Why Does Fluid Pressure Decrease and Velocity Increase in a Tapering Pipe?
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- Опубліковано 7 лис 2022
- Bernoulli's Equation vs Newton's Laws in a Venturi
Often people (incorrectly) think that the decreasing diameter of a pipe correlates to a smaller volume and thus higher pressure. But the ideal gas law has no place in INCOMPRESSIBLE fluid flow.
Others try to explain the decrease in static pressure using Bernoulli's Principle, however, unless you have a VERY good handle on Bernoulli's, that is mostly a self supporting argument.
Back all the way up to Newton's 2nd Law to understand why there is a decrease in pressure in a pipe taper.
Fun fact. In 1965 the Wood brothers used a fuel holding tank with this design which allowed them to dump 58 gallons of fuel into the tank of Jim Clark's Indy car in 15 seconds, while everyone else took 45 seconds to a minute. Thereby helping him secure the 1965 Indy 500 victory.
Fluid pressure DOEN NOT REDUCE in a venturi.
It becomes directional.
Pressure only appears to decrease tangentially to the flow.
If you measure along the flow, pressure actually INCREASES in a venturi.
The overall pressure remains much the same.
R.
@@RalphEllis That is what static vs dynamic pressure means. In Bernoulli's Equation (shown in this video), static pressure + dynamic pressure is constant in a system. If there is an increase in dynamic pressure (what you are calling "directional" pressure) then there must be a corresponding decrease in static pressure (what you refer to as "tangentially to the flow".
How is that related to Bernoulli? Isn't the flow always the same because of continuity?
Venturi effect. Does not increase or decrease pressure. It only increases velocity much like placing your thumb over the water hose.
Thanks for that, never heard that before but that is cool
The explanation via Newton's 2nd law is a good one. However, what it clearly indicates, is that due to increasing velocity, there is necessarily a (positive to the right) acceleration, and therefore there must be a corresponding pressure gradient to explain this acceleration (to produce the necessary force). It does not state why the velocity (and hence acceleration) changed in the first place. That links you back to conservation of mass, or continuity.
So: Continuity explains why the velocity increases, and then via F= m(dv/dt) we can infer the necessity of a pressure gradient.
Well put!
YES, YES. However, that is STILL a deductive INFERENCE, NOT a cause and effect explanation. I give full detail 2 weeks after this comment (above).
@@Observ45er I am also unsatisfied with this video's answer. Feels like a chicken and egg scenario. I am interested in your answer, however I can't find it.
@@INTEGRALPHYSICS Are you working on a corrected version?
@@rever4217from am intuitive mechanics perspective look at it this way.
The constricting pipe has water bouncing off it, these water molecules bounce backwards into the flow. Increasing the pressure of the oncoming flow.
This increased pressure results in a pressure gradient.
By the time the pipe becomes straight again there is no more water bouncing back increasing pressure, and thus the pressure remains steady (and net lower than all sections to the left as shown) but all the water now has a higher velocity due to the previous sections of pipe having accelerated it due to the pressure gradient.
To think about this question intuitively, the pressure will stack up when water flows from a wide diameter to a smaller diameter. So the Pressure will be higher at the low-velocity part but remain unpressurized at the high-velocity part.
It's like pinching the soft water hose will let the water spray further. When doing so you will feel the force to pinch the hose, which will lead to pressurizing the original water flow.
The video made me understand it. Your explanation made me GET it.
I think there's something to do with the difference b/n STATIC and DYNAMIC pressure. You're example helped me understand something about "pressurized" because I was always taught that a resistance to flow (ie, smaller diameter pipe or something) INCREASES pressure
I have some googling to do lol
Good point 👌
What about pressure in 2 different pipes of different diameters originating from same source. Or when we introduce pressurized air to water is it only the velocity gain or also the pressure gain.
I came here looking for a scientific reasoning to a magical ability im writing and I learned alot more then I thought I would lol.
oh crap magical pressure regions, it's Stormlight Archive all over again!
I really don't know why nobody ever explains it like this, love it!!
Thanks!
@@INTEGRALPHYSICS hey, what is still confusing me is the pipe diameter and pressure. Won't the smaller pipe have greater pressure as water flows through?
Outstanding. One step further would be to realize that it’s not the fluid going from slow to fast that causes the pressure to fall, but rather that the pressure difference accelerates the fluid from slow to fast. Same thing, but more clarity.
I could be wrong, but...
I don't buy that explanation for the phenomenon: it seems circular. If I accept that explanation then I have to ask why the pressure difference exists in the first place. We appear to have a cause and effect problem: did the pressure difference cause the change on velocity, or did the change in velocity cause the pressure difference? Put another way, just because the equation balances doesn't tell us cause and effect. I see it that the most fundamental fact is energy conservation. The facts are as follows: 1) the fluid isn't compressible; 2) the mass flow past any point in the pipe must be the same as the mass flow past any other point (before or after the taper); 3) the energy flow past any two points must also be equal. So if the cross sectional area after the taper is smaller then the velocity simply must be higher. For any molecule, therefore, energy conservation mandates that if velocity increases then pressure must drop. Newton's Second Law allows the equation to balance, yes, because it too relies on energy conservation, but it does not explain WHY the phenomenon occurs. This is a problem with math - or rather the misuse of math. The math doesn't incorporate the sequence, the process. It is a language for expressing the activity around the phenomenon, yes, but it doesn't explain the phenomenon in terms of cause & effect.
@@julianopificius6910 agreed, the maths simply explains how it works in terms of energy and stuff like that. But there is a deeper fundamental physical explanation that is missing. F=ma and all other rules like that are observations to transcribe what we see, they don't actually explain why and how a specific mechanism works
This may be right or wrong but, imagine a pipe 3 water molecules wide, which then converges into a pipe which is one molecule wide. There is pressure in the system as we know, so the water in the wider part is being forced into the thinner part. All of a sudden, 3 molecules which could stand side by side are now forced into a pipe too narrow, so they have to queue up behind each other in a line. This basically thins and elongates the flow of water, and because the 1 molecule wide flow cant extend backwards into the 3 molecule wide section, it has to move forwards faster. Imagine squeezing toothpaste out of a tube, you may move your fingers a little but a greater length of toothpaste will come out than how much you displaced your fingers, because its being extruded through a narrower section. So basically, the narrowing of the tube squeezes the molecules towards the centre of the pipe. This causes them to spread out lengthways, which is where the mass flow rate is maintained. The reason why they dont spread out backwards and only extend forwards, is because the pressure from the water behind is forcing them to only travel one way
@@julianopificius6910 I've got the same issue as you, which I made a post about as its own post; and only then, I saw this.
