Physics: Fluid Dynamics: Fluid Flow (1.6 of 7) Bernoulli's Equation Derived
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- Опубліковано 7 вер 2024
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In this video I will show you how to use Bernoulli's equation to find the pressure and velocity of a fluid in a pipe of various diameters.
Next video in this series can be seen at:
• Physics 34 Fluid Dyna...
Believe me I studied this topic in my civil Engineering graduation in 1983- 87, I felt that I am in my class room of subject Fluid Mechanics . Wonderful Sir , you are amazing .
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sir you have been there for me for at least 3 years now. amazing
I'm on military service so reviewing mechanics to prepare for going back to my school I appreciate your detailed explanation sir greetings from korea
Thank you for your military service. You should be able to find all the topics you need on this channel. All the best when you go back to school.
I just started watching your videos and I just wanted to say thank you so much. Your videos are the most helpful on youtube and I am so glad you have created this channel!
Wasn't taught any of this in university, thanks for the video!
Glad it was helpful!
Thank you so much. Your explanation is excellent. Excellent enough to make a 9th grader like me to understand such a complex thing.
These videos are really help me understand about bernoulli's equation. Your explanation is perfect. THANK YOU
This guy is serious stuff. I wish i could learn from him more with more depth
Such a simpler and more straight-forward derivation than those in most texts. Thanks!
Glad it was helpful!
Love this video... Watching all the way from Papua New Guinea...
Thank you. Welcome to the channel!
The initial configuration considers the fluid between left end of tube and beginning of the region of small length X2 . The final configuration has the same fluid between the end of region X1 and right end of tube. The total energy of the bulk of the fluid between both regions does not change during the time dt (= X1/v1=X2/v2) the fluid takes to enter region X2 and leave region X1.
The work done by the contact (fluid) forces f1 and f2 at both ends of the fluid during the motion is f1X1-f2X2.
The contact force of the tube on fluid is perpendicular to fluid and hence does no work on fluid. No friction forces either. The only other force that does work on fluid is gravity.
The change in PE of the fluid involves cancelling the PE of the bulk of the fluid between both of the regions at the ends of the tube.
That is why only the PE of both ends appears. Similarly for the change in KE, however you are assuming that the velocity of the fluid at any given point in the tube does not change with time.
thank you sir thank you so much. I can understand it clearly.now I can answer it in my semester exam once again thank you sir.
Beautifully explained. I love this video.
Glad you enjoyed it! 🙂
Thank you you're the reason I'm gonna pass my calculus journal
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I have a fluids exam tomorrow, it was a very clear explanation, thank you teacher, greetings from Turkey..
Glad you found our videos. Welcome to the channel and good luck on your exam tomorrow. 🙂
I watched this video for the second time and it was wonderful teaching. I learnt more rather than pervious time ❤❤❤❤
Going back and revisiting a topic a second time (and even a third and fourth time) definitely aids in the understanding. I often need to go back a few times before I get a complete understanding of a new topic. Glad it was helpful. 🙂
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I say thank you sir i helped in this videos and I conducted this chanel more others
I say thanks and go forward it .
Welcome to the channel! 🙂
Now I finally understood it! thank you!
Great!
This video and explanation is a joy to watch.
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great teacher of the decade
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Holy! i just started my second year at uni, and i think you cover basically every single one of my subjects (and also cover them a lot better than my professors do haha)
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I'm from Kenya. You're such a good teacher.
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Brilliant video, I have a test tomorrow and I've already seen 2 videos before this on how to derive it- this is hands down the best video to study Bernouli's equation from! Earned a subscriber.
Thank you. Glad you found our videos (there are almost 10,000). All the best on your test.
i wish i had the teachers as knowledgeable as you
Thank you for the compliment. 🙂
You are amazing professor! Watching your videos was like enlightenment from blurry knowledge I got from college 😅
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@@MichelvanBiezen I'm a flow and dynamics simulation practicioner now and had to recollect some concepts for my work. I'll be sure to hit subscribe and follow your videos. All the best!
