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B Bernoulli vs Newton - air flow characteristics

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  1. Nov 15, 2016 #1
    One thing that has always puzzled me is the fact that in a venturi, air accelerates as it approaches the narrow part of the structure. there are those that argue with the fact that pressure has to raise first , because as we all know, acceleration has to be caused by an increased force ( raised pressure)
    However, being true to what ive learned over the years, im sticking to the law and equations of bernoulli and trying to figure out how air accelerates, as pressure goes down as the entrance to the narrow part of the venturi has less and less volume. we all know bernoulli's equation of pressure energy, (air pressure) kinetic energy(speed and mass) and potential energy (density, height), all being equal for the flow on both sides of the venturi.

    one thing i have heard is that the air molecules are vibrating (moving around) at near 1000mph speeds, so when the air molecules hit the sides of the entrance of the venturi, the molecules pointed in the right direction speed up the flow, and the others are bouncing off the sides back into the flow.. so, the air molecules get spaced apart, the pressure drops and the speed increases... the opposite happens on the reverse side (the diffuser side) where the air flow hits the greater volume, the speed decreases, and the pressure increases..

    so, its kind of like a chicken and egg situation. does the lower molecules getting spaced out due to the converged flow, speed them up, so is less mass, with the same force that they started with at the entrance? in other words to keep consistent with newtons 2nd law, the force says the same, but the mass went down, so the speed could go up. or is it a newton 3rd law where the pressure does go up as the air is compressed at the mouth of the venturi, causing an equal and opposite reaction of the air to accelerate based on the increased force at the mouth of the venturi (this doesnt seem right as we know, the pressure always goes down and flow speeds up.

    over an airplane wing, there is a similar paradox. the air does get compressed at the leading edge, and is that higher edge what feeds the higher speed, lower pressure air flow over the top of the wing? i dont think so, as you would think the under flow speed would accelerate, yet it doesnt. so, what causes the faster flow over the wing... the fact that the laminar flow, is taking a longer path, so it needs to accelerate to keep the same mass flow rate over it? this causes the molecules to space out and speed up? so, the force stays the same, the mass value or density goes down, and the velocity goes up. (where it goes back to the original speed as it comes off the wing at the rear.)

    the confusion for most is that its the fast moving air that creates the lower pressure , when in fact , its really the change of the speed of the air that reduces or increases the pressure of the flow field..
     
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  3. Nov 15, 2016 #2

    boneh3ad

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    This is the first incorrect assumption. It is not a fact that pressure has to rise to cause a gas (or any fluid) to accelerate. Quite the opposite, in fact. The force on a given "piece" of a continuous fluid is a result of the pressure difference from one side to the next. Therefore, the force will be pointing from the side with high pressure and toward the side with low pressure. Fluids accelerate from high to low pressure.

    I don't entirely follow your logic in this (and the following) paragraph. The kinetic theory of gases says that each molecule translates randomly while colliding with other molecules, but I am having a really difficult time figuring out how you are trying to relate that to a Venturi nozzle.

    The flow over an airplane wing is not like the flow through a Venturi nozzle. A Venturi is a closed system except at the inlet and outlet. An airplane wing is an open system. For an explanation of how an airplane wing works, I would direct you to this Insight article discussing Newton vs. Bernoulli.

    The easiest way to think about it is that mass has to be conserved. This means that through a given section of pipe, the same amount of mass has to be passing through it as was passing through the upstream and downstream locations. This means that, in order to squeeze the same mass flowing through the smaller section, the velocity must increase. That must happen to avoid violating mass conservation. It also must satisfy Newton's laws, meaning a force has to accompany that acceleration. This is essentially what you see with Bernoulli's equation. The flow accelerates and the pressure decreases. That is in line with my first portion of this response.
     
  4. Nov 16, 2016 #3

    rcgldr

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    Ignoring how it got there from a zero mass flow state, once in a steady mass flow state the pressure in the narrow section of a Venturi is lower. Assuming no change in total energy, the kinetic energy of the air has become more "organized" (less random) in the narrow section, with a higher net component velocity in the direction of flow than in the wider part of the Venturi, but the total energy has not changed (ignoring issues like a change in temperature or density). This reduction in the randomness of the vibrating molecules reduces the static pressure sensed by the walls of the narrow part of the Venturi. The average speed of the molecules remains the same ... ( correction - as noted by boneh3ad below) As the average component of velocity in the direction of flow increases, the average component of velocity perpendicular to the flow decreases. Change the frame of reference to match that of the flow velocity, and that flow velocity with respect to that frame is zero, and all of the energy from that frame of reference is static pressure, which doesn't change (assuming total energy remains constant, like no change in temperature or density). So in a sense, from the molecules "perspective" the static pressure remains constant because the mass flow is zero with respect to the molecules "perspective".

