📹 Why Does Fluid Pressure Decrease and Velocity Increase in a Tapering Pipe?
Bernoulli’s Equation vs Newton’s Laws in a Venturi Often people (incorrectly) think that the decreasing diameter of a pipe …
What are the 3 reasons productivity increases?
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Key performance indicators, motivation, and physical wellness contribute to increased productivity. Employee engagement with work and employer is directly related to productivity. Managers and leaders should create a motivating environment to keep employees focused and engaged.
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The labor market has two extreme views on bosses and their impact on worker productivity. One view suggests they are irrelevant, while the other believes workers are indistinguishable and a firm’s output depends on their efficiency. However, a significant portion of resources is devoted to supervision, with front-line supervisors comprising 10 of the non-managerial workforce in manufacturing and 12 in retail trade. In The Value of Bosses, authors Edward Lazear, Kathryn Shaw, and Christopher Stanton found significant differences in productivity between the best and worst bosses.
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Professional development is vital for managers as it aids in providing constructive feedback, setting clear goals, managing time effectively, and developing strong problem-solving skills. It also showcases their leadership competency, keeps them updated with industry trends and legal obligations, and refines interpersonal skills. Prioritizing professional development ensures valuable employees stay with the organization, as employees tend to leave managers rather than companies.
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Productivity is crucial for long-term living standards and businesses, leading to higher wages, economic growth, profitability, and tax revenues. However, the UK’s slow labor productivity growth since 2008 is often referred to as the “productivity puzzle”. An interactive calculator can help businesses understand their productivity and compare it with other industries by requiring three pieces of information.
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📹 Two Minute Tutor Why does the Current Increase on a motor when the Load increases with Tom Kleinman
In this video you’ll see an explanation to why the current increases in a motor when the load increases. Its described the …
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.
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.
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.
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.
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.
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.
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?
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. 😅😅
U GUYS NEED TO SEE THIS I asked chat GPT: i understand that due to bernulis law, as fluid in pipe flow goes from a wide section of the pipe to a narrow section of the pipe, the velocity and kinetic energy increases and the pressure goes down, but intuitivly i am finding this hard to understand please explain on a simply logical practicle level (without using any equations) why it is that pressure will go down (surely as velocity of the fluid increases so would the pressure) – note: you might need to very simply explain basic science behind what pressure is defined as to answer this THIS is what it told me: ChatGPT Absolutely, let’s break it down in simple terms without equations. Understanding Pressure: Pressure is essentially the force applied over an area. Imagine you have a box with a lid. If you push down on the lid with your hand, you’re applying pressure. Now, if you shrink the area (maybe by pressing with just your fingertips instead of your whole hand), the force is concentrated over a smaller area, resulting in more pressure. Bernoulli’s Principle: Now, think about a fluid flowing through a pipe. When it goes from a wide section to a narrow section, the same amount of fluid has to pass through both areas because the flow must be continuous. So, if the pipe narrows, the fluid has to speed up to maintain that continuity. Fluid Movement: As the fluid accelerates, it gains kinetic energy—like a car accelerating on a highway. Now, here’s the key: the fluid molecules are moving faster, colliding with each other and with the walls of the pipe more frequently.
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!!!
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.
Just try to Google or look for high flow shower heads and all you will get are a huge bunch of recommendations that show you “high pressure” units which flow very little actual water. Worse yet, if you leave a comment such as this one, you’ll receive responses that only demonstrate how little most people know about the subject.
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!
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…
Thank you for this clear answer ! It was not intuitive for me but after I saw the article 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.
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.
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.
Thanks @INTEGRAL PHYSICS. Like @nozack5612 mentioned, the explanation through Newton’s second is good but still left me missing an understanding of why the nozzle creates the pressure/velocity change. To round it out I offer this explanation (after researching more and thinking this through). My aha moment relies on considering the following: 1) static pressure fundamentally is a measure the fluid particles change in momentum to a surface (think walls of a container or more commonly the cross sectional area of a shape), and 2) continuity of mass flowrates between point 1 and 2 and the relation to incompressibility (i.e. the average number of particles in a given volume cannot change). Try to ignore the physical nozzle and imagine a setup where steady, incompressible flow goes from a larger diameter pipe to a smaller diameter pipe–the same fluid, the same density, the same mass flowrate. Take a cross section of the larger diameter pipe, there are more particle collisions (high static pressure) there because there are more particles flowing through that cross section at an instant in time. Now in a cross section of the smaller diameter pipe, with the same flow (i.e. flowrate) there are less particle collisions (low static pressure) because there are less particles flowing through that cross section at an instant in time. And since there are less particles in the cross section, to match the same mass flowrate as in the larger section the velocity must increase (i.e. the particles have to move faster through the pipe, otherwise that would mean the density is changing somewhere in the pipe!
