Physics 34.1 Bernoulli's Equation & Flow in Pipes (11 of 38) Flow Continuity at a Junction
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- Опубликовано: 26 сен 2024
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In this video I will how the flow of continuity changes at a junction in a pipe in terms of velocity and area of the pipes.
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• Physics 34.1 Bernoull...
Took this humble man HOW LONG to draw all that up (edit the video takes, set up the space, prepare, etc etc)? For
Glad you liked it. 🙂
helped me with physics class, now currently helping me think out my irrigation system lol
it all comes full circle, love it
What is the professor name, his teaching style is adorable and easily understood.
I'm building my car exhaust pipes, and I was looking for something like this to be explained. Thank you for the information
Glad it helped.
Great video, simple and clear explanation!
What happen if P3 is to atmosphere and P2 continue in the pipe ?
Thank you ....well explained... Great videos Sir ...
Glad you liked them!
You state that the change in pressure is due to increased friction losses due to increased velocity but... Bernoulli's equations explicitly assume a frictionless pipe.
edit - I wrote the following because I missed the tiny half-second where he stated his assumption that pipes A2 and A3 are smaller than A1. In that case his statement about friction losses is correct, though still a bit misleading without also mentioning the additional pressure change predicted by Bernoulli's equations. Below is the rest of my original comment with some corrections.
Also, velocity is not guaranteed to increase. In your equation "A1V1 = A2V2 + A3V3" you can set V1 = V2 = V3 to drop out the velocity figure and produce the equation "A1 = A2 + A3" which demonstrates the necessary relation between the pipes to achieve constant velocity between the pipes. For instance if the two pipes have half the cross-sectional area. In this case Bernoulli's equations predict the same pressure in pipes 2 and 3 as in pipe 1.
Now, if all three pipes are the same size: "A1 = A2 = A3" then the pipe size can be dropped out to produce "V1 = V2 + V3" in which case V2 and V3 must have lower velocity than V1. In this case friction losses (which bernoulli is ignoring) would actually be less than in a single pipe of that size.
In real life there are always pressure losses due to friction. In Bernoulli's equation these are ignored and changes in pressure are only due to changes in height and changes in velocity.
@@MichelvanBiezen Agreed, I just wanted to clarify that even in the absence of friction the change in velocity must still be accompanied by a change in pressure. In many scenarios it is much more significant than the frictional loss.
I wanted to bring attention to the friction issue because I thought it highly likely that some incorrect implications made while talking of the y-bend would mislead some people that watched this
video.
Also, I admit that I also slightly incorrectly stated my case in my last paragraph. in my proposed scenario (all three pipes the same size) V2 and V3 will have smaller velocity than V1 and thus a higher pressure in the two right hand pipes. I will edit my original comment to fix that. Also, 'pressure due to velocity change' is a bad way to look at it. I'll change that too.
@@MichelvanBiezenThanks for taking that minute to reply, it led me to think about my own exact wording and assumptions and has improved my ability to conceptualize and explain these principles.
You obviously understand this well. Thanks for the excellent input.
Thanks for the nice explanation!
I have troubles to understand how you would write bernoulli's equation for the 3 pipe system? Would it be the same as you wrote it on the left side of the board, or would it become P1 +1/2 rho v1^2 + rho g h1 = P2 +1/2 rho v2^2 + rho g h2 + P3 +1/2 rho v3^2+ rho g h3?
Thanks a lot!
Very good,thanks
🇦🇺👍🏻
Glad you enjoyed it
@@MichelvanBiezen I am running 100 mm stormwater pipe from house (160 m2 roof catchment ) to the back yard into a number of French drain trench’s all level and linked together so as to slow any run of water to neighbours and mostly to put that good water into the ground.
Hence the research: at the end of the solid 100 mm pipe I want to T it 70% on way 30% the other and was worried about pressures,etc.
I am still working on it.1 mm of rain on 1 m2 =1 litre,10 mm =10 litres at 160 m2 and 10 mm of rain that is 1600 litres, say in 1 hour ( that the type of rain we have been getting ) , so dived by 60 sec is only 26 litres.not much hey.i think about 6 % of the pipes volume.
Interesting stuff .thanks Michel .
Ps.i live in Michel rd in Brisbane ,QLD, Australia 💧
Looks like a good way to determine that your pipe is big enough. Last year we had about a foot or rain in a couple of days and at times our drain pipes couldn't keep up and backed up all the way to the roof. (And we live in California). Welcome to the channel! 🙂
Thank you.
It’s raining here now.
👍🏻
Thank you Sir.
You are most welcome
How does the pressure change from the big pipe to the 2 smaller ones?
If the diameters are different then the velocity increases in the smaller branch and decreases in the larger branch. And therefore in the smaller branch the pressure drops and in the larger branch the pressure increases.
@@MichelvanBiezen there is 2 smaller branches and 1 bigger branch tho
thank you so much!!
Glad it helped!
