Vacuum or pressure to move spaghetti through a hole

[Chestermiller]

You are crediting viscous sheer stress from air tangent to the spaghetti strand for providing the inward impetus into the mouth. I want to see a second law analysis on the air to justify such a claim.

The inward impetus on the air (pressure difference times cross-sectional area of the annulus) must be at least equal to the impetus that it is able to transmit to the spaghetti strand. But the spaghetti strand is also subject to the same pressure difference and has a cross-sectional area larger than that of the annulus of air.

Accordingly, it seems clear that the primary inward impetus on the spaghetti is direct atmospheric pressure and not lateral viscous friction.

See the following quote about pushing on a wet noodle from the link https://en.wikipedia.org/wiki/Wet_noodle:

(pushing on a wet noodle is) An example of unproductive action, because pushing an actual wet noodle, as opposed to pulling it, accomplishes nothing.[3][4] George S. Patton is said to have used a wet noodle on a plate to demonstrate an aphorism on the need for leadership, saying "Gentlemen, you don't push the noodle, you pull it."[5]

I hope you're not trying to push on a wet noodle.

I'm going to work on a model of the problem you have in mind. This model will assume that there is no drag on the noodle by the lips (no friction). I will estimate the tension variation along the noodle, and then examine the stability problem related to the noodle tendency to buckle if the pressure outside pushes on the noodle. I'll report back.

 

[Chestermiller]

@jbriggs444 If you liked my previous post, you are going to like this one even more. I have finally seen that what you have been saying is correct.

The easiest way to model this is to evaluate it in terms of gauge pressures, rather than absolute pressures (this is permitted because compressibility effects can be neglected). Even if the noodle is curved over the front contour of your lower lip and dangling down, the gauge pressure at the very bottom of the noodle is zero, and the gauge pressure normal to the noodle surface (outside your mouth) is also zero. So, in terms of gauge pressures, the only tangential forces acting on the noodle are the tension created by vacuum inside your mouth and the tangential component of gravity away from your mouth. If you apply enough vacuum within your mouth, it will be sufficient to overcome the gravitational force, and the noodle can be sucked in. That is, the tangential forces are tensile and balanced. This is almost the same thing as sucking in a liquid through a straw (or even better, a crazy straw).

The noodle will not buckle because, in terms of gauge pressures, the noodle is under tension over its entire length. It is being pulled into your mouth, rather than being pushed. From the standpoint of absolute pressures, the absolute pressures normal to the surface of the noodle stabilize it even though, in terms of absolute pressures, it is being pushed and is under absolute compression in the tangential direction. I hope the latter makes sense.

I now also see that the hydrodynamic lubrication mechanism I described, while present, is secondary.

Chet

 

[jbriggs444]

Thank you, Chet. I'd been wracking my brain trying to figure out if there was some subtle angle that I'd been missing.

 

[Nidum]

Tie the outboard end of the spaghetti strand to a fixed anchor point .

Have the strand nominally horizontal but sagging loose .

When you attempt to ingest the strand in the normal way what happens ?

 

[Stephen Tashi]

The effect of the pressure on the rod's flat end will be negligible. So the force on a noodle and on a rod will be about the same (assuming they are both being held manually outside the mouth by applied tension).

Taking the viewpoint of the original post, the "pressure" is the result of forces perpendicular to the walls of the rod, so if the rod is horizontal and we neglect or eliminate the pressure on end of the rod that is outside of the mouth, then how do these vectors produce a net force in the direction of the mouth?

 

[Chestermiller]

Taking the viewpoint of the original post, the "pressure" is the result of forces perpendicular to the walls of the rod, so if the rod is horizontal and we neglect or eliminate the pressure on end of the rod that is outside of the mouth, then how do these vectors produce a net force in the direction of the mouth?

This was addressed in a subsequent post.

 

[Stephen Tashi]

This was addressed in a subsequent post.

Are you referring to post #43 ?

 

[Chestermiller]

Are you referring to post #43 ?

No. Post #52

 

[Stephen Tashi]

No. Post #52

That post is talking about the noodle instead of the rod, but I anticipate the answer for the rod would also attribute the net force to "the tension created by the vacuum inside your mouth". However, the original post is ( I think) about how to understand the forces as vectors Why does the vacuum inside the mouth exert a net "pull" on the end of the rod?

In order for "the vacuum" to exert a net force on the rod, the pressure outside the mouth must be greater than the pressure inside. But if we view the pressure outside the mouth as caused by discrete force vectors acting (only) perpendicular to the sides of the rod then why does the pressure on the outside to the rod have any effect on a force acting along the length of the rod - i.e. as far as force along the length of the rod goes, why should "pressure" on walls of the rod have any more effect than a "vacuum" would upon those walls?

I think an explanation involves the fact that "pressure" on a surface has different results than a force vector normal to that surface. Can we say that "pressure" exerts "a force in all directions"?

 

[Chestermiller]

That post is talking about the noodle instead of the rod, but I anticipate the answer for the rod would also attribute the net force to "the tension created by the vacuum inside your mouth". However, the original post is ( I think) about how to understand the forces as vectors Why does the vacuum inside the mouth exert a net "pull" on the end of the rod?

In order for "the vacuum" to exert a net force on the rod, the pressure outside the mouth must be greater than the pressure inside. But if we view the pressure outside the mouth as caused by discrete force vectors acting (only) perpendicular to the sides of the rod then why does the pressure on the outside to the rod have any effect on a force acting along the length of the rod - i.e. as far as force along the length of the rod goes, why should "pressure" on walls of the rod have any more effect than a "vacuum" would upon those walls?

I think an explanation involves the fact that "pressure" on a surface has different results than a force vector normal to that surface. Can we say that "pressure" exerts "a force in all directions"?