    Only at startup or transitions in mass flow rate. Assume an initial state of zero mass flow and equal pressure everywhere. In order to start or change a flow, the pressure differential slightly leads the acceleration related reaction, because the pressure differential (or any form of "information") propagates at the speed of sound (not instantly). At some point, the pressure differentials and flows within a system become steady, in which case pressure versus speed2 is a coexistant relationship, rather than cause and effect.

    A wing produces lift by diverting (curving) the relative flow (update - flow relative to the wing). The curvature of flow coexists with pressure gradients perpendicular to the flow (Euler equation for curved flow). Bernoulli's equation can be derived from Newton's second law and the acceleration related to curvature of a flow, which effectively ties Newton and Bernoulli explanations for lift.
     
    Last edited: Nov 16, 2016
  5. Nov 16, 2016 #4
    Great responses.........thanks..... I understand that the venturi principles but just wanted to better understand the cause and effect. RCGDR, thanks for the coexisting relationship description. the molecule level description is an interesting one... ive heard that the venturi neck down, acts as a "velocity filter" so that the energy of the molecules is routed in a particular direction of the flow, causing the acceleration , and thus the pressure drop.

    This all stemmed from a discussion with someone that couldnt accept that in a venturi, where mass flow has to be kept constant ( conservation of energy law) that he wasnt buying the fact that as the flow enters the venturi , that the pressure goes down and speed goes up. if speed goes up, he was convinced there had to be a increase of force to cause it.....since the mass flow is constant, i said that the trade off was the speed and pressure changes. none the less , we got hung up on the molecular causes or forces for the acceleration (newton). since the force is already present with the differential pressure required to cause flow to begin with, i used an analogy of a car accelerating at a constant rate (example) and suddenly you toss out your passenger (mass becomes less) there is greater acceleration , even though the force has remained constant. dont know if that is the best analogy, but that's what i responded with.
    is there something that can be said to describe what happens as the fluid flow enters the narrowing of the volume in a venturi? someting like" the mass flow has to be kept constant, so the molecules space out to fit in the narrowing path, this speeds them up". or is it the velocity filter characteristic that describes it best. looking for the "trigger" that speeds up the air flow into a venturi.

    so, we know that the venturi is kind of a special case with requirements of streamline flow and limits on angles . over a wing, there are not such confines, but bernoullis principles are still at work. sure, the faster moving air going over a longer radius path, lowers its pressure, by speeding it up and therefore provides a pressure differential for the wing to create lift . newton would say that the force existing under the wing is greater than over it, so there is a upward force ( an acceleration proportional to the force and mass) also newtons 3rd law with an elevator directing flow downward, so that the diverted air also has a equal and opposite reaction causing an upward force too.

    anyway, the other question asked of me, was why does the air follow the curvature of the wing. why do fluids have laminar flow over certain curved surfaces that cause the speed to increase and therefore their pressures to drop? i guess there is an example of a wing with too great an angle of attack , where the air doesnt have laminar flow after the initial acceleration, and detaches, turbulence forms and pressure rises negating the pressure differential vs the bottom of the wing, killing the lift.

    Getting back to bernoulli, and basically the reason for lowered pressure for accelerated flow, the two hanging balloons is a common example.. they blow between them and the lower pressure pushes the two balloons together. but most say the fast air causes the lower pressure , when actually its the curvature of the balloons both front and rear that cause this phenom. i did a test with flat plates and they didnt move together when fast air was shot between them. curve the front and they do. curve the back.. and they didnt.. well, they did a little, but not as much. so, the main point was to understand that its not the fast moving air that is at a lower pressure because it is traveling faster than surrounding air, its the acceleration of that air around the objects that creates the lower pressure , validating bernoullis ideas and laws.
     
  6. Nov 16, 2016 #5

    boneh3ad

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    I will start by stressing that any discussion of kinetic theory applies only to the flow of gases, and while liquids generally obey the same macroscopic laws (e.g. their pressure still decreases with speed), the actual rules governing individual molecules is different. That's actually a pretty remarkable fact, when you think about it: the microscopic behavior different but the macroscopic behavior is largely the same.

    Anyway...