ThankYou!
now i totally get this equation. thank you
You're welcome!
Pls teach more . You teach very patiently and that's amazing 👏
Glad you found our videos and that you liked it. 🙂 We have over 9000 videos on this channel covering most of physics, chemistry, mathamatics, and some engineering.
It helps me understand why volume in both side elemeneted, thank you sir.
Hello, this video is very informative, can you make example of computation of velocity for presurize pipe the submerge under the sea water using the bernoulis equation, the scenario the pipe is coming from the pipe and the last point of pipe submerge on the sea water and its open pipe at the las point, thanks for you positive reaponse
We do have plans on making more videos on fluid dynamics in the future, but currently we are working on a few other topics.
this is clear simple accurate. kudos
Thank you.
It's some Gangsta proof, thank you good sir
Glad you enjoyed the video! 🙂
Thank you so much ,sir.....God bless your talent.
Thank you. (We like the videos on your channel!) 🙂
Thank u Sir, your teachings are so simple to understand 👏👏
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Excellent... U explained pretty well...
Thanku...
#GodBlessYouSir
I do not understand. I understand that same amount of water should go in and go out but this drawing does not reflect that. I ask where are ends of tube? Should be 2 drawings as beginning of process and end of process. is this pipe part of greater system. What does it mean that water coming in to one end of pipe? What is initial state and final state? V1 is fluid coming in? Is it show that V1 came in and V2 have not yet come out??
Sir,
I thought that the expression "W = int p dV" was used for a moving frontier situation. While for a steady state, reversible process, with well defined inlet and outlet section the expression would be "W = int -V dp".
So the work balance between point 1 and 2 would be "W2 - W1" so both sides of the balancing equation would have the same syntax.
That's my doubt. Did I get it wrong?
By the way, THANKS A LOT for your effort in this channel!
Because v2>v1, momentum and energy increasing. So does it mean, conservation of momentum and energy is violated? From where comes extra energy?
Energy is conserved, which is the basis of the Bernoulli equation.
@@MichelvanBiezen do you have a video about it?
This video draws the parallel between energy and Bernoulli's principle.
what a beautiful presentation.
Glad you liked it
@@MichelvanBiezen I wrote the exact thing in the paper today with the utmost clarity. thank you so much for your help dude :))
Thank you so much sir, it was great. Very amazing, steps by steps. Excellent
Glad you liked the approach. 🙂
Thanks alot for the lecture. I now understand it perfectly 💯
Glad to hear that
oh, you've got a brilliant method to demonstrate bernoulli's equation "respect".
Thank you professor. How does this Bernoullis derivation (ie P+ρgh + 1/2ρv^2) compare with Energy and Head, (ie. Total Head (H) = P/ρg + v^2/2g + z). How do you derive this from the Bernoullis equation you derived? P/ρg(pressure head) + v^2/2g(velocity head) + z(potential head). The two equations seem very similar ie. P(work done)+ρgh(Potential Energy) + 1/2ρv^2(Kinetic Energy). The Bernoulli equation looks like it has been divided by ρg to get the equation for Total head where the constant has been replaced with H. What are the underlying reason for that, how does this relate to the Hydraulic grade line and Energy grade line?
Bernoulli's equation assumes no energy loss due to flow in pipes.
@@MichelvanBiezen thank you professor.
Thank you so much for this guidance professor!
You're very welcome! 🙂
Thank you so much, at least I understood
You are welcome!
Well explanation,sir!
Thank you.
Thanx for the lesson.. Really
You are welcome.
Great job 👏
Thank you! 😃
Good presentation...i understand Bernuoli's equation. Sir can you presnt how colebroke equation application on fluid pipe sizing
We still have to make the fluid dynamics videos we are planning to make in the future
4:45 I do not see how the work done on the tube of fluid due to the contact forces at either end, W_1-W_2, only involves the potential and kinetic energies of the small pieces of fluid at either end.
same here.
thanks, great content.