You're correct that the pressure forces normal to the cylindrical surfaces of the noodle don't affect things. It is only the pressure forces on the free ends that play a role. These are related to tangential tensile forces within the noodle. The difference between these forces on the ends support the gravitational component of tangential force along the noodle, and also provide any tangential acceleration along the tangential contour of the noodle. The noodle basically has a varying tangential tension along its length. Post #52 shows that the problem can be analyzed more easily in terms of gauge pressures and associated tensile forces. Think of a noodle hanging in tension under its own weight as a first step in the thought process.

 

[Stephen Tashi]

You're correct that the pressure forces normal to the cylindrical surfaces of the noodle don't affect things. It is only the pressure forces on the free ends that play a role.

I like your fluid mechanics explanation better than that!

As you indicated in another post, the small area of the free ends makes the net forces on them negligible.

We can think of the rod as a piece of uncooked spaghetti. Suppose the free end of the spaghetti that is outside the person's mouth is pressed against a wall so there is no air between it and and the wall. There is no air pressure on that end. Will the person be able to suck the spaghetti into his mouth? (I don't claim to know.)

 

[jbriggs444]

As you indicated in another post, the small area of the free ends makes the net forces on them negligible.

Of course, that is wrong. The pressure differential multiplied by the cross section of the noodle is the net force that applies.

On the case of a strand of uncooked spaghetti end-on to the wall, that does not seem realistic. One does not generally see flat polished ends on spaghetti strands make airtight seals with walls.

 

[Stephen Tashi]

Of course, that is wrong. The pressure differential multiplied by the cross section of the noodle is the net force that applies.

The question in the original post asks why something like that should be the case. For example, in the case of a cylindrical rod, if we analyze the rod with a "free body" diagram, where do we draw the force vectors and how do we explain their causes?

On the case of a strand of uncooked spaghetti end-on to the wall, that does not seem realistic. One does not generally see flat polished ends on spaghetti strands make airtight seals with walls.

I agree. But the situation is interesting as a thought experiment for inquiring what elementary mechanics predicts. It seems to me that the effects of "pressure" aren't easily analyzed as set of vectors. In the idealized world of elementary mechanics the wall would not exert a force on the end of the stick of uncooked spaghetti unless there was a "reaction" force that arose because some some other force pushed the spaghetti toward the wall. Would the "pressure differential" between the two ends of the stick be zero?

 

[Andy Resnick]

It seems to me that the effects of "pressure" aren't easily analyzed as set of vectors.

Well that's just it, isn't it? Pressure is the isotropic part of the stress tensor. Stress is a tensor quantity that expresses more than just pressure. Shear stress can't easily be formulated in terms of a vector- at least not in any useful way.

https://en.wikipedia.org/wiki/Cauchy_stress_tensor

 

[Chestermiller]

Over the past several days, I have spent lots of time thinking about this problem, and I would like to present what I have come up with. My focus has been on addressing the questions that @Stephen Tashi has been asking, and on using a solid mechanics approach of the type that @Andy Resnick has been recommending.

The analysis considers a cooked spaghetti noodle, and neglects its bending stiffness; so it is treated as being very flexible. The component of the gravitational force perpendicular to the noodle axis is neglected, but the component of the gravitational force tangent to the noodle contour is included. So the stresses in the noodle do not vary over its cross section. The force balance on the noodle is confined to consideration only of the tension and stress variations in the direction tangent to the noodle contour.

The principal stresses are locally approximated as being oriented in the tangential (axial) direction $\sigma_z$, the radial direction $\sigma_r$, and the hoop direction $\sigma_{\theta}$. We employ Hooke's law in 3D to describe the deformational behavior of the noodle material, and to analyze the state of stress and strain in the noodle:$$\epsilon_z=\frac{\sigma_z-\nu(\sigma_r+\sigma_{\theta})}{E}$$
$$\epsilon_r=\frac{\sigma_r-\nu(\sigma_z+\sigma_{\theta})}{E}$$
$$\epsilon_{\theta}=\frac{\sigma_{\theta}-\nu(\sigma_r+\sigma_{z})}{E}$$where $\nu$ is the Poisson ratio and E is the Young's modulus. In our system, because of cross sectional symmetry, the cross sectional stress distribution will be transversely isotropic, such that $$\sigma_{\theta}=\sigma_r$$ and $$\epsilon_{\theta}=\epsilon_r$$ This enables us to eliminate the hoop stress and hoop strain from the analysis to obtain:
$$\epsilon_z=\frac{\sigma_z-2\nu\sigma_r}{E}$$
$$\epsilon_r=\frac{(1-\nu)\sigma_r-\nu\sigma_z}{E}$$

I've used the following diagram to analyze the problem:

The room atmospheric pressure outside the mouth is $P_a$, and the reduced pressure inside the mouth is $P_v<P_a$. So the pressure difference $P_a-P_v$ supports the component of the noodle weight tangent to the noodle contour.

Four sections of the noodle are identified in the figure. Section AB is entirely within the mouth, and does not support any weight; the pressure acting on the surface of the noodle is isotropic and uniform at $P_v$ in this section. Section DE is outside the mouth and is oriented vertically; the tension in the noodle varies axially in this region, although the pressure on the external noodle surface does not vary from $P_a$. Section CD is also outside the mouth, and is contact with the lower lip (but not the upper lip); so the contour is curved, and only a fraction of gravitational force acts tangent to the contour. In section BC, the noodle is in contact with both lips, and the pressure on the noodle surface varies from $P_a$ at location C to $P_v$ at location B.

I think I'll stop here for now and continue in my next post. Please let me know if you prefer for me to analyze this problem in terms of absolute pressure and stresses, or in terms of absolute pressures and stresses.