@@julianopificius6910 YES! YES! YES! YES! YES! YES!
Did I say YES!!!
Equations NEVER show / explain cause and effect!.
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I have a full, corrected explanation 2 weeks after yours (above), but in short:
The walls decreasing in diameter is a restriction that RAISES the pressure in the LEFT section AND up stream.!. The right section is like a hole in a pressure tank partly relieving the pressure.
There is a conversion of some dynamic pressure to static pressure at the sloping wall that is 'communicated up-stream [that is a characteristic of fluids to communicate pressures gradually away from a new pressure region - Pressure Gradient.
It is JUST LIKE the small nozzle on a garden hose shooting farther. Here is a demo showing it being measured:
*ua-cam.com/video/hZ5fZ3K4_mE/v-deo.html*
@@nade5557you just explained this whole video for me😂. I'm sitting here thinking he didn't explain why necessarily just proved that it does. (At least to me anyway as I am not fluent in the language of maths) Your explanation is the why this does what it does. If there wasn't a drop in pressure, backflow could or would occur. Thank you for this, my scalp was getting sore from scratching my head😂
that was nice from you. that is what I got from you" imagine if you and your friend pushing an object to each other. Now the stronger one will push the object to the weak one" . Now just substitute your self with pressure. if the pressure on narrow side of the pipe was higher that particle wouldn't have moved to the narrow side
I wish my physics and hydraulics profs had explained this in so much depth. Brilliant!
It finally clicked for me! Thanks a lot :)
Worth mentioning is another (wrong-ish) explanation that the increase in velocity decreases random motion, thus decreasing the pressure exerted on the pipe. However, Bernolli's principle only applies in streamline flow, i.e. no random motion.
Thanks!
Right! Many people try to find a reason for the reduced pressure by thinking of the molecule vibration and always make wrong assumptions. It is common to assume that the random motion decreases toward the surface and increases down stream making it no longer random about a center in all directions - bad assumption.
All the physics and all Engineering can be trace back to the 3 laws of Newton and the 3 laws of Thermodynamics
It is so nice to see someone able to apply the fundamental principles that so many others pass right by. . . . . However . . . .
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That said. you have a few rough spots there. You are SO CLOSE, but still missed something important. Marked thus below if you can't wait ******
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Yes, at time 1:27, using only Bernoulli's Equation is a c--p answer. It only says WHAT happens, but NOT why [[however, I show here that you do the SAME THING below [deductive reasoning] yet call THAT [below] "the" explanation.
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First, at time 2:18. The work MUST come from the Pressure Gradient.
{Are you familiar with that common fluids term? It is a difference in pressure between two locations}
A net force IS REQUIRED to accelerate the mass. You can't get around that first principle. That is something that CLEARLY explains a cause and effect -- it tells us the WHY there is acceleration.
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Side issue: Unfortunately, you say that it is the same as the "explanation" from Bernoulli's equation ... BUT ... Bernoulli's Equation does _NOT_ "explain" anything. It only shows _WHAT_ happens [and how much], but not WHY!.
In fact you even say: "Remember, Bernoulli's Equation is derived from the work-Energy Theorem." Therefore the B-Equation is not a fundamental law of physics; the energy stuff is.
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Back to the main topic:
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Your talk about Newton's Second Law at 2:45 to 4:50 is spot on. [[This actually just repeats the part about your 'work' talk at 2:18]]
Namely a force is the _CAUSE_ of acceleration [of a mass] of the fluid. That is an real explanation! [[Actually, the First Law is the one that tells us that a force causes acceleration, but your path is ok too - except that equation also does not tell us that force CAUSES acceleration - deductive reasoning. It just verifies that it agrees with Newton.]]
.However, you have NOT explained WHY that Pressure Gradient occurs - ONLY that it must be present [because we see some acceleration --> there must be a force]. Deductive reasoning, but not an explanation of the physics cause and effect. . .
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So ^WHY does the Pressure Gradient occur?* What is the CAUSE of this EFFECT.??.
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First, people are fooled into focusing on the static pressure decrease on the right, instead of the higher pressure on the left.
[[You appear to understand that you are talking about what is commonly called "Static Pressure"]]
For starters:
You totally missed the lesson of the finger over the garden hose demonstration.
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Do you see? When you say: "If we see B , then there 'must be' an A; this deductive, not a definitive cause-effect explanation.
SO. . . All you've done is shown with the various "physics laws" is that the pressure decreases, but still NOT WHY it decreases.
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BTW: At time 2:35 there is nothing to click to see the Work-Energy explanation.
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****** So, here is THE _why_ EXPLANATION: ******
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The lower static pressure on the right is NOT the result.
The higher pressure on the left is a result!.
Here is the CAUSE of that INCREASED pressure and, THEREFORE, the cause of the Pressure Gradient:
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The diameter decrease is a restriction of the flow. THAT CAUSES a pressure INCREASE on the left section.!.
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HOW a.k.a. WHY?
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Fluid approaching the pipe walls as they narrow, increases the pressure on that section of wall. Fluid moving toward a wall is the cause of an increased pressure against the wall. Just like a wind increases pressure on any surface it approaches - blows against. We easily feel this when wind blows on us. If a surface stops the flow we have stagnation and ALL the kinetic energy [dynamic pressure] is converted to Potential energy: a.k.a. "stagnation Pressure".
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But we have sloping walls with fluid approaching them, so only some of the kinetic energy is converted to potential energy - static pressure. This is an increase in the pressure ON the sloping wall. This pressure "communicates" inward and UP-stream into the large section, thus INCREASING the pressure there.
