri 3 ปีที่แล้ว +3

    Great video! I wish I had this at the start of my fluids course!

  • @asifraj321
    @asifraj321 ปีที่แล้ว

    Amazing tutorial 👍. Looks like whole fluid dynamics is discussed in single video. It Clears most of the doubt.

  • @kirbacilpezo
    @kirbacilpezo 3 ปีที่แล้ว

    You guys doing very good job man. A civil engineer I appreciate it.

  • @vishnuprabhu1722
    @vishnuprabhu1722 3 ปีที่แล้ว

    Great video! Filled with lot of information. Keep posting. We just enjoying your way of creating video.

  • @calculusguru1063
    @calculusguru1063 ปีที่แล้ว

    You are a legend well done efficient engineer brilliantly explained

  • @guillaumequerinjean218
    @guillaumequerinjean218 3 ปีที่แล้ว

    Took my fluids 1 exam yesterday. Damn, can wait to have fluids 2! Awesome content mate!

  • @rlshunt824
    @rlshunt824 3 ปีที่แล้ว

    This guy should have 1 M subscribers.

  • @myusername3689
    @myusername3689 2 ปีที่แล้ว

    Lift induced drag simplified: Downwash tilts lift vector slightly backwards, lift vector backwards means that the lift is not only pulling upwards at the aircraft, but also backwards, which mimics drag. Downwash is caused by the shape of the airfoil and also caused or amplified by vortices.

    • @dougball328
      @dougball328 ปีที่แล้ว

      Downwash is not caused by the shape of the airfoil. It is the result of the circulation generated to produce lift. L=rho* V*gamma) where gamma is the circulation strength.

  • @centaureacyanus7026
    @centaureacyanus7026 3 ปีที่แล้ว

    Incredibly well explained! I honestly can't say how grateful I am for your videos, which really help for my engineering studies. Thank you so much!

  • @ashrafulislam7021
    @ashrafulislam7021 3 ปีที่แล้ว

    I thought you have over 1 million subscribers. Your content quality is so awesome.

  • @Obi1-KenBone-Me
    @Obi1-KenBone-Me 2 ปีที่แล้ว

    this 16 minutes video was more helpfull then the 2 hours i spent trying to understand the drag chapter from the principles of flight manual

  • @A.Hisham86
    @A.Hisham86 2 ปีที่แล้ว

    Every time I watched your content, it feels like I assist a course of 1 hour! It's really long, but interesting content! :)

  • @ingGS
    @ingGS 3 ปีที่แล้ว +1

    You are the best, you are the absolute best.

  • @faaizansari6908
    @faaizansari6908 3 ปีที่แล้ว +4

    @ 6:25 it should be steeper in laminar than in turbulent boundary layer. By the way, cheers to your work man👍

    • @jishnuram5777
      @jishnuram5777 3 ปีที่แล้ว +1

      Yes i also think so pls correct me if i am wrong

    • @mecheazy5028
      @mecheazy5028 3 ปีที่แล้ว

      Yes!

    • @pedroferrer9436
      @pedroferrer9436 3 ปีที่แล้ว

      He is right because stress is proportional to dv/dy, so turbulent is steeper in reference to the y axis

    • @TheEfficientEngineer
      @TheEfficientEngineer  3 ปีที่แล้ว

      Yes Pedro is correct. By steepness I'm talking about how quickly the velocity changes as you move away from the surface. The change in velocity is more gradual for the laminar profile, and so the shear stress is lower.

    • @arkitkabir6950
      @arkitkabir6950 3 ปีที่แล้ว

      For turbulent flow although velocity gradient is high and flow is unsteady, when we take statistical average it generally provides uniform profile unlike laminar where it gradually increases. Hence above velocity profile is correct.

  • @deepeshyadav1303
    @deepeshyadav1303 3 ปีที่แล้ว

    I was looking for an answer for a project and here you are!