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 😉
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.
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
This really doesn’t explain why the pressure drops. It just says that because the fluid accelerates, we can deduce that the pressure must be lower. It has not yet identified the cause of that drop. It seems to me the only way for the pressure to drop is that there is less back pressure somewhere further down the pipe. It is that drop in pressure that allows the fluid to accelerate into the tapered part of the pipe. The work that is done is to accelerate the fluid. The source of that energy is the pump that is providing the high pressure fluid that is entering the pipe.
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
Thanks for this article. 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.
It is so nice to see someone able to apply the fundamental principles that so many others pass right by. . . . . However . . . . .. 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 **** . 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. .. 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. .. 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. . Back to the main topic: .. 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.
Nice explanation, but. I Think you fudged a little right at the end. In your last line bottom right, you have “A” for both P1 and P2. But P1 is under the left “High Pressure” gauge, and P2 is under the right “Low Pressure” gauge. The area of the first is A1, and the area of the second is A2, and A1 is NOT equal to A2. What you need here I believe are differentials at your “M” and then that needs to be integrated from P1 & A1 to P2 & A2. One gets the same answer, but then the maths are correct, which is necessary in physics.
Well … not good enough for me. This is the same kind of explanation as Bernoulli – “three must be power pressure if particle accelerates”. And does not explain why so happens. Simple dynamics says, when flowing particle hit wall in conical section – it creates force/pressure here. Rest must come from particle theory – but how?
If we consider the same example with a compressible fluid in subsonic regime, it is deduced that along the direction of motion in the converging section, the pressure decreases, the velocity increases, and the density decreases (the gas expands). If the gas expands, to maintain a constant mass flow rate, the compressible fluid must accelerate more than an incompressible fluid. Adopting exclusively the point of view of the second law of Newton (riding on my particle), I would like to understand where this extra acceleration that a compressible fluid has compared to an incompressible one comes from. It must necessarily derive from a greater pressure gradient that is probably related to the expansion, but how? All texts settle the matter by saying that the decrease in enthalpy corresponds to the increse inkinetic energy. Ok, from an energy point of view, it’s all clear. But from a Newtonian point of view and with respect to the net forces applied to the particle, what changes from a compressible fluid to an incompressible one? Thank you very much for your eventual answer.
Great visuals, thanks for sharing! Pressure is such a powerful force that can help explain lots of physical effects around us, and you do a great job explaining. We did a section on Bernoulli’s effect on air flight (Magic Levitation! youtu.be/0j2K5feCBWY), and will plan to revisit at some point with some of the great details you covered. Thanks again!
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.
Another good way to visualize this is that, if we look at the larger diameter hose; it will require more pressure to push the particle through the smaller diameter, thus after the pressure has increased to push the particle “smaller” then the pressure will decrease in the smaller hose due to “work” diverging to zero. Because work is being most performed when the hose diameter is changing. This is what I had gotten out of my Physics class haha.
You should explain it without using formulas at all: Without a greater pressure in the thick pipe, water wouldn’t move at all because the cone acts as a restriction. Restrictions tend to slow things down to a halt. Therefore if water is moving through it anyway, as with any restriction, pressure must be greater in the thick pipe. Or For the water to accelerate through the cone, caused by the narrowing of the pipe, it needs greater pressure on one end. So, since the water keeps flowing despite the acceleration, that needs a pressure difference to occur, pressure must be higher in the thick pipe. What you did was really just using different equation. A simpler one, yes, but not ultimately enlightening for people not good with numbers.
Going even deeper, how would Feynman explain the pressure drop based on the atomic theory? One of his most famous explanations is why liquid in a container gets cooler when the lid is removed. Most of us just say, “oh well it’s the latent heat of vaporization etc., etc. Feynman: “The fast ones leave”.