How about water flow from a single into a T formation with A remaining constant in the T sections?
Velocity halved?
I'm okay with that. I need to move water to some trees at rear of yard while not overwatering grass.
Yes, we still need to add additional videos on that. When the flow goes into smaller tubes and velocity increases the pressure will decrease accordingly.
Given A1, A2, A3, and v1, "A1 v1 = A2 v2 + A3 v3" is 1 equation for 2 unknowns (v2 and v3). There must be a second equation to determine v2 and v3. What is that equation?
this is exactly my point.
How would this result change with a compressible fluid (air)? Would the decreased cross-section cause a higher pressure and cause less air to flow in the thinner pipe?
We just posted a video today that addresses that. (It was part of last year's JEE exam.)
Very intuitive to understand. Not a hard concept but can trip one up while solving a fluids problem😅
Glad it helped!
I'm just here for fun, I just want it to learn something new. I feel bad for those others who are stress out in learning this stuff. Best of luck in your exam
The trick is to remain relaxed going into a test. (and to be prepared before the test) But yes, it is much more fun not to have to study for a test, but just to enjoy learning and gaining understanding.
Am having exam after few mins and I was going to fail because of this
Thank you for saving my educational future
what if the two new pipes that come from a junction have the same area as the original, is the velocity halved ?
Yes. Essentially, you are doubling the area which will result in half the velocity.
@@MichelvanBiezen awesome, thank you so much
In the 3rd figure, will the angle between the two pipes and the main pipe affect the velocity?
Yes, the angle on the junction will make a difference. We haven't covered that yet in our videos. (something for the future).
U are awear by this
didn't catch if A1 = A2 + A3 in split diagram, if not, would pressure have to be included in the equation?
It would not. As long as the density remains constant, the equation is really just talking about conservation of mass. The amount of fluid going through A1 has the equal the sum of fluid going through A2 and A3.
Nice practice problem!
What if there was a 3rd outlet right at the junction (the corner turns into another junction)? How would that affect continuity?
Great video, thanks a lot! I just have one question:
If I understand it correctly even if I know A_1 and v_1 and also A_2 and A_3 I still have no way so know the velocities v_2 and v_3, I still need to measure at least one of those. Or is there a way to at least make a reasonable guess?
You can set up 2 equations to find the 2 unknowns. The second equation equates the fluid flow on both sides.
@@MichelvanBiezen wow, thank you for the fast answer, and making the effort to read your youtube comments!
Maybe I am completely stumped, but I thought the first equation equates the volume flows (Q = A*v and Q_1 = Q_2 + Q_3)? And that means that I have to measure the volume flow coming out of each pipe (or at least one pipe) to know the velocity and if I can't measure that and only know the volume flow going in (Q_1 = A_1 * v_1) and the areas A_2 and A_3 I have no way of actually knowing the velocities.
For example, if I have a pipe, that splits in 100 subpipes, where I know Q1 and all the areas (which are all different and don't sum up to A1) then I am screwed if I can't measure the volume flow of at least 99 of the pipes separately, because I can't assume that A_2*v_2 = A_3*v_2 = ... = A_100 * v_100 if the areas are different, or can I?
Tell me: I'm screwed, am I not? :)
@@sylviawaise7424 Maybe you can use Bernoulli equation. Please tell me if you have already answered this question.
@@alancuevasguzman2970 ruclips.net/video/gn4JMIwDzp8/видео.html
Thanks for the great video, I have a question. If you wanted to calculate the pressure at the end of the smaller pipes just before the fluid leaves them, how would you go about that? This in the case that hot water is being pumped through the large pipe inlet.
You would want to use Bernoulli's equation to find the pressure at any point in the pipe. It is dependent on the velocity, so once you have the velocity in the smaller pipe and a reference pressure you can determine that.
@@MichelvanBiezen Thank you very much Prof ♥️
Sir I have a question, what if it is reversed? A2V2 + A3V3 = A1V1? What I mean is, the flow is reversed, fluids are going into A2 and A3 and out to A1. How do you solve that problem?
Does it mean that if A2V2 has 20mL/hr going in and A3V3 has 125mL/hr going in, the total output mL/hr is 145mL/hr?
Would you please enlighten me regarding this problem. I have been trying to solve this for quite some time now and attempting to apply it in my work with IV pumps.
Hi, I need to know the answer as well, do you have any answer already?
@@kehhkhuantan2550 I've found the answer. Whatever goes in and however many, they all add up cumulatively. A + B = C, coversely C = A + B if they split into two directions; the resulting rates would be different depending on the area of the tube with constant input from C.