  • @sameerdesai9494
    @sameerdesai9494 3 ปีที่แล้ว

    cant thank enough for these videos of yours! Waiting for more

  • @dougball328
    @dougball328 ปีที่แล้ว

    I would recommend a brief explanation of Reynolds number. It is the ratio of the inertia forces to the viscous forces. A simple example is fill a coffee cup full of water. Very slowly tilt the cup. The water will run over the lip and down the side of the cup. This is because the viscous forces are keeping the water attached to the cup. No tilt the cup more until the water flows out of the cup and into a stream away from the cup. Now the inertia forces are dominate. Having said that, I found the video to be quite informative and accurate. (As an aerodynamicist I designed airplanes for nearly 40 years, mostly commercial but a few others tossed in for good measure and professional stimulation)

  • @redpheonix6307
    @redpheonix6307 3 ปีที่แล้ว

    i'd just say..... you ought to get more than 316k subs bro. good job and keep up.

  • @KrishnaCalling
    @KrishnaCalling 4 หลายเดือนก่อน

    Please continue series on aerodynamics ...your videos are just superb...i request you

  • @blackguardian89
    @blackguardian89 3 ปีที่แล้ว +1

    Another amazing video! Great work! Thank you!

  • @brunomartel4639
    @brunomartel4639 3 ปีที่แล้ว +1

    This is art

  • @RealityVision
    @RealityVision 3 ปีที่แล้ว +2

    Most memorable and happiest success is achieved when you do a work with much deeper and broader view, with sharper focus. Everyone succeed in life but that should be happier and sweeter to you and your environment 😁 have a nice day 😊🙏

  • @giovanniluddeni663
    @giovanniluddeni663 3 ปีที่แล้ว +1

    From what I've read, shark-like roughness won't be advantageous for planes but mostly for boats and similar bluffer bodies, since the most of the gain comes from moving the curve Cd/Re in a way that makes the Cd to fall in the critical pit (the lower pit in the plot). Planes are obviously surrounded by a fully turbulent flow, so this would not be possible. It's the reason why golf balls have bumps while smaller/bigger balls are flat. Very nice video!

    • @dougball328
      @dougball328 ปีที่แล้ว

      Riblets are another means of reducing turbulent friction drag. Riblets are microridges running in the direction of the local flow. The flow tends to sit on top of the ridges - the drag is reduced because the flow is not 'touching' the full wetted surface of the wehicle. As the video suggested, implementation is the issue - as well as how to maintain the integrity of the surface.

  • @ryan_christopher97
    @ryan_christopher97 3 ปีที่แล้ว

    Hey man, you're a legend and your videos are sensational! ❤️

  • @dresdenkiller
    @dresdenkiller 3 ปีที่แล้ว

    This video was anything but a drag!

  • @gaeb-hd4lf
    @gaeb-hd4lf 3 ปีที่แล้ว +1

    damn these animations are top notch

  • @jeemain9071
    @jeemain9071 3 ปีที่แล้ว

    No wonder why your video takes large time🤟🤟🤟🤟🤟

  • @Thierry080
    @Thierry080 3 ปีที่แล้ว

    Very nicely explained and animated, great job as always!

  • @santoshmaurya87
    @santoshmaurya87 3 ปีที่แล้ว +1

    Your all lectures are very useful for us thanks for making this video.🙏👍❤️

  • @gustavocortico1681
    @gustavocortico1681 3 ปีที่แล้ว

    My friend, I hope you are making money, because you deserve it.

  • @dougball328
    @dougball328 ปีที่แล้ว

    The Efficient Engineer alluded to asymmetric vortex shedding leading to instability but never went any further (at least not in this video) A good example of this is the baseball knuckleball. A pitcher throw the ball trying to not spin it. By not spinning, the laces do not trip the boundary layer. The flow separates somewhere on the ball and this sheds a vortex and causes a force imbalance. This shedding moves around the ball, the forces change and push in different directions, and thus the ball's flight path is erratic. The curve ball is just the opposite. The pitcher spins the ball rapidly so that the flow goes around one side more than the other. This produces a 'lift' (or sideforce) thus causing the ball to curve.

  • @russellchattaraj1217
    @russellchattaraj1217 3 ปีที่แล้ว

    Oh gosh how is so conceptually clear !

  • @smitboraniya6752
    @smitboraniya6752 3 ปีที่แล้ว

    I learned more than what I had learned in my fluid mechanics cource of mechanical engineering. And most importantly Many doubts of mine are cleared in this video.