Chet

 

[Stephen Tashi]

My personal preference is that you first analyze the simpler case of horizontal rigid rod (an uncooked stick of spaghetti). I suspect that if we try to represent "pressure" as family of arrows that push against the rod perpendicular to its surface then we must assume that the vertical surfaces at both ends of the rod are exposed to pressure in order to arrive at a component of force in the horizontal direction.

If we have a curved piece of spaghetti or a curved rod then forces perpendicular to its curved surface can have horizontal components. In that case, it is not mysterious that "pressure" can exert forces that push the rod into the mouth.

Your analysis takes for granted that the pressure differential produces a horizontal component of force. I believe it does, but my interpretation is that the original post is asking for an explanation of how it produces a horizontal component of force.

It's amusing (and perhaps a choking hazard) to consider a variation on the problem. Physics labs usually have sets of cylindrical brass weights. Suppose "the class clown" experiments with the weights by trying to suspend them off the ground by sucking on them. He looks directly down at the floor and, with the weight in his mouth, he sucks on it to keep the weight from falling. Then he tries the experiment on other objects - pieces of string, pencils, lengths of copper wire etc.

I wonder if the results such experiments would agree with calculations based on elementary mechanics. More weight would make things harder to suspend, more cross sectional area would make them easier to suspend. The trade-off between these aspects could be studied. For example, what is the longest length of bare #14 copper wire that the class clown can suspend by sucking on it?

Class clowns often outwit simple models. We might have to resort to your viscous flow model to explain things.

 

[Chestermiller]

My personal preference is that you first analyze the simpler case of horizontal rigid rod (an uncooked stick of spaghetti). I suspect that if we try to represent "pressure" as family of arrows that push against the rod perpendicular to its surface then we must assume that the vertical surfaces at both ends of the rod are exposed to pressure in order to arrive at a component of force in the horizontal direction.

If we have a curved piece of spaghetti or a curved rod then forces perpendicular to its curved surface can have horizontal components. In that case, it is not mysterious that "pressure" can exert forces that push the rod into the mouth.

Your analysis takes for granted that the pressure differential produces a horizontal component of force. I believe it does, but my interpretation is that the original post is asking for an explanation of how it produces a horizontal component of force.

I'm going to take your advice, and first analyze a horizontal rigid rod. Then I'll move to a model of a vertical rigid rod. Then finally I'll model a flaccid spaghetti noodle.

First let's consider the case of a stationary horizontal rigid rod held in place by your lips.

In this case, no pressure differential is required between your mouth and the outside atmosphere. Your lips must merely apply an upward force to the rod to balance its weight (not shown in the figure), and they must also apply a moment to the rod (shown in orange as a couple) to prevent it from rotating.

Let's next consider the case of a horizontal rod advancing into your mouth with velocity V.

In this case, a pressure differential is required to balance the viscous shear stress between your lips and the rod, given by Newton's law of viscosity: $$\tau=\eta\frac{V}{h}$$where $\eta$ is the fluid viscosity in the annular gap and h is the annular gap opening. The pressure difference is related to the shear stress by:$$(P_A-P_V)\pi r^2=2\pi r L\tau$$where r is the radius of the rod and L is the length of contact of the rod with your lips. So, combining these two equations, we get:$$(P_A-P_V)=\eta\frac{2 L}{r}\frac{V}{h}$$ (There is a additional air flow between the outside atmosphere and the mouth required to sustain the pressure differential, i.e., to provide the seal, but this air flow is small)

In the case where there is a pressure differential, note that the two ends of the rod do not have to be flat. Even if the ends are rounded, the net pressure force is still $(P_A-P_V)\pi r^2$.

Comments about the horizontal rigid rod case?

 

[Andy Resnick]

The room atmospheric pressure outside the mouth is $P_a$, and the reduced pressure inside the mouth is $P_v<P_a$. So the pressure difference $P_a-P_v$ supports the component of the noodle weight tangent to the noodle contour.

I think this is the wrong approach- the fluid flow around the spaghetti is the essential part, not any solid-body mechanics. The pressure difference generates fluid flow through the annulus; this fluid flow is what generates sufficient shear stress to draw in the noodle (uncooked or not). The problem should first be simplified by 'looking down'- this reduces the problem to an axisymmetric 2-D velocity profile with coordinates (r,z). The z-direction flow velocity in the annulus can be approximated in the lubrication condition and scales as ΔP = d²u/dr². The boundary conditions are u(0) = 0 (no-slip condition at your lips) and u(H) = U, the velocity at the fluid-spaghetti interface U = 1/2μ ΔP H².

There's still a no-slip condition at the fluid-spaghetti interface, so the spaghetti experiences a shear stress (hydrodynamic drag force) per unit length approximately given as 2πR*μ dU/dz = πΔPRH; the total hydrodynamic drag force is πΔPRHL, where L is the length of the annulus. This must be greater than or equal to the gravitational force acting on the spaghetti (length L') F = πρgR²L', in other words 2ΔPHL/ρ'gRL' > 1 for the spaghetti to be pulled in.

The spaghetti is a passive player; all the action is created by the film of moving fluid.

 

[Chestermiller]

I think this is the wrong approach- the fluid flow around the spaghetti is the essential part, not any solid-body mechanics. The pressure difference generates fluid flow through the annulus; this fluid flow is what generates sufficient shear stress to draw in the noodle (uncooked or not). The problem should first be simplified by 'looking down'- this reduces the problem to an axisymmetric 2-D velocity profile with coordinates (r,z). The z-direction flow velocity in the annulus can be approximated in the lubrication condition and scales as ΔP = d²u/dr². The boundary conditions are u(0) = 0 (no-slip condition at your lips) and u(H) = U, the velocity at the fluid-spaghetti interface U = 1/2μ ΔP H².