Looks like a circular argument to me. You are saying that the particle accelerates because there is a force difference due to the pressure difference, but then suggest that the pressure difference is due to the acceleration of the particle while suggesting that the conservation of energy explanation isn’t very satisfying. I find the conservation of energy explanation much more logical than the explanation presented here.
😂😂😂 People sometimes complicated things more than they should… When people have more info in their heads then they can handle they get lost and entanglemed in it 😂😂😂 …. Much simpler… Then the pressure always decreases as you go farther from the surce… There would be no flow otherwise 😂😂😂😂 you need a potential difference to get cinetic energy 😂 Why? … drag, friction between liquid and pipe and between layers of liquid (velocity is not constant across the section 🤷 highest in center lowers towards the edges)… So actually the total force decrease with the increase of distance from the sorce, because the friction ads up… The opposing force is at maximum at the end of the pipe… So p=F/A decrees the force and you have a pressure drop… Actually pressure drops all the way from source to the end of pipe. 🤷 Then, the source is pushing in the pipe a mass of liquid… The farder way the shorter the pipe renaming, means the mass is decreasing… F=m*a, a=x/t² and v=x/t =>x=v*t => F=m*x/t² => x=(F*t²)/m => v*t=(F*t²)/m => v=(F*t)/m so… When time constant…. If you decrees the force at the same rate you decrees the mass you have a constant velocity…. If you pay very good attention to the last formula, you can see that by reducing the mass would increase the speed even if the force is constant 😂 Newton’s laws work only in a fixed reference sistem (when mass, space and time are constants).
The way my brain intuits it is to think first of the particles that move from the larger area to the smaller area without any interaction with other particles on the way, then factor in every particle that interacts with the walls or other particles on the way, those particles impart energy of non parallel vectors before being inside the small area and therefore the remaining particles simply have more parallel vectors and on average must then be ‘faster’.
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.
“Cause” would include “why” it accelerates. You just accepted the presence of acceleration. Modern physics often replaces “why” with math analogies. Math doesn’t “cause” anything. I liked the article -my problem is with the WORLD, not you. This explains my point: “The wheels on the bus go round and round.” This song describes everything you see the bus do exactly like math does, but it is not an understanding of a bus, because the wheels going round are incidental, NOT CAUSAL. The variables in gravity are incidental, not causal. EVERYONE BELIEVES angular momentum causes the gyroscopic effect, BECAUES MATH SAYS SO. It is not true. AM is a pretend vector that only works AFTER THE RIGHT-HAND RULE! Watch my latest gyro explanation with new math that describes an acceleration vector field. Trained physicists WILL NOT see it, that’s why it’s not published. I will pay you to release me from this by proving mine wrong. Let me know if YOU can see “causality” after being taught something else.
Never a good idea for a physicist to say “incompressible” in block capitals! “The compressibility of water is a function of pressure and temperature. At 0 °C, at the limit of zero pressure, the compressibility is 5.1×10−10 Pa−1. At the zero-pressure limit, the compressibility reaches a minimum of 4.4×10−10 Pa−1 around 45 °C before increasing again with increasing temperature. As the pressure is increased, the compressibility decreases, being 3.9×10−10 Pa−1 at 0 °C and 100 megapascals (1,000 bar).” cf Wikipedia; R.A.; Millero, F.J.. “Compressibility of water as a function of temperature and pressure”. Journal of Chemical Physics. 59: 5529. But yes, it is so small water is virtually incompressible, but even so, we have to allow for that in hydrogeology for aquifer calculations .
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.
A pitot tube placed anywhere in your diagram will read the same everywhere. It is only the static pressure perpendicular to the flow that differs. The question remains, WHY does the static pressure drop when velocity goes up? I have an idea how it works. The particles spend less time in the higher speed area and so cannot exert as much pressure as they can when not moving. In addition the collisions they do have with the wall are at an oblique angle due to their speed and so less pressure is exerted. Imagine shooting a bb gun at the wall of a tank, it dumps all of its momentum into the wall but shoot the same bb gun at the walls of the inside of a tube and they just skip off keeping most their energy. —->o| vs —->o=====–>o Thoughts anyone?