  • @sriharsharevu4316
    @sriharsharevu4316 3 ปีที่แล้ว

    Wowwww....not only efficient but more output.

  • @ariabakhtiar7998
    @ariabakhtiar7998 3 ปีที่แล้ว

    You will go far. Thank you for helping me with static.

  • @Henry-tong
    @Henry-tong ปีที่แล้ว

    this video is amazing
    i've learned so much from this single video 😀

  • @Peter-nighthawk
    @Peter-nighthawk ปีที่แล้ว

    Thank you for the perfect job. Very well done!

  • @sudhidm3122
    @sudhidm3122 3 ปีที่แล้ว

    Most beautiful explanation on aerodynamics ever...👍🙏👌👌👌👌👌👌

  • @angelalexandrov2831
    @angelalexandrov2831 3 ปีที่แล้ว

    This is an amazing channel. Keep up the good work

  • @tacoclocker
    @tacoclocker 2 ปีที่แล้ว

    A lot of help for my biomechanics course

  • @safooh94
    @safooh94 3 ปีที่แล้ว

    As usual great content that is supplemented by stunning visuals 👍

  • @carlosrodriguezronchel2031
    @carlosrodriguezronchel2031 13 วันที่ผ่านมา

    This is brilliant! Congrats

  • @Innotutorial
    @Innotutorial 3 ปีที่แล้ว +1

    Brilliant Video as usual.👏👏 Always helpful, inspiring and motivational 🙌👏

  • @QMCESAR
    @QMCESAR 3 ปีที่แล้ว

    Excellent video. Thanks for the very well explained video.

  • @sachinsahani6117
    @sachinsahani6117 ปีที่แล้ว

    Amazing helped a lot to understand from scrach

  • @NeeXnBeatz
    @NeeXnBeatz 2 ปีที่แล้ว

    Man your work is just crazy, thanks a lot

  • @crustybasterd1352
    @crustybasterd1352 2 ปีที่แล้ว

    Amazing channel, so glad I found it!

  • @shafaqparveen5070
    @shafaqparveen5070 3 ปีที่แล้ว

    Really and informative video with clear concepts. Thanks

  • @christianh8636
    @christianh8636 7 หลายเดือนก่อน

    Very good explanation, thanks!

  • @uchia_yt8177
    @uchia_yt8177 ปีที่แล้ว

    What a legend man❤️
    Helped a lot

  • @NPRBEST
    @NPRBEST 3 ปีที่แล้ว

    You are revolutionizing education!! Keep it up! Thanks a lot

  • @MuhammadArslan-ne8fi
    @MuhammadArslan-ne8fi 3 ปีที่แล้ว

    The app is as Brilliant as this Channel.

  • @faizansultan8067
    @faizansultan8067 3 ปีที่แล้ว

    finally
    love you man
    please upload more videos on structural anlysis please

  • @excalibur2889
    @excalibur2889 3 ปีที่แล้ว

    Great work man .....
    It's my humble request plz plz upload videos more often

  • @andremunno2045
    @andremunno2045 3 ปีที่แล้ว

    your videos are astounding

  • @carmelpule8493
    @carmelpule8493 3 หลายเดือนก่อน

    If the wing is moving forwards in stationary air space, the drag is the force required to ACCELERATE forwards mass of air near the wing..
    If the air is moving in a wind tunnel with the wing stationary, the drag is the force required to DECELERATE the mass of air near the wing.
    ( parallel to the wing flight path)
    LIFT is created by ACCELERATING the air mass particles downwards ( orthogonal to the wing flight path) using compression effects below the wing and a partial vacuum effect above the wing.

  • @shreyashbhosalefc6330
    @shreyashbhosalefc6330 8 หลายเดือนก่อน

    Thankyou sir very helpful and I understood many thinks about it because of you 😀 😊

  • @aykikard
    @aykikard 3 ปีที่แล้ว +1

    UNBELIEVIBLE CONTENT, SO FUCKING GREAT OMG AAAAAAAAAAAAAAAAAAAAAAAA

  • @dweeder1453
    @dweeder1453 ปีที่แล้ว

    Really well explained

  • @wathsalahiruni646
    @wathsalahiruni646 6 หลายเดือนก่อน

    you explain these brilliant way❤ there are more complicated to understand lecture note😢