There's still a no-slip condition at the fluid-spaghetti interface, so the spaghetti experiences a shear stress (hydrodynamic drag force) per unit length approximately given as 2πR*μ dU/dz = πΔPRH; the total hydrodynamic drag force is πΔPRHL, where L is the length of the annulus. This must be greater than or equal to the gravitational force acting on the spaghetti (length L') F = πρgR²L', in other words 2ΔPHL/ρ'gRL' > 1 for the spaghetti to be pulled in.

The spaghetti is a passive player; all the action is created by the film of moving fluid.

Thanks Andy. To me it is clear that this problem involves a coupling between the solid mechanics and the fluid mechanics. I have carried out the hydrodynamic lubrication modelling that you have suggested in the above post and, for a rigid horizontal rod, have obtained the result I indicated in post #67:
$$V=\frac{rh}{2\eta L}\Delta P$$
Note that, for this case, the "pressure flow" component of the lubrication flow is negligible compared to the "drag flow" component.

I plan on continuing the analyses, first for a vertical rigid rod model and then for an actual flexible noodle model (where the solid mechanical part needs careful consideration). I'm confident that, when you see the details of the analyses, you will be happy with what I have done.

 

[Baluncore]

What is objectionable about carrying out this often repeated experiment in public?
A. The sound.
B. Etiquette.
C. Sauce dispersal.
D. All of the above.

I believe the fluid involved as a lubricant must be the sauce. The lip-seal against the spaghetti allows some sauce to enter with the spaghetti. If too much sauce enters, then a lubrication seal failure will occur allowing air to enter, making the characteristic popping sound, suggesting answer A.

It is necessary for the experimenter to dynamically adjust the lip-seal so as to regulate the lubricant wedge formed from the external lip reservoir. Unless the experimenter has a beard, too good a seal can lead to a poorly balanced nutrition as the sauce drips from the chin, suggesting answer B.

There is also a conservation of momentum and energy consideration. As the tail of the spaghetti travels upwards and then turns to enter the superior orifice, an effect like a whip-crack occurs that disperses excess lubricant sauce vertically, suggesting answer C.

Notes:
I find it interesting that, within reason, the diameter of the spaghetti or noodle is not critical in determining the exercise of this experiment. The limitation is actually determined by the ratio of the height of the lip-seal above the source reservoir : to the pressure difference available across the lip-seal.

I have carried out an experiment that showed I can only blow about 1 psi of static pressure before air is first pushed into the salivary ducts, with the associated risk of air embolism. It would appear that I operate on an internal pressure of about 1 psi. I can however suck a depression of about 14 psi. Given that the density of cooked pasta is close to unity, that limits the length of a pasta “barometer column” to be close to 9 metres. Unfortunately, spaghetti is not locally available in lengths greater than about 500 mm, so I cannot immediately confirm that height by experiment.

I do however notice that “two minute noodles” come in a pack that is often extruded, dried and then packed as a single length. By identifying and tagging the free end it would be possible to rehydrate the noodles without stirring, then to draw a single noodle thread back from the bundle.

But my concern here becomes one of quality control, that of the Chinese noodle product versus the Italian pasta product.

I suspect that the tensile strength of a pasta thread can be enhanced by optimisation of the rehydration process. By adding excess salt to the water, osmotic pressure will significantly reduce the entry of water into the pasta, which will then remain “al dente” and so have a greater structure to water weight ratio, giving a greater tensile strength.

Further experimentation with the “pasta barometer” is clearly needed.

 

[Spinnor]

Just for reference I got up on my porch roof this morning and sucked on a long clear plastic hose stuck in a gallon of water. My sucking abilities were able to lift a column of water about 10 feet. I think that translates to a nearly 5 psi air pressure difference between the inside of my mouth and outside air pressure. Your abilities may vary.

Cooked spaghetti is also very slippery as we all know.

Assume no friction, assume that cooked spaghetti has the same density as water, assume a pressure difference of 5 psi the smart guys here should be able to calculate the theoretically longest piece of hanging cooked spaghetti that a person could suck into their mouth. I think it should be of order 10 feet.

 

[Andreas C]

I'm impressed, but I see nowhere in the equation the optimal cooking time for spaghetti at STP??

Spaghetti doesn't really cook at STP...

 

[Chestermiller]

In this post, I present the results of an analysis of hydrodynamic lubrication flow in the gap between the lips and the spaghetti noodle. The figure below shows the steady flow of a Newtonian viscous fluid situated between two infinite parallel plates, driven by a combination of an axial pressure gradient, and drag flow produced by axial movement of the upper plate at a velocity V .