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To prove this, we can simply observe that if we add a narrow section [a small nozzle \to a garden hose the water shoots farther. There is a smaller cross section and, therefore less water, BUT had the pressure NOT changed, it would shoot the same distance. In other words Newton--> less water, same pressure -->less mass --> smaller area=less force, THERFORE same acceleration. SO: Proof the pressure increased upstream IN the hose by the addition of the smaller diameter.
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The analogy is that the left hand section is like a pressurized tank and the narrow section is a hole letting the pressure out. . .
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Here is a video showing the manometer-MEASURED pressure increasing upstream when a restricting nozzle is added [the garden hose demo]:
ua-cam.com/video/hZ5fZ3K4_mE/v-deo.html
This is the most well thought out comment I have ever seen on UA-cam. Spot on. Thank you.
@@INTEGRALPHYSICS I got some error and YT won't let me post more..?..
cant lie, that ellipse ruler seems so freakin' useful, i might get one
This explanation is actually very useful to understand physiology and blood pressure. There is a lot of tapering in blood vessels... Thanks!
Even most engineers i know cant explain this concept as well as u have done. Thank you
That's because their job is to use it, not explain it; They're two different things.
...and thanks!
Rotate it 90 degrees clockwise. Now we have a better intuition of pressure because of gravity. The key is "what is ahead?" The molecules at the top part (wide) are almost stuck since they have a small sink at the bottom, so they are pressing the walls. On the other hand, the molecules in the lower part (narrow) are almost free, because they have nothing ahead (below), so they are almost not pressing the walls.
No, this example is poor, because changing the height of the fluid ALSO changes the pressure in the fluid.
A vertical pipe has increased pressure as the depth increases adding confusion into the mix.
@@meateawthe example I propose is an open tube on both sides, like a funnel. The pressure only comes from gravity
The easiest way to explain it is by looking at what changes when the pipe gets narrower. The point where the pipe becomes narrower causes water molecules to impact the wall of the pipe at an angle, which will deflect the molecules to the middle. This will increase the pressure in the middle of the pipe. Higher pressure in the middle effectively funnels water molecules into the narrow pipe. Another way to think of it: "Take 3 marbles, and line them up next to each other. Sqeeze the 2 marbles at the end and see what happens to the middle one. It is flung outwards.
Thank you for this clear answer !
It was not intuitive for me but after I saw the video I feel like it's intuitive :
It's logic that the fluid goes to a place where there is some resistance of the flow which generates an increase of pressure, and when it passes this place, there is no resistance anymore so the fluid is less under pressure.
Hence why I don't eat taco bell...
Clever explanation. Better than I got in school 😊
Great video, and I want to thank you for explanation in such way. This is the first time, since couple of years, that honestly I finally understand this case. I always felt at the back of my head, that it was not clear for me. Now it is.
I’m a practical tool and die designer and I build machine tools.. really enjoyed that which I already knew but just couldn’t explain it. “Work” is a concept many don’t understand. “Work” hardening is also another concept many can’t fathom. Unrelated here but then again aren’t they ?? Thank you.. I just subscribed.. Encore!!!
The SR-71's engines ( P&W J-58's ) are a perfect example of this theory in action ...plus it actually uses supersonic air and transforms it to high pressure sub-sonic air ...!
Thank you for the great explanation brother, I was in need of a quick brush up and luckily this video confirmed that I can retain SOME information. Just a heads up to anyone with epilepsy, just skip the the 11 second mark.
Bernoulli’s Principle may be just Newton’s Second Law, but it is not intuitively obvious. What would happen if we started with a flow where static pressure was constant throughout, but fluid necessarily accelerated into the constriction? We could not set this up physically, but it could be the initial condition of a computer simulation.
The answer is that the fluid would decompress in the constriction until Bernoulli’s Principle was re-established. Waves of decompression would travel at the speed of sound in the fluid both upstream and downstream. However, if the fluid is almost incompressible, then there is hardly any energy associated with the overpressure, so decompression is an insignificant process. In the resulting steady state after decompression, we can then fall back on the association between Bernoulli and Newton.
Yes, and it can be stated more generally that the momentum equation of the Navier Stokes equations, rho Du/Dt = - delta p + div tau + rho g is derived by (per unit volume) Newton's 2nd law. The density rho times the substantial or material derivative of the velocity vector u is the mass x du/dt = ma portion, and the pressure gradient and divergence of shear forces (tau) + gravitational force are the applied net force. Bernoulli's equation is a particular case of the Navier Stokes momentum equation and is therefore likewise derived via Newton.
One mistake that many do is to consider the velocity variation as the cause of a pressure variation, while it is the opposite. Indeed, a change in velocity means an acceleration, which means a force applied. Usually, in a fluid the "forces", so what can cause a velociry variation, are mainly relered to pressure, viscosity, gravity.
The same for the aerodynamic of a wing: the profile of the wing imposes the bend of the fluid lines (since the air cannot compenetrate the solid body of the wing), which causes the modification of the pressure around the wing itself, which determines the forces on the wing (lift and drag) and the change in fluid velocity around the wing. Babinsky gave a good explanation for aerodynamics in his paper "how wings work". Obviously the viscosity plays also an important role, keeping the streamlines attached to the wing body (otherwise they would simply deflect at the wing nose and then remaining straight instead of curving).
What I suggest for flows in simple pipes is always to solve the continuity eq and the momentum eq of the NS equations in their integral form. Help you visualize the physics of the problem.
i have watched so many videos on betnoullis principle but this does justice to it ...thank you
I don't think it's the same kind of pressure we are discussing here. There's static pressure and there's dynamic pressure. Static pressure is the pressure exerted on the walls of the pipe (what pressure gauges read). Dynamic pressure is the force at which a fluid is moving per the area of the pipe. When we take a closer look at the equation again we find that the dynamic pressure is a function of the flow velocity: the higher the velocity, the higher the dynamic pressure.