    This is essentially correct, though it contains some loose language. Kinetic theory states that a gas can be modeled essentially as a collection of independent tiny particles moving in more or less random motion as observed by someone moving with any bulk motion of the gas. The temperature of the gas is a measure of the total translational energy of the molecules, the density is the sum of all of their masses in a given volume, and the pressure is related to the mean-square of the random motion (be careful here, @rcgldr, because you used the word average, and the average speed does indeed change) . Essentially, if you have a gas molecule moving at velocity ##c_i##, then subtract the average of all ##c_i## over some volume of your fluid, you get the random motion of a single particle, ##C_i = c_i - \overline{c_i}##. Pressure is then a measure of ##\bar{C^2}##. Specifically, it is
    [tex]\dfrac{p}{\rho}=\dfrac{1}{3}\overline{C^2}.[/tex]
    Now, the bulk motion of a fluid is represented by the average velocity of all the molecules in a certain volume, which is ##\overline{c_i}##, so as this value increases, as long as the temperature doesn't change, then the value of ##\overline{C^2}## decreases, and so does the pressure.

    You always try to describe things this way and I really wish you would reconsider your words a bit. The term "relative flow" doesn't actually make any sense without specifying "relative to what". It would make more sense to say "the flow relative to the wing". Further, your use of the Euler equation in this discussion doesn't actually make any sense. in fact, Euler's equation is a direct representation of Newton's second law. It is a momentum balance under the assumption that the flow is inviscid. In essence, it is the Navier-Stokes equations with the viscous terms dropped (or rather, the Navier-Stokes equations are the Euler equation with viscous terms added). The Euler equation also does not change for curved flow.

    Further, you are complicating matters with this explanation. The Euler equation can be derived directly from Newton's laws, and the Bernoulli equation can be derived directly from the Euler equation. Therefore, the Bernoulli equation can be derived from Newton's laws and is therefore compatible with them.

    I've never heard it described that way, but I suppose that makes some degree of sense. The walls leading into the constriction would tend to reflect molecules with steeper angles backward more, while letting those with a more streamwise velocity continue along their path with less of a change in their direction. This would preferentially allow the molecules with motion in that direction into the constriction. I suppose that does make some sense.

    Conservation of mass, not energy.

    Of course a force has to cause it, but that force has to be pushing from behind. Since pressure acts both from in front of a parcel of fluid and behind it and therefore exerts a force in both directions, the pressure behind that parcel must be higher in order to accelerate it. Therefore, as the parcel accelerates, it must move into regions of lower and lower pressure.

    The molecules don't space out assuming we are talking about incompressible flow. They will maintain the same average spacing (since that is effectively the definition of density).

    The length of the path over the top of an airfoil has absolutely nothing to do with why the air over the top speeds up. Read the article I linked before. It discusses why this isn't true.

    Newton's laws and Bernoulli's equation are in complete and total agreement when it comes to airfoils. Either one can adequately describe lift just fine. Either you talk about the air moving faster over the top than over the bottom, meaning the bottom has a higher pressure and the net force (lift!) is directed upward, or else you can think of it as the wing deflects the air stream downward, and that downward shift in momentum must arise from a force directed downward on that air stream. The equal and opposite force to that downward force on the air is an upward force on the wing: lift! Both are correct. The complication is understanding why the air moves faster over the top and why the air is deflected downward by a wing. Those two concepts are related and more complicated.

    The simple answer is that if the fluid didn't follow the wing, it would create a void or a vacuum. Since that region would feature very low pressure, the higher pressure outside of it would tend to push fluid back down into that region. So, a fluid follows the curvature of the wing because if it didn't, the forces resulting from pressure would rapidly push the system back toward a situation where it did follow the curvature.

    This question has nothing to do with laminar flow. The pressure and velocity have an inverse relationship whether the flow is laminar or not. As we've discussed before, the simplest answer to why the pressure drops with an increase in speed is conservation of energy (as is often expressed through Bernoulli's equation). If the bulk kinetic energy increases without any other source of energy change, the energy stored in the random motions of the molecules that we know as pressure must decrease.

    Again, this is not an issue of laminar flow. What you are describing here is a situation called boundary-layer separation and the lost of lift is what we call stall. This is a situation caused due to viscosity and cannot be described with Bernoulli's equation or Euler's equation. The first thing to consider is that the pressure along the surface of an airfoil is not constant. It typically starts out high, decreases for a while (the flow at the surface accelerates in this region) and then starts to increase again (at which points the flow decelerates).