By applying the methodology alluded to by Andy Resnick in post #68, we obtain the following equation for the axial velocity profile of the fluid (as a function of the cross-channel coordinate y):
$$v_x=\frac{(p_1-p_2)}{2\eta L}y(h-y)+V\frac{y}{h}\tag{1}$$where $\eta$ is the fluid viscosity. The velocity gradient at the upper boundary (aka the fluid shear rate at the upper boundary) is obtained by differentiation of Eqn. 1 with respect to y to yield:
$$\left(\frac{dv_x}{dy}\right)_{y=h}=-\frac{(p_1-p_2)h}{2\eta L}+\frac{V}{h}\tag{2}$$
From Newton's law of viscosity, the shear stress $\tau$ in the x-direction exerted by the upper plate on the fluid in the gap between the plates is equal to fluid viscosity times the velocity gradient:
$$\tau=\eta \left(\frac{dv_x}{dy}\right)_{y=h}=-\frac{(p_1-p_2)h}{2L}+\eta \frac{V}{h}\tag{3}$$
By Newton's 3rd law, this is equal and opposite to the shear stress in the x-direction exerted by the fluid on the upper plate: $$\frac{(p_1-p_2)h}{2L}-\eta \frac{V}{h}$$
In our problem, the upper (moving) plate is representative of the noodle, and the lower plate is representative of our lip. If we use the above relationship for the shear stress to carry out an axial force balance on the noodle, we obtain:$$\pi r^2(\sigma_2-\sigma_1)=2\pi rL\left(-\frac{(p_1-p_2)h}{2L}+\eta \frac{V}{h}\right)\tag{4}$$or equivalently,
$$(\sigma_2-\sigma_1)=-\frac{(p_1-p_2)h}{r}+ \frac{2\eta LV}{rh}\tag{5}$$where $\sigma$ is the axial tensile stress within the noodle.
For a horizontal rigid noodle, from analysis of the solid mechanics behavior of the portions of the noodle outside the lips, we find that:$$(\sigma_2-\sigma_1)=-(p_2-p_1)\tag{6}$$Combining Eqns. 5 and 6 then yields:
$$V=\frac{rh}{2\eta L\left[1+\frac{h}{r}\right]}(p_1-p_2)\tag{7}$$
In the case of a vertical rigid rod or a flaccid noodle containing vertical sections (or curved sections with vertical components along the contour), solid mechanics analysis must be modified to include the effect of gravity on the tensile stress variations. Therefore, for these cases, Eqn. 6 does not apply.

 

[DaTario]

I would say that the viscosity of fluids, which are present at the surface of spaghetti, plays an important role in forcing the spaghetti itself.

 

[Chestermiller]

I would say that the viscosity of fluids, which are present at the surface of spaghetti, plays an important role in forcing the spaghetti itself.

What are you saying that's different from what we have already said?

 

[jartsa]

Let us consider a soft but straight string of spaghetti. If the opposite ends are at different pressures, then there simply must be a force pushing the string: pressure difference multiplied by area.

As the spaghetti is soft, it can not transmit a pushing force. That may seem like a problem, but consider this: When we suddenly decrease the pressure at our end of a very long rigid rod, the far end can not immediately exert a pushing force on our end, but still our end starts to move immediately.

 

[Chestermiller]

Let us consider a soft but straight string of spaghetti. If the opposite ends are at different pressures, then there simply must be a force pushing the string: pressure difference multiplied by area.

As the spaghetti is soft, it can not transmit a pushing force. That may seem like a problem, but consider this: When we suddenly decrease the pressure at our end of a very long rigid rod, the far end can not immediately exert a pushing force on our end, but still our end starts to move immediately.

This is an incorrect assessment of what is happening (both for an uncooked noodle and for a cooked noodle). If you are convinced that the solid mechanical behavior of the noodle is much more important than the fluid mechanics behavior (discussed by several Science Advisers and Mentors), please provide a valid solid mechanics analysis of the situation (including stresses, strains, external loads, and deformations) based either on the Theory of Elasticity or on the (more straightforward) Strength of Materials approach. Your analysis should include actual equations and their solutions.

Chet

 

[PAllen]

I'm not convinced the solid noodle case needs any explanation except pressure. Consider replacing your lips with an airtight frictionless aperture. The solid noodle will clearly be sucked in. There is no fluid involved at all. The flaccid noodle is the interesting case.

Also, gravity can be made irrelevant by imagining the experiment in a pressurized cabin of a rocket in orbit. I do not think there would be any difference in behavior for this experiment.

 

[Andy Resnick]

Consider replacing your lips with an airtight frictionless aperture. The solid noodle will clearly be sucked in.

With all due respect, this is silly- linear slide and fluid bearing companies would love to hear from you. Please provide some evidence, as opposed to a fertile imagination, that an "airtight aperture" is frictionless, and that an "airtight frictionless aperture" allows one object to slide freely through another.

 

[PAllen]

With all due respect, this is silly- linear slide and fluid bearing companies would love to hear from you. Please provide some evidence, as opposed to a fertile imagination, that an "airtight aperture" is frictionless, and that an "airtight frictionless aperture" allows one object to slide freely through another.

It's an idealization, as often done for problem simplification. The idea is to separate what can be explained by pressure from what cannot. How well it could be approximated in the real world is a separate question e.g. I have no idea whether a precisely machined aluminum noodle and graphite apperture would approximate this.

 

[Chestermiller]

I'm not convinced the solid noodle case needs any explanation except pressure. Consider replacing your lips with an airtight frictionless aperture. The solid noodle will clearly be sucked in.

Not so fast. What do you think the stress distribution within the noodle looks like in this situation? If the part of the noodle outside the mouth is surrounded by atmospheric pressure $p_a$, the axial tensile stress within the part of the noodle outside the mouth is $-p_a$ (compression). And, if the the part of the noodle inside the mouth is surrounded by vacuum pressure $p_m$, the axial tensile stress within the part of the noodle inside the mouth is $-p_m$. So, across the aperture (the lips), the tensile stress within the noodle has to change from $-p_a$ to $-p_m$. The only way this can happen is if there is friction (shear stress) at the surface of the aperture. If there is no friction, the noodle will have to be constantly accelerating, with an acceleration equal to $(p_a-p_m)A/m$, where m is the mass of the noodle and A is its cross sectional area. However, I don't think that constant acceleration approaching this is observed in practice.