What I have personally experienced from my few years as a mechanical engineer in the oil and gas industry is that. When flow is stationary, readings on pressure gauges increase and are almost nearly the same irrespective of pipe diameter. But once there's movement, the smaller diameter pipe records a lower reading on a pressure gauge than that of the bigger one. This is because in the smaller pipe fluids move faster so there's less time for molecules to stay at point to be read by a pressure gauge. But in the bigger pipe flow velocity is lower therefore molecules stay longer at a point and hence are picked up by pressure gauges. If pressure gauges could be installed parallel at the centre of a pipe's diameter we will see that pressure gauges in a small pipe will read higher than a bigger pipe, because fluid will rush with more speed into the pressure gauge.
So the confusion is really about understanding static pressure and dynamic pressure. In a smaller pipe, static pressure is lower and dynamic pressure is higher due to a higher flow speed. But in a bigger pipe, static pressure is higher whilst dynamic pressure is lower due to a lower flow speed.
similar to a decrease in lanes on a freeway. before the decrease there are more lanes, the cars are moving very slow and all packed tightly together but after the decrease in lanes the cars are moving fast but also all spread out from each other
The way I see it intuitively, is that since the particles are accelerating during the taper, for any particle the one further is faster and the one behind is slower. That means by the time they reach the shorter pipe, they are more spaced out. The reverse is true for a outward taper. Same thing happens to cars in traffic!
Hey yes, I think intuitively, this makes more sense... we need to imagine that everything is flowing... and not just stationary stuck there... I think understanding that everything is flowing is the pivotal part of fluid dynamics as compared to simple newtonian motion understanding where bodies flow as a whole solid block... which is much more straight forward to visualise... If fluids are flowing, then pressure will build up and velocity within the fluid changes... personally, this is hard to intuitively grasp because my brain does not process both velocity flow and pressure distribution at the same time... Here's an explanation, because, once u block up the end and the fluid stops flowing, then the pressure throughout the pipe becomes equal, no matter the cross section..
I've been thinking about this a lot, and if you take it down to the molecular level, in air, the molecules are moving in all directions at one speed and when we say that the gas is really moving is that there are more molecules moving in one direction than another, but the individual speed of each molecule is still the same (or so I think) plus the pressure is nothing more than the number of times per second that the molecules hit a surface and how fast they hit it. And that complicates these mental experiments even more. 😅😅
A good representation of the fact is how we can use water jets to cut through solid steel in a matter of seconds.
@gabrielhacecosas, I like your explanation, but my head’s hurting trying to intuit the pressure in the next bit of pipe, if the narrow section was followed by pipe at the original diameter. It seems to me like it would drop further but the flow would slow but I think I’m mixing behaviour of a gas (cools as it expands) and liquids (less compressible). It’s got me thinking though, which is fun.
@@michaellinner7772 it's in the name i guess if i had to explain it to a kid or dumb it dowmn I'd say : water jet , meaning pressured water moving really reallly fast so it cuts through almsot anything 😂,like the dc comic flash 😂
i was wondering about this for so long and this video was the most reasonable one i find in the net but stil not completely convinced cuz realistic feeling convince me that pressure increase with the increase of velocity
Finally a video that helped in clearing the concept. Good work.
Thanks!
Just came up with this now. I think a good way to visualize it is a sand timer...when the sand hits the constriction, the sand packs together and there is high pressure with all the sand packed together and the sand is moving slowly. The sand that manages to pass through the constriction moves quickly as it drops and has few sand particles around it... low pressure.
As a hvac student theres a much simpler awnser for this. There is ALWAYS a pressure drop due to RESTRICTION. Restriction in a tapering pipe, restriction in a evaporator coil you name it
A simpler way to think of this: is because the taper creates resistance to the airflow, so therefore the system must exert higher pressure to maintain the air flow. Higher pressure requires more energy. More energy means more heat. This carries over to electrical resistance too.
yes - rarely is the requirement for an energy input mentioned...
That's almost close.
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Sounds like you have it, but to be sure:
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In this case, the narrowing of the pipe is a restriction (whether by a nozzle or finger). The fluid is, in effect, 'hitting' the inward-sloping wall, thus pushing more and increasing the pressure along the sloping wall, AND because pressure acts in all directions, this increases the pressure in the FAT section.
Now you can view the narrow section as an opening in the now pressurized fat section, letting fluid escape at a higher speed because the pressure there is lower there. It is the pressure difference ALONG the flow that Accelerates the fluid mass - This is Newton.
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So. . .
Using your view, it is the P and therefore the F in the fat section that has increased above that of the narrow section. This is a NET P in the direction of the narrow section.
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It is analogous to the narrow garden hose shooting farther. The narrowing causes the pressure inside the hose to increase. This makes it even higher above the atmosphere than it was, thus accelerating the water even more and shooting farther.
It is a difference in NET PRESSURE that Accelerates fluid toward the lower pressure. Newton in fluids.
See it in this demo:
ua-cam.com/video/hZ5fZ3K4_mE/v-deo.html
But what is the logic behind this decrease in pressure? Explain by logic not by equations, please. this is a request from me.
it's the same principle as a planes wing...the fluid (air) flow is faster over the top and therefore has less air pressure that the slower flow under the wing and thus gives it lift...
and if we look at it in terms of vectors, the faster you go in the horizontal direction, the less of an effect the vertical direction has...so the 'direction of flow' pressure will be greater than the vessel wall pressure...the faster it goes, the less wall pressure...
This is an accurate way to describe it for sure
Seeing that the pressure is only lower when the water is moving is a point. Ie static pressure would be equalised along the pipe but as soon as the end is opened the water has somewhere to go but cant continue to carry the extra force with is as now more water gets restricted by the funnel and as the water ahead of it is moving towards a lower energy state ie the pressure drops but the speed increases.
I was always more interested when the flow is in the opposite direction.
I, a lowly operator, could not convince the engineer at a plant I used to work at that pressure increases at an enlargement. He was not having it.
You should have explained the operation of a feedwater injector to him.
@@robertmurdock9750 never dealt with those but I know how a volute on a centrifugal pump works!
It's possiblle that he was unable to quantify "pressure" many people have difficulty with this.
As a plumber I explain this to apprentices like this
" what is the pressure of the water after it comes out of your shower head?"
They ponder this a bit and usually get it wrong ( it's 14.7psia if you are at sea level )
I then ask this question
"Would you rather have a shower with 1 gallon per minute ( gpm ) and 100 pound square inch ( psi IN the pipe feeding the head ) or 100 gpm and 1 psi?