Sorry but this is so dumb, you basically said: pressure is lower to the right because the fluid flows there, which is a circular explanation. Actually the other way around is the logical one: the fluid flows because it gets pushed by the higher pressure region to the lower pressure region. An explanation for pressure diffenrential can be that the inclined walls in the middle section are resisting the flow, pushing particles back and increasing the pressure (you can understand this better if you imagine a sudden decrease of the cross section area, where the walls are vertical). So it’s the pressure behind increasing more than the pressure in front decreasing. In my long hours of trying to understand things related to bernoulli and lift.. I came to the conclusion that the pressure differential IS the origin of the acceleration and has to be explained first. As to its explanation there’s no universal clue as to why pressure increases or decreases, you just look at the case you have and try to understand it at particle interaction level, that’s where the pressure comes from
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.
There’s exactly no difference between the reason that you offered vs all the other ones before it. They are all the same, and you used Newton’s equations to derive the formula’s involving kinetic energy. Maybe viewing it this way helps you, but I see nothing wrong with the 1st explanation you started with, they are not wrong.
This article doesn’t answer the real question. Why does the pressure decrease when the pipe is constricted? Intuitively, the pressure should increase. Given that the pressure is higher before the constriction, the explanation in terms of Newton’s second law is compelling. But that the pressure is higher before, and lower after, is precisely the source of confusion which is not directly addressed. What would occur if the pipe was widened by an increasing taper rather than constricted? Would pressure somehow *increase*? What would cause such an increase? Is the outcome the opposite of our intuition because the fluid is moving? Why does a moving fluid behave in ways that seem opposite to a static fluid? Further, does this apply to all fluids, to compressible fluids only, or only to incompressible fluids? Our intuition about contricting a volume increasing pressure (squeezing a balloon, for example) usually involves compressible fluids. Any attempt to satisfy a confused intuition ought to specify what kind of fluids are being discussed.
Sorry to seem a bit dumb here but by using the part where newton’s 2nd law is applied…. F1 will always be higher if the fluid is accelerating – in this case – left to right. So would that pressure difference not be the same even without the narrowing of the tube in that circumstance? OR are is this for constant velocity where the acceleration results due to the narrowing of the pipe? So is it that bernoulli’s equation is irrelevant if the fluid through the pipe is all accelerating?
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.
Forces are just gradients in the conserved fields (gradients in potential trajectories through state space) so the invocation of newtons laws is also just a complicated rehashing of conservation of energy. To “really” explain this in this form, I think you’d need a particle based answer where it’s interacting with the walls. Some explanation of “how” the force is applied that’s more than just “pressure” which is a statistical concept. What happens to particles that hit the pipe wall and how does that rob them of vertical momentum and direct it forward.
It’s interesting that the correlation between fluid flow and electrical flow seems to be inverted. While electrons moving from atom to atom thru a conductor, i.e., a wire, as the wire diminishes in diameter, the pressure (voltage) remains the same, but the flow (current) is reduced. Interesting conundrum..
Good discussion until the last part. I don’t think the right hand side provides the explanation. Your analysis on the right hand side is all done in the horizontal direction (along the axis of the pipe). However the pressure gauge senses the pressure perpendicular to the flow (static pressure). That is an orthogonal direction. Thus you really didn’t address it with the right hand side (all horizontal) equations.
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.
That is still not ‘why’. That is till saying ‘what is happening’, which to me is still the same as the work energy explanation. ‘Why’ would be getting down to what is causing the force to be different, not stating that since there is acceleration, the force must be different. What is the interaction happening between each molecule that is causing the difference in force is what you need to explain.
You did not explain anything useful because you converted pressure to a force and did not explain where the force comes from. You state the side on the right has a different pressure acting over an area than the the left but that does not explain where the pressure differential is derived. You’ve simply snuck Bernoulli back into the explanation. What you basically did was simply spoke in terms of force where Bernoulli speaks in terms of pressure. The question is the origin of either. Conservation of energy is the key to driving velocity higher on the right and in turn increases dynamic pressure. Bernoulli is a correct accounting of all pressures involved. If no pressure head is present then the only thing left is static and dynamic pressure. Conservation of energy forces one to go up if the other goes down.
Another alternative intuitive way to look at it is comparitively it comparing it to flight. We know wings fly becuase air moves over the top faster than the bottom and thay is because faster moving air exerts less pressure around it than slower moving air. The same applies to water. Faster moving water exerts less pressure than slower moving water.