 

[PAllen]

Not so fast. What do you think the stress distribution within the noodle looks like in this situation? If the part of the noodle outside the mouth is surrounded by atmospheric pressure $p_a$, the axial tensile stress within the part of the noodle outside the mouth is $-p_a$ (compression). And, if the the part of the noodle inside the mouth is surrounded by vacuum pressure $(p_m)$, the axial tensile stress within the part of the noodle inside the mouth is $(-p_m)$. So, across the aperture (the lips), the tensile stress within the noodle has to change from $-p_a$ to $(-p_m)$. The only way this can happen is if there is friction (shear stress) at the surface of the aperture. If there is no friction, the noodle will have to be constantly accelerating, with an acceleration equal to $(p_a-p_m)A/m$, where m is the mass of the noodle and A is its cross sectional area. However, I don't think that constant acceleration approaching this is observed in practice.

But then the friction only serves to slow the rod down, producing an eventual constant velocity similar to terminal velocity of a body falling in atmosphere.

 

[Chestermiller]

But then the friction only serves to slow the rod down, producing an eventual constant velocity similar to terminal velocity of a body falling in atmosphere.

Yes. In my judgment, the terminal velocity is attained very rapidly in the noodle situation. At least, that seems to me to be a reasonable approximation. That is, the noodle advances much closer to constant velocity than to constant acceleration.

 

[Andy Resnick]

It's an idealization, as often done for problem simplification. The idea is to separate what can be explained by pressure from what cannot. How well it could be approximated in the real world is a separate question e.g. I have no idea whether a precisely machined aluminum noodle and graphite apperture would approximate this.

Ugh- aside from aluminum noodles being unappetizing, you haven't even done a zeroth-order approximation, But, fine. Let's pretend.

Consider dry lubricants- graphite powder, for example. That's a real-life version of dry water, so we eliminated your odd insistence that the fluid can be abstracted away. And indeed, even though the powder acts as a fluidized bed, the viscosity is very low- let's go with your simplification of a frictionless interface- and make it zero viscosity. We physicists could also suggest using superfluid He, but there's the non-simple problem of what happens if you aspirated liquid He.

Now what happens? Most likely, you can't suck up the noodle- unless you are an astronaut orbiting the Earth (as you also suggested), because then the tiny ΔP will indeed create an imbalanced force, and you could indeed aspirate the noodle. [Edit]: a frictionless interface means the noodle will move freely under any imbalanced, momentary axial force and the housing cannot arrest the motion. So the device must be in free-fall (true free-fall, not attached to an orbiting craft).

[Edit]: So, by removing viscosity, your simplified problem does not describe a broadly applicable class of behavior, it is actually restricted to a highly specific (and useless) physical situation.

 

[PAllen]

Now consider the flaccid noodle, with the apperture having frictionless lubricant. Being frictionless, it cannot exert any force on the noodle by flowing. Yet, I believe, in such a case, the noodle would still be sucked in - very fast. As an approach to understanding this, consider replacing the noodle with a long balloon at above standard pressure, standard pressure on one side of the apperture, and vacuum on the other. The balloon would be sucked in by expansion on the vacuum side pulling the other side in by tension and flow of the balloon material. Now, get from here to a more plausible model of a noodle. I am thinking the noodle effectively flows in, and boundary flow is irrelevant or secondary in nature.

 

[Chestermiller]

Now consider the flaccid noodle, with the apperture having frictionless lubricant. Being frictionless, it cannot exert any force on the noodle by flowing. Yet, I believe, in such a case, the noodle would still be sucked in - very fast. As an approach to understanding this, consider replacing the noodle with a long balloon at above standard pressure, standard pressure on one side of the apperture, and vacuum on the other. The balloon would be sucked in by expansion on the vacuum side pulling the other side in by tension and flow of the balloon material. Now, get from here to a more plausible model of a noodle. I am thinking the noodle effectively flows in, and boundary flow is irrelevant or secondary in nature.

Again, without friction, you could not maintain the tensile stress difference in the balloon between inside and outside the mouth without an unrealistically huge acceleration of the balloon. In the case of a limp noodle, the same basic principle applies. The tensile stress difference can only be maintained by acceleration of the noodle or by friction at the surface of the aperture.

 

[DaTario]

What are you saying that's different from what we have already said?

Dear Chestermiller, once I have figured out what seemed to be the relevant physical notion in OP (imo) I immediately decided to contribute. I have noticed that you and Andy Resnik have given similar answers (but more specific than mine) just after having published my comment. If appologizing is necessary here, I am for it.
It was an interesting question, which is associated to some topics of my liking. By the way, I would like to be explicit in saying that am not disputing authorship here.

 

[DaTario]

As a somewhat experienced spaghetti eater I have the impression that, if we could see the movement of the spaghetti in slow motion, some transversal vibration could be observed. I guess the phenomena seems to involve an intake of pasta, sauce and air. If this empirical consideration shows up to be correct under a controlled experimental test it may become likely that the air intake is to cause the cylindrical shaped pasta to vibrate transversally while entering the mouth.
DaTario

 

[PAllen]

Is my understanding correct that it should be possible to distinguish models experimentally, as follows (unfortunately, I have no relevant equipment or access to a lab):

Have a chamber with a rubber orifice which can be lubricated with different fluids, and is also connected to a vacuum pump. Then testing against rods and noodles of different thickness, ideally measuring the force exerted when the pump is running and the outside end of noodle and rod is attached to a force measuring device:

- boundary flow model would suggest that for a given lubricant, the effect is proportional radius (really circumference, but same difference for proportionality); and that different lubricants (high viscosity oil, low viscosity oil, sugar syrup, etc.) could make a significant difference.

- pressure dominant case would predict force proportional to radius squared, with minimal difference by lubricant, especially for radius not too small (only impact is friction, which would be less relevant as radius got larger).[edit: and friction would be zero for a rod held static by attachment to a force measuring device]

Unfortunately, while using my mouth, I can easily determine there is more force for bigger radius, I have nowhere near the precision to distinguish proportional to r versus r².