The pressure is only there to get the medium to its point of use, after its out of the pipe it is at atmospheric pressure.
Velocity does play a role here but as mentioned FLoW is the thing you're after
@@MrDmadness Can you explain why a narrow nozzle results in higher force? That is, when a hose has a narrow nozzle, you feel the push-back or recoil force far more. Is it that once it exits the pipe it's back at atmospheric pressure but still has the velocity? Where is the "extra" force or energy in the equation coming from?
@@DiscoFang it results in a higher rate of flow, force is area x pressure. What youre feeling is the motion if the flowing water encountering a restriction. Essentully you are feeling water hammer.
Thanks for this video. I have realized that I was always wrong to think that the pressure in the smaller part of the pipe, was going to increase. Thinking to watering plants with a plastic pipe, if you put a finger partially closing the pipe you feel higher pressure. But isn’t so. It’s higher speed of the water.
That higher speed is more kinetic energy and it is converted to increased static pressure by the partial blockage. I give full details 7 days after this (above).
thank you for not just hand waving it to be due to Bernoulli's principle. Ive watched like adozen videos that discuss preasure etc. and ALL of them just say "due to Bernoulli's principle thing XYZ happens"
if this is only true for flow, then my answer is simple: the drop in pressure occurs faster than enough material can flow to maintain the pressure.
the permeability of the thin pipe is lower, even though the material flows through it at a higher speed.
of course, I mean this only in the case that the material flowing through has some compressibility, and thus the pressure release is not immediate.
and I have a feeling that the pressure release I mean is related to the speed of the wave propagation in the material. the faster the sound wave propagates in the material, the smaller the pressure difference between the tubes.
When I studied this years ago this very concept would annoy me to no end because of how unintuitive it can become if you think about it for a second in any other way than this.
Great video
In this case, the narrowing of the pipe is a restriction. The fluid is, in effect, 'hitting' the inward-sloping wall, thus pushing more and increasing the pressure along the sloping wall, AND because pressure acts in all directions, this increases the pressure in the FAT section.
Now you can view the narrow section as an opening in the now pressurized fat section, letting fluid escape at a higher speed because the pressure there is lower there. It is the pressure difference ALONG the flow that Accelerates the fluid mass - This is Newton.
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So. . .
Using your view, it is the P and therefore the F in the fat section that has increased above that of the narrow section. This is a NET P in the direction of the narrow section.
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It is analogous to the narrow garden hose shooting farther. The narrowing causes the pressure inside the hose to increase. This makes it even higher above the atmosphere than it was, thus accelerating the water even more and shooting farther.
It is a difference in NET PRESSURE that Accelerates fluid toward the lower pressure. Newton in fluids.
See it in this demo:
ua-cam.com/video/hZ5fZ3K4_mE/v-deo.html
Thank you for this amazing education! You are a god send. Wondered abiut this for years
Great intuitive explanation! Your graphics and handwriting is absolutely Formidable! Thank you!
Glad you think so!
THANKYOU HAVE BEEN LOOKING FOR THIS SINCE FOREVER
Yeah, I get this question a lot... I figured it would help someone out there in UA-cam land.
That's an absolutely fantastic explanation. Why did no one expalin it this way at uni? Thanks
Super Explanation. Thanks a ton!
If i had this kind of explanation in my fluid mechanics class, i would have aced all my exams 😅
Very well explained and something I used to deal with on a daily basis and within valves.
Thank you!
Why does pressure drop in the globe valve?
Thank you for this elegant explainer.
Glad it was helpful!
Pressure in pipe is momentum transfered by the fluid molecule with pipe wall normal to the direction of flow
As per continuity if area decrease to maintain same flow rate velocity has to increase in the direction of flow which means particle has resultant velocity more towards flow direction reducing the momentum sharing time aka impuse which means force exterted on pipe wall reduce which reduce the pressure
find the flow velocities v1.v2. v3 in the conduit shown in fig belw. the flow rate q is 800l/min and diameter d1.d2.d3. at section 1.2 and 3 are 50,60 and 100mm repectively
well pressure in Bernouli's equation enters like the scalar potential would enter in mechanical energy conservation for a particle, and since particles tend to move from higher potential to lower potential. Fluid elements also tend to move from higher pressure to lower pressure.
If the velocity on the left side is forced, then the taper part in the middle acts as resistance. Hence the pressure on the left side increases. Since the velocity is forced and remains unchanged, thr velocity on the right side of the taper must be higher
YES! That IS correct! The author is SO CLOSE to getting to the true explanation by focusing on fundamentals, but misses some important things. I posted a full comment on his errors just above this.
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In short, The walls decreasing in diameter is a restriction that RAISES the pressure in the LEFT section. The right section is like a hole in a pressure tank. Here it is measured:
*ua-cam.com/video/hZ5fZ3K4_mE/v-deo.html*
That makes a lot of sense, but could that be the whole explanation?
A thought experiment to illustrate my question (for which I sincerely don’t know the answer): Let’s imagine a long tube with a constant thickness along its length. It suffers a pressure p1 from the fried it is carrying. Now, let’s cut the first half and make it thicker, with a transition area. If we now measure the pressure in the second half of the tube (the one with the same thickness as before), would it still be p1?
@@AntonioReis640 if you mean the fluid in that pipe is stationary, the pressure on both sides would be equal. But if you increase the internal volume of the tube and don't add fluid to occupy that additional volume, I guess the pressure would decrease a bit. But, the pressure would be equal in the entire tube. In order to flow, there has to be a pressure difference. The flow direction will be from high pressure to low pressure
Gas and Fluid dynamics are pretty hard to grasp to me. I'm not educated on the subject so I can be fully wrong. My experience on the subject comes from me building a flow bench once. I had to calculate the air flow by measuring the pressure drop indicated by water column. I got the calculation from a book but in fact it applied Bernoulli's equation. I used the flowbench to test a cilinder head I ended up butchering, which ended the project =)
@@AntonioReis640 I'm sorry, but I am unable to understand your mechanical configuration is with "carrying fried" and what the diameters (not thickness) are and where you're measuring pressure. . .
