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...
rcgldr said:
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). This reduction in the randomness of the vibrating molecules reduces the static pressure sensed by the walls of the narrow part of the Venturi
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
\dfrac{p}{\rho}=\dfrac{1}{3}\overline{C^2}.
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.
rcgldr said:
A wing produces lift by diverting (curving) the relative flow. 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.
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.
zanick said:
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.
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.
zanick said:
This all stemmed from a discussion with someone that couldn't accept that in a venturi, where mass flow has to be kept constant ( conservation of energy law)
Conservation of mass, not energy.
zanick said:
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.
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.
zanick said:
is there something that can be said to describe what happens as the fluid flow enters the narrowing of the volume in a venturi? something 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.
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).
zanick said:
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 .
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.
zanick said:
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.
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.
zanick said:
anyway, the other question asked of me, was why does the air follow the curvature of the wing.
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.
zanick said:
why do fluids have laminar flow over certain curved surfaces that cause the speed to increase and therefore their pressures to drop?
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.
zanick said:
i guess there is an example of a wing with too great an angle of attack , where the air doesn't 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.
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 positive, 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.
zanick said:
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.
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.