 

[jartsa]

This is an incorrect assessment of what is happening (both for an uncooked noodle and for a cooked noodle). If you are convinced that the solid mechanical behavior of the noodle is much more important than the fluid mechanics behavior (discussed by several Science Advisers and Mentors), please provide a valid solid mechanics analysis of the situation (including stresses, strains, external loads, and deformations) based either on the Theory of Elasticity or on the (more straightforward) Strength of Materials approach. Your analysis should include actual equations and their solutions.

Chet

Sorry but I prefer energy considerations:

Let's say a big tank is filled with air at 1 atm and also some cooked spaghetti, and another big tank is filled with air at 0.9 atm. These tanks are connected by a tube, and at the middle of the tube there are some kind of mechanical lips.

Now a physicist goes into the tank, applies dry ice on the end of a noodle and sticks the frozen part through the "lips". Let's say there's only one long noodle.

Now if one liter of spaghetti is sucked from tank1 to tank2, then the energy of tank1 decreases by: 100000 N/m² * 0.001 m³ = 100 J
And the energy in tank2 increases by: 90000 N/m² * 0.001 m³ = 90 J
Total change of energy is 10 J (Tanks are big, so pressures do not change)

If one liter of air goes from tank1 to tank2 that also causes a 10 J decrease of pressure energy in the tanks.

What I'm getting at here is that some amount of energy is used to propel the spaghetti from tank1 to tank2, the energy is generated by x liters of spaghetti leaving tank1 and y liters of air leaving tank1.

If the volume of the spaghetti entering tank2 is much larger than the volume of air entering tank2, then the air was not important energy source for the motion of spaghetti.

So the question is: When sucking spaghetti, does more spaghetti or air enter the mouth?

Oh yes, let's put both tanks in a heat bath, so that the total energy in the tanks can actually decrease when the pressure energy does some work. ... Correction, let's just wait till tank2 reaches the same temperature as the surroundings.

 

[Chestermiller]

Is my understanding correct that it should be possible to distinguish models experimentally, as follows (unfortunately, I have no relevant equipment or access to a lab):

Have a chamber with a rubber orifice which can be lubricated with different fluids, and is also connected to a vacuum pump. Then testing against rods and noodles of different thickness, ideally measuring the force exerted when the pump is running and the outside end of noodle and rod is attached to a force measuring device:

- boundary flow model would suggest that for a given lubricant, the effect is proportional radius (really circumference, but same difference for proportionality); and that different lubricants (high viscosity oil, low viscosity oil, sugar syrup, etc.) could make a significant difference.

- pressure dominant case would predict force proportional to radius squared, with minimal difference by lubricant, especially for radius not too small (only impact is friction, which would be less relevant as radius got larger).

Unfortunately, while using my mouth, I can easily determine there is more force for bigger radius, I have nowhere near the precision to distinguish proportional to r versus r².

I'm a modeller, and, as a modeller, I am very confident that these issues can be resolved without resorting to experiments (at least initially to get the lay of the land).

I feel very frustrated. I've been trying to get responders to focus exclusively on the noodle, using simple free body diagrams and force balances (and perhaps a smidgen of stress analysis), but no one seems willing. I contend that the uncooked noodle can be analyzed as a rigid- or slightly deformable rod, and that the limp noodle can be analyzed as either an inextensible- or slightly extensible rope.

I'm prepared to present such analyses myself, but I wanted to give others a chance. Anybody?

Please excuse my frustration.

 

[Baluncore]

Examination of Chestermiller's equation (1) in post #73 shows that there is a critical sauce viscosity above which the maximum sauce flow velocity within the channel is always lower than or equal to the velocity of the upper plate = spaghetti surface velocity. It suggests that with a thick viscous sauce the spaghetti must be propelled by the axial pressure difference within the spaghetti rather than by the drag of the moving sauce. It raises the question of the relative strength of the two propulsion forces. Indeed, for a thick sauce, the sauce would be drawn through the channel by drag from the spaghetti.

 

[Chestermiller]

I have carried out the solid mechanics analyses of the noodle I alluded to in my previous post, and have come to the following conclusions:

1. For a horizontal rigid noodle, it is not possible to suck the noodle into the mouth using a significant pressure difference and with a constant noodle velocity (i.e., no acceleration) without friction at the lips. At constant velocity, the frictional resistance is necessary to balance the pressure difference. Otherwise, the noodle will be constantly accelerating.

2. For a vertical rigid noodle or a dangling limp noodle, it actually is possible to suck the noodle into the mouth using a significant pressure difference and with a constant noodle velocity even without friction at the lips. The gravitational force on the noodle compensates for the acceleration of the noodle required in case 1. This does not mean that there is no significant viscous frictional drag at the lips in actual practice (with both the frictional drag and the weight of the noodle balancing the pressure difference). We simply need to approximately quantify the magnitude of the frictional drag (using reasonable estimates of the parameters involved, such as viscosity, noodle velocity, and annular gap) to compare it with the contribution of gravity to the overall pressure difference.

P.S., If anyone is interested in the solid mechanics analysis for these cases, I can provide it.

Chet

 

[PAllen]

I have carried out the solid mechanics analyses of the noodle I alluded to in my previous post, and have come to the following conclusions:

1. For a horizontal rigid noodle, it is not possible to suck the noodle into the mouth using a significant pressure difference and with a constant noodle velocity (i.e., no acceleration) without friction at the lips. At constant velocity, the frictional resistance is necessary to balance the pressure difference. Otherwise, the noodle will be constantly accelerating.
Chet

I'm not sure why you keep stressing the constant velocity case. Crude experiments I can do readily establish that for the rigid cylinder case with constant pressure difference, and common lubricants, the cylinder does steadily accelerate. I did not reach the point where terminal velocity was reached due to friction increasing proportional to speed, but presumably such point is readily reached for a long cylinder.