    The second thing to consider is viscosity. As a result of viscosity, the velocity of the fluid where it touches the wall must be zero (relative to the wall), a condition called the no-slip condition. The consequence of this is that there is a small region near the surface where the velocity goes from zero (at the wall) up to its free-stream value (as you move farther away from the wall). This region is called a boundary layer. When the boundary layer enters a region where the pressure is increasing in the streamwise direction (a postive, or adverse pressure gradient), the velocity will slow down. Eventually, this can cause the velocity in the boundary layer to not only slow to zero, but even reverse. When it reverses, this causes a "bubble" to form in the flow featuring a large recirculating region of air inside it. This is called a separation bubble and it is what can lead to stall.

    This is a common misconception. First, your description of your flat plate experiment is not very precise so I won't comment on exactly what is going on there, but perhaps you can reason it out.

    Bernoulli's equation is only valid under certain conditions. One of these is that it is only valid along a streamline. However, it can be valid globally in the flow if all other conditions are met and each streamline in the flow originates from a reservoir with identical conditions (total pressure). In the case of blowing between two balloons, this is not the case. The air on the outside of the balloons has a certain static pressure and zero velocity, so its total pressure is equal to its static pressure is equal to 14.7 psi (1 atm). The stream originating from your mouth has total pressure added to it by the compression created by your lungs. Usually this is something on the order of 1 to 2 psi. So, it is not enough to say that the velocity of that stream is moving faster than the surrounding ambient air so its pressure is lower, because it started with more pressure energy in the first place. Instead, if the static pressure is going to fall below ambient, the air has to be moving sufficiently fast that it first accounts for the pressure added by your lungs, and then any additional velocity will cause it to fall below ambient pressure. In the case of blowing between two balloons, you have essentially just lucked out that your lungs don't add much total pressure, so the air stream really does have a lower static pressure than the surroundings and the balloons move together. The curvature of the balloons essentially exacerbates this effect.

    If instead you took a shop compressor storing air at 100 psi and blew that air between the balloons, the balloons would be pushed away from each other unless the air stream was moving very, very fast. This is because, instead of the velocity having to only account for a 1 to 2 psi difference as is the case with your lungs, it now has to account for an 85.3 psi difference due to the compressor (not accounting for any curvature effects). So, it is not appropriate to apply a straightforward comparison of pressures with Bernoulli's equation when two regions of air flow originate from different reservoirs.
     
  7. Nov 16, 2016 #6

    rcgldr

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    I updated my prior post with strikeouts noting your corrections.

    I was trying to convey what is presented in this section of a wiki article (also mentioned at other web sites).

    http://en.wikipedia.org/wiki/Euler_equations_(fluid_dynamics)#Streamline_curvature_theorem

    Does a Coanda like effect play a role here? Similar to ping pong ball hovering in a blow dryer air stream, even when the stream is angled by a few degrees. An explanation is that the air stream expands somewhat like an inverted cone, so if the ball gets off center, the outward angled component of off centered flow from the air stream gets a net outwards diversion due to Coanda effect, resulting in an inwards corrective force on the ball.

     
    Last edited: Nov 16, 2016
  8. Nov 17, 2016 #7

    boneh3ad

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    The Wikipedia article cites a valid source but, in my opinion, fundamentally misinterprets it or else is giving a very misleading explanation. One of the issues with what they are implying is that the air flowing under an airfoil doesn't have to curve downward over the entire length. It is also not part of the same radial pressure field as the flow on top.

    Re: the balloons, it is indeed an example of the Coanda effect since the air moving between the balloons is a fluid jet and it tends to follow the surface.
     
  9. Nov 17, 2016 #8

    rcgldr

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    I missed that part, although what happens to air flow near the trailing edge of a wing seems to depend on the wing, as the two streams merge back together.

    Given that (Coanda effect), does the air stream between the balloons need to be below ambient, or just not much above ambient? In the case of the air after it flows past a fan or propeller, the pressure is above ambient, and the air continues to accelerate as its pressure decreases to ambient, but I had the impression that it never drops below ambient, and instead eventually is slowed down back to zero speed due to an adverse pressure gradient as it collides with the non-moving air sufficiently "downwind" of the fan. If the fan fed into a venturi tube, then there's still the issue that air won't flow out of the venturi tube unless it's pressure is greater than ambient, but it would have a higher velocity component and lower pressure component, and perhaps in that case the pressure downstream could drop below ambient?
     
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