Glad you liked it! 🙂
instead of changing all Vs into ax it would have been easier to just change the two ax into V on the left side, otherwise great job, I really appreciate your work!
That was done for the purpose of illustrating where Bernoulli's equation came from
@@MichelvanBiezen yes, that was the overall goal but the last steps of your argument were structured in a sligthly awkward way. it would have been faster and more straight forward to change x1A1 and x2A2 into V1 and V2 instead of doing the reverse on the right hand side twice (you even had to speed up the vid). this would also make the last step easier because you were going to use V1=V2 anyway.
but I really don't want to nitpick too much, it was just an observation
Excellent sir
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Thank you sir ❤
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Thank you so much. You're a life saver
Great Lecture. Thank you
Glad it was helpful!
Thanks!
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Thanks very much i got it very well sir🤝🙏
Great! Glad you got the concept.
Thanks Sir.
Most welcome
Well explained sir 👏
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Amazing
Glad you think so.
thanks again and again sir.
How about work along point1 to point2
Not sure what you mean by "how about". Can you clarify what you would like to know?
Thank u sir
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Thank you
easy to understand
Thank you!
Great content sir
absolutely brilliant.
you are a god amongst men
No, no, not in the least. (Just ask my wife......) We are just glad we have the opportunity to make these videos.
thank you sir！Your explanation helped me to understand my presentation on this subtopic well! ;D And without further doubts im surely able to present this well!>w
Good luck on your presentation.
So basically it assumes you're comparing equal amounts of fluid and there are no losses of energy throughout the path of the fluid.
Yes, there are equal amounts of fluid and in this case no energy losses due to friction. We show energy loss in this playlist: PHYSICS 34.1 BERNOULLI'S EQUATION & FLOW
@@MichelvanBiezen oh, I have that playlist lined up already! Thanks for the reply, I love your work!
Sir, I studied Bernoulli's equation somewhere. The term "P" was written as static pressure, ½®v² was written as dynamic pressure and ®gh was written as hydrostatic pressure. I couldn't understand why P was written as static pressure. Can you please explain it sir?
A rose by any other name is still a rose. All three terms are terms of pressure. The (1/2) density x v^2 and density x g x h terms indicate how much the pressure changes due to the motion or height of the liquid.
@@MichelvanBiezen sir but what is the pressure P actually?
Inside any liquid there will always be pressure. You may want to watch the videos starting with this playlist: PHYSICS 33 FLUID STATICS
@@MichelvanBiezen Yes sir. That is hydrostatic pressure and increases linearly with depth. Is "P" in bernoulli's equation the same? I am confused because this relates to static fluid. But bernoulli's equation covers dynamics of fluid flow too.
What the actually force of flow formula?
Please help me sir.
ottimo
why the difference in the work done is equal to the change in KE and PE needs to be explained.
That is a concept that is learned in an earlier chapter: PHYSICS 8 WORK, ENERGY, AND POWER
@@MichelvanBiezen I can expect what will be there in the chapter: PHYSICS 8 WORK, ENERGY, AND POWER. Let me paraphrase my question, how can we talk about W1 and W2 rather than just W, as the elements of volume in question are connected.
Why can we take A out of the derivative ? Since it's not a constant
It is in that particular section. You are correct that if it wasn't you could not take A out of the integral.
@@MichelvanBiezen really grateful. You still replied to a very old video.
Thanks sir
sir tell me about venturimeter.please.
A venturimeter is able to measure the pressure of the fluid inside the tube which can indirectly measure the velocity of the fluid inside the tube, since the pressure adjusts accordingly.
thanks sir.can you tell me about the pitot tube.please
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Just like you did here.
In the words of the great Mike Tyson, fathinating
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