To me, this (plus your gravity example) establishes that the rigid case is primarily a matter of pressure difference modified by obvious factors like friction.

My mind is still open on the flaccid noodle case, especially for practical parameters.

 

[Andy Resnick]

I'm a modeller, and, as a modeller, I am very confident that these issues can be resolved without resorting to experiments (at least initially to get the lay of the land).

I feel very frustrated. I've been trying to get responders to focus exclusively on the noodle, using simple free body diagrams and force balances (and perhaps a smidgen of stress analysis), but no one seems willing. I contend that the uncooked noodle can be analyzed as a rigid- or slightly deformable rod, and that the limp noodle can be analyzed as either an inextensible- or slightly extensible rope.

I'm prepared to present such analyses myself, but I wanted to give others a chance. Anybody?

Please excuse my frustration.

FWIW, I very much appreciate the time and effort you have invested in this thread.

 

[Chestermiller]

I'm not sure why you keep stressing the constant velocity case.

I just had the sense that, when I suck in a noodle (through my actual lips), it travels close to constant velocity. Maybe I'm wrong, or maybe I'm subconsciously continuously adjusting the suction so that the velocity is close to constant.

Crude experiments I can do readily establish that for the rigid cylinder case with constant pressure difference, and common lubricants, the cylinder does steadily accelerate. I did not reach the point where terminal velocity was reached due to friction increasing proportional to speed, but presumably such point is readily reached for a long cylinder.

To me, this (plus your gravity example) establishes that the rigid case is primarily a matter of pressure difference modified by obvious factors like friction.

My mind is still open on the flaccid noodle case, especially for practical parameters.

I'm going to present my solid mechanics analysis of the limp noodle case to show how it works. I'm also going to make a rough calculation of the viscous drag force at the lips and compare it to the dangling weight.

 

[Chestermiller]

I'm reporting back on some calculations I've done to estimate the drag force on the noodle by the lips, and compare this with the weight of the noodle dangling from the lips. The calculations also give the minimum level of vacuum required to suck the noodle in. To get the dangling weight of the noodle, my results are similar to those of @OmCheeto in a previous post. The calculated weight is based on the following:

Noodle radius = 0.1 cm
Noodle density = 1 gm/cc
Noodle length = 30 cm

This gives a noodle mass of about 1 gram, and a noodle dangling weight of about 1000 dynes (0.01 N).

To crudely estimate the drag force by the lips, I used the following formula:
$$F=2\pi r L \eta \frac{V}{h}$$
where L is the length of the lip channel and h is the annular gap between the lips and the noodle. The calculation was based on the following parameter values:

L = 1 cm
$\eta=0.01\ \frac{gm}{cm\ sec}$ (i.e., water at room temperature, 0.01 Poise)
V = 6 cm/sec (noodle suction speed)
h = 0.001 cm

Using these values, I get a drag force of about 40 dynes. Thus, the drag force would be a small fraction of the dangling weight of the noodle and, in practice, can be neglected (This confirms @PAllen's contention).

The suction required to draw the noodle into the mouth (in cm of water) would be about equal to the length of the noodle, and would thus be equal to about 30 cm of water. This would correspond to about 3000 Pa, or 12" of water. This would be the minimum vacuum to suck the noodle in.

 

[BillTre]

I just read this thread and since I was making some spaghetti, so I did some experiments.

This may partly dis-entangle some variables:
wetness
diameter
water vs. sauce
horizontal vs. vertical noodle
straight vs, bent flexible noodle

Dry noodles (diameter = 1.93mm):
Using noodles that are about 1.93 mm diameter (dry):
1) I can not suck in a dry noodle with dry lips. It felt like too much friction.
2) I can suck in a "dry noodle if I wet my lips and the noodle with saliva (very thin film on the noodle, most likely less than 0.1 mm). Much of the wetness seems to get sucked into the noodle. Could only suck in an inch or two (2.5-5.0 cm).
This was most easily done in a vertical orientation (head tilted forward so mouth opening is approximately horizontal).
Horizontal dry noodles have to propped up outside the mouth or it runs into things inside the mouth.
Vertical dry noodles also work.
3) If I only wet a short distance of the noodle I can suck it in until my lips hit the dry part of the noodle

Wet noodles (diameter = 2.8 mm):
4) wet only from the cooking water; works well in either a horizontal or vertical orientation.
5) Wet with sauce (sauce from a jar, quick dinner), sucked (seemingly) more easily than with just water. Warning: In the vertical orientation I almost got some sauce in my eye (remember to wear your googles when experimenting!)
6) noodle, cooked but laying around and tacky on the surface: could suck it in, but much more difficult (in either horizontal or vertical orientation). Similar to the dry noodle

Cooked, wet hot dog (diameter = ~19.4 mm):
7) These sucked in very easily (horizontal or vertical).
They were very pliable and had a somewhat greasy surface.

I guess in the vertical orientation I could put a weight on the end to get a real idea of the applied force, but food is now gone.

Conclusions:
Horizontal vs. vertical (noodle or head) orientation does not seem to matter much.
Straightness of noodle doesn't seem to matter much.
Larger diameter may help.
Minimal wetness is needed to reduce friction (at least).
Sauce coating seems to work best.

I'll let you guys figure out the meaning of all this.

 

[Chestermiller]

NEWS FLASH FROM FOX NEWS: TODAY IS NATIONAL SPAGHETTI DAY

 

[Andy Resnick]

I just read this thread and since I was making some spaghetti, so I did some experiments.
<snip>

Gasp- perform experiments instead of endless noodling? :)