@@what9418 Be careful because the _FLOW_ does not have to be from high-to-low pressure. *Acceleration* is in the direction from high to low pressure. A flow headed toward a higher pressure will be slowing a.k.a. deceleration or negative acceleration.
Newton applies.
Bernoulli make some assumptions, but using just purely Newtonian analysis can give you an intuitive understanding why. Nature is very thrifty, and she loves to conserve everything. In this case it's mass flow rate that needs to be conserved. Due to the conservation of mass flow rate (ρAv), the fluid accelerates as it enters the narrower section. According to Newton's Second Law, this acceleration is driven by a net force, which is related to the pressure difference between the wider and narrower sections. Newton's Third Law tells us that the forces exerted by the fluid particles on the pipe wall are reciprocated with equal and opposite forces. The average of these forces per unit area is what we measure as pressure. In the narrower section, less net force is needed to maintain the higher velocity, which leads to a corresponding decrease in pressure.
Newton got almost everything right ;) He was right about gravity at the macro scale, so we'll give him that. I prefer Leibniz's treatment of Calculus and I think that's what we are taught mostly in school. Leibniz is the one that came up with the symbol for integration (he modified the summation symbol), and he came up with the dy/dx notation we are all familiar with today. Plus he invented binary notation, and as a programmer I have to say that gives him an automatic lead ;)
I am currently learning the basics of electronics. I’ve heard my dad describe this with regard to current and voltage and amps. I definitely still don’t have the straight, but I have a feeling this explanation will go along way toward me making solid progress.
I have a plumbing and electrical ticket. They are very very similar
Plumbing has
1. Pressure
2. Flow
3. Friction
Electricity ( the flow of electrons through a conductor )
1. Voltage ( electrical pressure )
2. Amps ( flow of electrons )
3. Ohms ( resistance to flow )
The formulas are even basically the same for calculations.
Plumbing has valves, electrical has switches.
Both stop or regulate the flow of medium.
:)
@MrDmadness I agree. However, I'm confused by the fact that a reduction in wire size does not reduce voltage (pressure) as it does in a fluid. Although the current (flow) is reduced.
@@roberta.6399 wait, a reduction in wire cross area increases resistance, which does decrease voltage. This is why thin wires overheat, because current does not change. No?
@@roberta.6399 The more correct analogy is: Fluid pressure drop (for a given fluid distance displacement) is analogous to voltage drop per unit length of wire.
@@roberta.6399 Yes, it is a bad analogy. because the current is reduced in the WHOLE circuit, not just a thinner wire section.
Nice try, but it fails.
This is what I was looking for!!! Had my car's exhaust modified with a 2.5in axle back muffler, but the pipe leaking to it is stock (2.25in) as well as the end pipe on the exit side (2.25in)..... I was curious what effect on flow having it tapered both ends would have. It's basically 2.25 tapered to 2.5 back to 2.25.
What would be result whenever you do an aspiration/suction on the smaller pipe instead of injection fluid/gas through the larger pipe?
Very good video. In addition it might be worthwhile to watch Eugene Khutoryansky's great graphic explanation of the Bernoulli effect demonstrating what happens at an atomic or molecular scale.
ua-cam.com/video/TcMgkU3pFBY/v-deo.html
Another way to look at it is that in the wide part of the pipe, molecules are going in all different directions. The ones in the smaller part of the pipe are preferentially selected to be the ones going horizontally rather than upwards or downwards, because the ones going upwards or downwards hit the wall of the constriction of the pipe.
@@doublewhopper67 At a microscopic level, they're all bouncing off each other. Look up "brownian motion." If two particles hit, they'll rebound in different directions. There's an overall tendency more one way than the other, but certainly not all molecules are moving "forward" at any one time. If none of them were moving sideways, you wouldn't have any pressure on the pipe walls at all, right?
@@darrennew8211 i agree with you most. Your explanation is very accurate.👍
Bernoulli equation applied at 2 points along a streamline is a conservation of energy equation: total pressure stays conserved, so an increase in dynamic pressure means a decrease in static pressure. That’s a perfectly valid and non-crappy explanation.
Yes, but is is non specific as to WHY.
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In this case, the narrowing of the pipe is a restriction (whether by a nozzle or finger). The fluid is, in effect, 'hitting' the inward-sloping wall, thus pushing more and increasing the pressure along the sloping wall, AND because pressure acts in all directions, this increases the pressure in the FAT section.
Now you can view the narrow section as an opening in the now pressurized fat section, letting fluid escape at a higher speed because the pressure there is lower there. It is the pressure difference ALONG the flow that Accelerates the fluid mass - This is Newton.
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So. . .
Using your view, it is the P and therefore the F in the fat section that has increased above that of the narrow section. This is a NET P in the direction of the narrow section.
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It is analogous to the narrow garden hose shooting farther. The narrowing causes the pressure inside the hose to increase. This makes it even higher above the atmosphere than it was, thus accelerating the water even more and shooting farther.
It is a difference in NET PRESSURE that Accelerates fluid toward the lower pressure. Newton in fluids.
See it in this demo:
ua-cam.com/video/hZ5fZ3K4_mE/v-deo.html
@@Observ45er "The fluid is, in effect, 'hitting' the inward-sloping wall". Not so, the flow will always be parallel with the wall near the wall, and in fact has zero velocity at the wall (no-slip condition), so the flow is definitely not 'hitting' the wall. This is continuum mechanics, not a rarefied gas where you can treat the fluid like billiard balls and have to rely on statistical mechanics.
The WHY is explained simply by the fact that the flow obeys the Navier-Stokes equations, from which the Bernoulli explanation follows.
Analogies are of course useful and a great tool to explain some things, but real world physical phenomena don't always have to follow some simplified analogy.
@@frikkied2638 It appears I am unable to respond any more.
" I am quite the educator" made me LOL
Awesome explanation thank you!!!
Can you tie in the logic with pressure at each end driving the flow to begin with? Without a differential and flow there is no pressure change by diameter and I'm having a block trying to conceptualize.
I've always used the thought that "faster fluids have less time to put pressure on the same area as a slower moving fluid, thus, the static pressure is lower" as a mnemonic.