I think the reality of pressure has to do with flow. If it went from one side to the other it means pressure has to be higher on one side. So, the pressure is stronger on the larger side or it would be flowing backwards. Not sure what determines pressure though. I’m assuming the problem, at least in one sense, is that this formula is simplified and doesn’t demonstrate the cause of the pressure in a real world sense. Which is why it confuses people. It’s crap presentation that is all too common today. The only correct educational material is complete and comprehensive. It’s all the information. wherever the presenter lacks information the education stops logically at that point as no other conclusions can be made without another source. This then goes into other issues. If people are not learning it it means the information is incomplete. Or you would get the result.
i like to think of it like this forget high and low pressure, just use the law of conservation of energy: energy can neither be created nor destroyed therefore all those particles have to go somewhere lol the left side is bigger and holding more lets say cars and lets also say everyone is condensed into a smaller area which is the right side of the example and its not that all the cars are gone its that their speed has dramatically reduced and are now in traffic but theres a way out and only a certain amount of cars can go thru at a time but this amount can never exceed how many cars we started off with so its always (Lower then what we started) “Low Pressure”, the real question we should be asking is how fast is each individual car coming out.
In this situation the instruments are measuring static pressure according to the vertical direction isn’t it ? The force differential that is applying on the particule is in the horizontal direction isn’t it ? So how can it be measuring a pressure drop in those conditions ? Maybe i don’t understand your explanation but it feels like it doesn’t seem to work.
So, your just saying that the air in the big tube is pushing on the air being accelerated into the small tube which is intuitively obvious. But the issue I have always had with Bernoulli, is that it suggests that the pressure in both tubes is lower than static pressure. Now that would be intuitively obvious if you had a fan sucking the air through, but not intuitively obvious if you had a fan pushing the air through.
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?)?
Ok, now please explain why reducing the pipe diameter of a nozzle lowers the pressure but increases the recoil force. That is: why a fire-hose with a narrower diameter nozzle is far harder to hold than a larger nozzle? Mythbusters actually made a contraption out of 4 fire-hoses that worked like a drone/jetpack to lift a man off the ground. They only got the lift when they reduced the nozzle size. It had a DRAMATIC effect.
If you had a pipe that was at its limits with the bigger diameter and then had the smaller diameter composed of the same material wouldn’t the smaller one explode because there is higher tangential pressure? That’s why I was confused. I thought higher velocity would mean it had more force resulting in more pressure but apparently it’s not directly related to the area being smaller. A smaller object at higher speeds does not have as much force as a larger object at slower speed.
I’m prepared to be wrong because I like to learn…. Same force over a smaller area is the answer. Net force per unit area is reduced. Assuming flow is ~maintained. An orifice can also act as a pressure reducer….(although this example may not be the strict definition of an orifice as it is a taper) High pressure lines are (or should) always as small as they can be (and still provide adequate flow). Strength of materials is a huge factor at higher pressures.
When I look at this the simplest thing I can think of is you are trying to fit the same amount of liquid in a smaller space. This can’t happen so it speeds up when the pipe gets smaller. I don’t really understand why the pressure drops but it does make me think of an airplane wing. If air is moving faster over the top there is less pressure then on the bottom. It stands to reason that if liquid is moving faster it is exerting more force in the lateral direction then in the vertical directions and therefore less pressure on the pipe. I imagine if you were to measure the force in all the directions you would find that its coming out the end of the pipe with far more pressure than if the pipe never got smaller. I don’t think the pressure disappears I think it’s just redirected to directional pressure. What would happen if you capped the end? The pressure would equalize is my hypothesis.
Your explanation doesn’t seem good. My explanation is this. For example, a website (with an open surface instead of a closed one, and a water level only half that of the website). Water flows from right to left. Assuming a constant volumetric flow rate. When the flow of water in the website is hindered by baffle A, the water level on the right side of A will rise. This will increase the speed of the water on the left side of A. For pipes, due to the convergence of downstream pipes, the flow of water is hindered, so the pressure of water upstream of the pipes increases to overcome the obstruction. Due to the increase in upstream pressure, the speed of the convergence pipe area increases. youtu.be/b6Ju1AgBWss
There is higher pressure on the left (in this drawing) because the narrowing tube is a restriction. The question is….what happens to the pressure just before the narrowest point in the restriction? Does it go higher than the pressure on the left and then go lower as it speeds up in the narrow tube? The volume is all piling up at the narrowest point in the restriction (increase in pressure) and then released in the straight section on the right, which would allow pressure to ease.
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.