@@kehhkhuantan2550 ruclips.net/video/gn4JMIwDzp8/видео.html
@@FirstLast-uz4zz ruclips.net/video/gn4JMIwDzp8/видео.html
I have a question: in regards to a horizontally lying bifurcating pipe, how would fluid travel if there were a complete blockage of A2 (I assume V2 is 0 despite the A2 pipe still existing) further down the pipe at the right side of the diagram, while A3 remains fully open? Would fluid through A1 flow straight to A3 and leave "old" fluid stagnant in the dead end bifurcation, or would there be a constant small forward and backward flow of fluid throughout the A2 closed pipe?
l have questions can you help me
We try to answer questions when we can via these comments. (But we will be on travel soon and unable to get to a computer for a while).
How will the pressure P2 and P3 change compared to P1? Could you please explain?
Pressure decreases if the velocity increases. So it depends on the relative cross-sectional areas.
Michel van Biezen thank you for your valuable feedback.
Michel van Biezen can you please give me a resource to see how p2 & p3 relate to p1 mathematically?
If A1=A2=A3, how does P1, P2, P3 relate to each other? Velocity would decrease (indicating pressure might increase) but the the flow in each pipe is lower than initial (so total pressure might decrease). Or is it possible for P1=P2=P3? Just can't get my head around this. Really appreciate your explanation on this.
@@HasthaChithiran bernoulli's equation is only valid along streamlines, so p2 and p3 are essentially unrelated
well, maybe that would be more for the v^2 kinetic formula
How if A1=A2 and A2 > A3?
A1 = A2 since the diameter of the pipe doesn't change. I don't believe that there was an indication on the size comparison between A2 and A3. (Note that each example is independent of the other examples).
@@MichelvanBiezen can you help me to find references that can help me to solve this problem sir?
I have a problem to find the flow and pressure of a supply pipe (condensate water pipe) that has the same diameter as the discharge pump and flow and pressure of the recirculating pump that has almost 1/2 dimeter of supply pipe
Sorry, I can't point to a good reference. (and we haven't covered that yet).
@@MichelvanBiezen ok, thank you sir
Great video sir,
Need one help in the third scenario
If A1=A2=A3, H1=H2=H3 and if A3 line is closed at an X mtr distance. What will be the effect of flow caused when fluid flows from A1 to A2. Will there be turbulence created at the intersection causing reduced flow rate and pressure.
If A3 is closed off, then the transition from A1 to A2 would have a sudden diameter transition, which would cause some turbulence. (we ignore turbulence in these simple examples). The flow rate will remain the same in both A1 and A2, but the speed in A2 would be greater and the pressure in A2 would be smaller.
help me
oil flows through a 4.0 cm i.d. pipe at an average speed of 2.5 m/s. find the flow in m3/s and cm3/s
dV/dt = Av (the flow rate = cross sectional area x velocity ) = (pi) R^2 v = (pi) (0.02m)^2 (2.5 m/sec) = 3.14 x 10^-3 m^3/sec = 3140 cm^3/sec
Sir u are very panchual on utube aap real analysis aur linear algebra for IIT jee karao
Engineering Fluid Mechanics I
Sorry sir iitjam course u should upload on utube
Physics Wallah 😂🤟🤟😎
ruclips.net/video/gn4JMIwDzp8/видео.html
I think at 1:30 you explained it thanks man!!
U are awear by this
but how do we calculate V2 and V3 if either is unknown??
By using the equation: A1v1 = A2v2 + A3v3
@@MichelvanBiezen thank you for your reply. what I meant was for instance, to get V2, one need to know V3 and vise versa. what if v2 and v3 both are not given?
If v1 is known and the cross-sectional area of 1, 2, and 3 are known we should be able to determine v2 and v3.
@@MichelvanBiezen no, you cannot. you need two simultaneous equations to solve two variable. let alone a1v1=a2v2+a3v3 is not sufficient to determine v2 and v3 if both are unknown. is there another equation I should be considering as well?
@@walterharoldbishop @michelvanBiezen this comment is correct; are we to assume there is some addition relationship between V2 and V3, so that the sum of these two terms equals V1? I do not believe that is the case, please confirm. I am in support of another equation is required, currently too many unknowns.
does the total pressure at A1 equal to the total pressure at A2 and A3, assuming there's no friction force along the pipe?
No, the pressure is not additive like that. Use Bernoulli's equation where P1 + (1/2) (density) v1^2 + (density) g h1 = P2 + (1/2) (density) v2^2 + (density) g h2
For split up area, if v1 = 600cu./hr (diameter = 4") what will be the area for A2 so i get 189cu.m/hr?
ruclips.net/video/gn4JMIwDzp8/видео.html
Do you have a. Video on the exact opposite? Two smaller pipes joining into 1 and the best way to join them and how to figure the velocity in the larger pipe after the junction? And would be curious & helpful to know what happens if/as the angle of junction of the smaller paralell pipes increases? (Opposing force invreases. OR... is there a different/better/more efficient way to have two join into 1 that has the best end result for end velosity with least amount of energy/pressure waste (friction where they join) Thank you. If 1cwere made. I will point 1000"s of people in the aquarist community to this video. We are starving for this info.
Our plan is to put a comprehensive course together for fluid motion in pipes. We haven't been able to get to it yet.