But that is just not correct. Pressure is the combined effect of particle collisions on a given surface. Those collisions 'i.e. the time they have to put pressure' is determined by the speed of sound in the fluid, it's completely independent of the flow velocity, especially for water.
@@Michallote If a mnemonic serves its purpose, you can't call it incorrect. A mnemonic is not the thing.
Really clear explanation. Kudos.🎉
Glad it was helpful!
Would that explain why the fluid would gain higher pressure if we put an enlarged pipe after that small one?
The pressure goes higher but the fluid would still flow forward.
I was wondering the same thing but I think going small pipe into large pipe your pressure would go down upon entering your larger pipe. I believe it has to do with the flow direction. An example traffic jam on two lanes suddenly hitting a 6 lane freeway, velocity could increase and pressure decrease.
Oh the velocity is used as kinetic energy to thst is converted into potencial energy that is used to pump the water trough smaller pipe so it slows down
What I’ve never understood is why once you get to choked flow, at M=1, to continue accelerating the flow you have to flare out the pipe, I get that density effects become important and so you’re conserving mass flow proper rather than volumetric flow, but why does the density drop faster than the area as you flare the pipe out (this must be the case or velocity would not change right?)?
Energy equations often have the advantage and elegance of not having to deal with the nitty gritty as Newton Second law. I appreciated the mental gymnastics you present, but even more the value of energy equations ;-)
You should try to use this for 2 stroke expansion pipes. It includes the speed of sound. And how the air flow pressure differences. Just and idea
You have excellent hand writing 🙃
liked a lot your explanation. its very intuitive!
Glad you liked it!
Wow very clean 👌
This might be the observation of an ignorant - but in the drawing shown above, the assumed flow is from left to right i.e., from the large diameter pipe to the small diameter pipe. This lets one argue that the pressure HAS to be lower in the small diameter pipe otherwise the fluid couldn't flow from left to right. If the flow is reversed i.e. the fluid flows from the small diameter pipe to the large diameter pipe what happens then? If the pressure situation remains the same then the fluid must flow from an area of low pressue to an area of higher pressure. What are the forces that provide the energy to allow this?
Helped a lot, thank you
You're welcome!
The "work energy theorem" comes from the Newton 2nd law (by integration) so the two explanations are equivalent.
So it mainly depends on how you're trained in physics (force or energy approach). Ideally, you've got to master the two approaches (and the link between them).
Very good and scientific analysis behind the Bernoulli equation. My visualization of it was that as the individual molecules accelerate, they create more distance between themselves, and if the change in velocity was great enough, the distance between particles will be greater than at atmospheric, thus the vacuum.
That isn't correct because water is constant density and with air, the pressure change is SO SMALL at these speeds, that the density change is irrelevantly small.
The pressure changes for this and flight are amazingly small and so is the density change of air.
What you and the author are missing is that the sloping sides as the diameter decreases is the cause of a pressure INCREASE in the fat section. That slope converts some dynamic pressure kinetic energy to static pressure in the wide section.
Think of that fluid running toward, or a glancing blow to the slope as if it ids a "partial" stagnation pressure.
@@Observ45er Well, fluids may not compress but they do still translate potential energy into kinetic energy both during compression and expansion as can be seen during cavitation. My idea was that even though there is no density change there is the "lack of propensity" to compress relative to the liquid towards the wider end of the tube, and if that situation were to be extrapolated, it would even translate into "less compression" than at atmospheric.
@@ChuddleBuggy I'm not following all of that.
RE: "they do still translate potential energy into kinetic energy"
Yes. As Euler showed, a Pressure Gradient [potential] is the cause of fluid acceleration [kinetic].
ok. An analogy is a compressed spring accelerating some mass.
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RE: "there is the "lack of propensity" to compress relative to the liquid towards the wider end "
If I understand this, it is a directional preference for pressure to act, but a fundamental property of fluids is the omni-directional property of pressure. So you are violating that first principle.
Also, if there is this 'resistance to compress', why would the pressure be higher? Isn't this 'lack' a resistance to an increase in pressure? That would prevent pressure from increasing, if true. . .no?
I'm not seeing the reasoning. But in any case, that's not it.
There are well-understood first principles that apply.
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I have a full comment explaining, but in short:
The sloping walls at the pipe narrows is a restriction for flow.
This surface with fluid moving toward it, is easily seen as a cause of increase in pressure in the wide section, on the left.
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This is no different than a wind blowing on us and we can directly feel the pressure increase. The decreasing diameter is a restriction that is the cause of increased pressure on the left.
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Focusing on the pressure decrease to the right is where people go astray.
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This is something we easily see in our every day, layman experience when we use the garden hose nozzle to shoot that long stream, or put a finger over the end to shoot it far.
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Here's a demo that clearly shows the pressure rise caused by a restriction, measured with a manometer. ua-cam.com/video/hZ5fZ3K4_mE/v-deo.html
@@Observ45er I understand the part where the pressure increases due to the increase in resistance down the line. That's intuitive enough. Where we might be misunderstanding each other is why the pressure after the constriction decreases even to the point of becoming less than atmospheric.
As i stated in my earlier comment about "translating potential energy into kinetic energy", what i meant is that even though the liquid may not have increased or decreased in density by an appreciable amount, the liquid will still have possessed the potential for creating an effect due pressure difference it would impose.
Another way to look at it would be that since the velocities of the flow between the wide are of the pipe and the narrow area then there must be a pressure difference between the 2. Of course, the flow volume would be the same, but the velocities would be vastly different, which would introduce the reasoning behind the increase in velocity as a response to the unity of the flow volume throughout the entire system, thus causing the analogy to become a bit more unwieldy.
At any rate, the miniscule change in density of the liquid as it passes the restriction into the narrower tube is in fact the reasoning upon which my analogy is based.
@@ChuddleBuggy I'd have to analyze that further, but your original comment is incorrect and I see no foundation for a tiny compressibility explaining r5he venturi's behavior.
How do we apply the same logic in reverse scenario in which the size increases?
I think that something is missing in the P=F/A explanation.
In that scenario: Continuity requires the fluid slow down. To slow down the fluid in the taper, there must be more pressure in front of the fluid than behind.