Or you could say the pressure in the big line is a result of the stricture plus other resistance. The pressure in the little line cannot be greater than the pressure in the big line and for any resistance less than infinity in the small line, the pressure in the small line will be less than the pressure in the big line. The change in velocity is just a red herring. The velocity in the small line is greater because the ratio of pressure to resistance is smaller.
This is a great article. Personally I think the argument really needs the continuity equation to be proven or explained. It’s a little unsatisfying to assume the velocity increases because the continuity equation says so while the approach in this article is to reject abstract explanations and dig deep until an intuitive core can be found which the rest is built on. It really is a great article, but saying there has to be an acceleration as the velocity is higher in the small diameter tube still doesn’t feel like a proper answer to why
I really like this article (and I’ve thought about the question before) but am not satisfied. I have the same issue as you, about the standard explanation: that it relates true facts (for the equation to hold, if this variable does this, then that variable must do that ) but in doing so, it still doesn’t answer the human question “why” does it behave that way? What causes it? Well, your answer (which I 100% agree with), while being true, just pushes the causality issue one further equation out; and while true, still leaves it unanswered. We know that the particle accelerates to the right, and to satisfy F=ma, the a implies an imbalance in the F ‘s, which, applied over an area, means a decrease of pressure to the right. All true facts and the equations are satisfied, but… why is there an a in the first place? Normally for physical problems we know the forces applied, and from those, that they cause the acceleration. But here it’s backwards: we went from the acceleration to the force, but still don’t know why either exists. How is it that a constriction in the pipe, causes a force to the right? Is the water smart, and when it sees the constriction it knows that without creating the force, it won’t accelerate to the right, therefore won’t be able to elongate and fit into a tighter diameter area, and therefore will violate either constant mass flow or constant density? Of course not, but then why? How? 🙂
The pressure reduction is due to the expanding exit and not the narrow part of the system. The width of the entry may not be important but the exit, the wide exit creates a sudden increased volume hence the reduced pressure. I would like to see the same experiment be done without the expanding exit and see if there will be any differences
I just try to imagine a traffic scenario. When you get caught in a traffic bottle neck on the freeway you are going at a relatively slow speed, but after the bottle neck is finished the cars can accelerate. When the cars accelerate again you notice how theres more space between you and the car in front. Since pressure has a direct relation with density, there will be less pressure after the bottle neck. Lack of density is lack of pressure. I may be totally wrong but that’s just how i rationilize it for me.
As an Aeronautical engineer and (former) assistant teacher of Physics and Aerodynamics at college, I protest. Not that it is wrong, but it adds confusion to say the least. First of all, what is “a particle of air”. Are you seriously talking about individual molecules? Because in this case forget about fluid dynamics (that uses the continuum hypothesis) and go to statistical mechanics where the speed of the particle is all over the place both in magnitude and direction and pressure is not a thing (you have impact and inter-molecular bond forces). If you are talking about a differential volume of air (what we call a “parcel”), then there is no real meaning in saying that the pressure in the front and back are not equal to the pressure on the sides. The pressure is a scalar (or a tensor which is equal perpendicular to any plane) and increases by an infinitely small differential of pressure for every infinitely small differential change in position. Now if you take a finite VOLUME of air, then yes, the pressure at the front will be lower than the pressure at the back and there will be a gradient on the sides that goes from the pressure on the front to the pressure on the back. And actually, work-energy can be totally used to derive Bernoulli not relying on itself. You just take a plane upstream of the reduction and a plane upstream of the reduction and consider conservation on energy of the whole volume between the planes. Bernoulli was originally derived from conservation of energy.
Still not intuitive and not an explanation which would make droping in pressure understandable enough. To say that pressure must drop because we need to keep conservation of energy, or we need to keep 2 Neutons law valid is not to explain really why the pressure is dropping. It should be explained somehow differently. Maybe with the liquid or gas molecular forces and forces of the narrowing pipe walls also temperature, volume and pressure changes.
Depending on your great explanation I have a very important question. What will happen if I pressed oil in a chamber with diameter 50 cm and it ends with just 2 cm opening and want to calculate the difference in pressure between the two sections of the chamber. Isn’t the pressure in the small area more than the pressure in the big one?
The pressure in the taper actually increases, regardless of the pressure gauge readings. If you were to remove both gauges and fit two plugs with equal size small holes, you will find that the column of water at the tapered end is dramatically higher than the other end. Equations won’t change realities.