Because it has to.
Thank you for ur efforts ❤
It is in fact bernouli principal, ivs been a plumber my entire life. An increase in velocity causes a decrease in pressure, this is taught in 1st year. Something you're not equating properly is pipe wall friction, though newton's 2nd law does apply here. Break everything down to joules if you want to know where the friction losses are and how much is lost.
For easier understanding, since water has a mass, I imagine that the water is like a bubble gum that when you pinch one portion and stretch it out, it would be like going into the narrower pipe being stretch out and consequently with lesser weight, or lesser pressure.
Hi Guys, As this is on the topic can anyone advise the formula or provide the flow required the following. I have a tool in for a CNC lathe that has coolant through holes. In total there are 2 x 1MM dia holes and 2 x 2MM dia holes. All of which are fed from a large hole in the back of the tool. Can someone advise what flow rate would be required to maintain 1000PSI through all 4 of these holes simultaneously. Many thanks.
An even easier way to get the physical intuition of Bernoulli is the following:
1) put only one water molecule in the narrow section of the tube
2) acknowledge that the prime mover is gravity (assuming there is no water pump!, since many municipal water supplies get pressure from gravity acting on a huge, elevated water tower)
3) NOW PUT A RUBBER STOPPER AT THE RIGHT SIDE OF THE NARROW PART OF THE TUBE
Presto the pressure in the narrow tube section is the same as the large left side volume *_because of Newton's 3rd law_* as follows:
- gravity creates pressure in the large left volume, and it pushes rightward against the one water molecule in the narrow tube section
- the pressure coming from the large, left-side water volume pushes the single water molecule rightward,
- the rubber stopper feels that 'push' from the water molecule,
- the rubber stopper 'pushes back' leftward against the water molecule (Newton's 3rd Law)
- the water molecule now pushes (aka pressure!) with equal force:
a) against the rubber stopper on its right,
b) against the large volume of water on its left,
c) and AGAINST THE WALLS of the narrow part of the tube
equal pressure in all directions, OUTWARD, from the water molecule in the narrow tube section
4) NOW REMOVE THE RUBBER STOPPER
The water molecule in the narrow section of the tube has LOST Newton's 3rd law (the pushback from the rubber stopper) and can no longer exert equal pressure against the walls of the narrow tube section and the large, left-side volume of water
Although the water molecule does accelerate and attain velocity, THE ACTUAL REASON FOR THE PRESSURE DROP IN THE NARROW TUBE SECTION is the loss of Newton's 3rd Law pushback from the rubber stopper.
A) the water molecule can no longer exert pressure against the walls of the narrow tube it is in due to the loss of pushback force (Newton's 3rd Law) due to the missing rubber stopper
B) the water molecule moves rightward and is replaced by another water molecule that also cannot exert pressure against the walls of the narrow part of the tube
So there is a pressure drop in the narrow part of the tube.
CAREFULLY NOTE:
1) the left larger volume of pipe gets a PARTIAL Newton's 3rd Law pushback, leftward-directed, due to the TAPERING DOWN on its right end (the taper down to the narrow section of the tube), so it has higher pressure
2) the pressure in the narrow part of the tube can be made EQUAL to the pressure in the large, left-side volume by putting the rubber stopper at the right end of the narrow section of the tube. This re-asserts Newton's 3rd Law, because the rubber stopper pushes leftward against the water molecule in the narrow tube section
Bernoulli is a loss of "Equal and Opposite Reaction". The increase in velocity is SECONDARY. You have to blame the pressure drop against the walls of the narrow tube section - on the pressure drop caused by the missing rubber stopper.
Why is the velocity higher for the water in the narrow tube section? The physical intuition is F = ma. The mass "m" of the water in the narrow tube section is less than the mass of the water in the larger, left-side volume. The force from the large volume of water comes from gravity and does not change. So acceleration "a" must increase in the narrow tube section. To see this, mentally 'grow' the narrow tube section to the same size as the larger volume to the left. The force F is from gravity and does not change, and the velocity is the same in all parts of the tube
Simplistically, if you push on a large mass (say, a stalled car) with constant force Fc, then use the same force Fc on a wheelbarrow, does the wheelbarrow (the smaller mass) accelerate more than the stalled car? YES.
good explanations I haven't seen before, relating i back to newtons 2 nd law, but cant we go further modeling multiple particles to explain the increase in speed.
You’re trading the potential energy of the pressure in the fluid ahead of the nozzle for kinetic energy in the fluid after the nozzle. That’s what nozzles do. ;)
Superb! Congratulations! :)
wow just wow. What an explanation.
Bernoulli was an engineering condition, ranging from Steam Turbine numbers to meet conditional probabilities to daily carburetor replaced by fuel injection for momentum-obsessed.
Nicely done!
Thanks!
After all ,You did not say why the presser decreases either ! . You just proved this event .
Great explanation
Even in an expanding pipe (pipe expanding in flow direction), the force towards flow direction (larger section) must be greater for flow to be occurring. By this explanation, in that case pressure is lesser in the larger section?
Perfect presentataion. Thank you. raphael nyc
Very good!
Yo, this might sound weird, but what kind of pen are you using in this video? It looks so clean
Excellent sketch skills!
Thank you! Cheers!
Brilliant video. I learned alot. More importantly, what is that pen and where can I get it?
Micron Pens
May be a more intuitive or comprehensible way of saying what you said at 4:37 is; Since we know F1 is larger than F2, the pressure P1 would also be higher than P2. And since, P1 and F1 being larger than P2 and F2, the fluid accelerates from left to right from a lower velocity higher pressure to a higher velocity lower pressure region.
Also, may be another way to look at the Bernoulli's Equation is; since the dynamic pressure increases as the fluid gets higher velocity, it stores more kinetic energy into it. And, at the same time, due to having a higher acceleration, the fluid particles are more or less less static and thus have low static pressure. Correct me please, if I am wrong.
I always enjoy thinking through this problem because you can look at the problem from the perspectives of Bernoulli's, Energy or Force. Each way of thinking is reinforced by the other. IMO, in order to fully understand this problem you really need to be able to see it through the lens of all three.