Vacuum or pressure to move spaghetti through a hole

[houlahound]

Just solve for "x".

 

[houlahound]

The relevant physics starts at about 3.00.

 

[Chestermiller]

This is a continuation of my previous post. There I showed that, if the noodle is held in place manually so that it is prevented from being sucked into the mouth, the tension that must be applied to the noodle from the outside is $F=\pi r h \Delta P$, where r is the radius of the noodle, h is the annular gap between the noodle and lips, and $\Delta P$ is the pressure difference between the inside and outside of the mouth.

If we ease up on the tension applied manually to the noodle from the outside, the noodle can begin to slip axially into the mouth with velocity V. I carried out a lubrication flow analysis on this problem, and obtained the following relationship between the outside noodle tension F, the noodle velocity V and the pressure difference $\Delta P$:$$F=\pi r h \Delta P-\frac{2\pi r \eta L}{h}V$$where L is the length of the lip channel and $\eta$ is the viscosity of the fluid in the gap (air or water or oil or sauce). This result, of course, agrees with the previous finding for the case in which the tension is high enough to hold the noodle stationary (V=0). Eventually, if we ease up on the noodle tension enough, the tension will drop to zero, and we will obtain the maximum suck velocity of the noodle:

$$V=\frac{h^2}{2\eta L}\Delta P$$

 

[houlahound]

You have assumed a smooth, incompressible noodle?

 

[Chestermiller]

You have assumed a smooth, incompressible noodle?

The present hydrodynamic lubrication model recognizes the fact that the most important physical mechanism responsible for the noodle being sucked through the lips and into the mouth is provided by the viscous drag and pressure flow of the fluid in the annular gap between the lips and noodle. When the liquid advances axially through the gap, it drags fluid with it. Additional fluid flow is provided by the pressure difference between air outside and the air inside the mouth. Both these components of the fluid flow contribute to the axial shear force on the surface of the noodle. The model takes all this into account.

 

[houlahound]

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

 

[Chestermiller]

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

I always use 10 minutes.

 

[houlahound]

Cheers thanks, I have one further question;

1. Does this have anything to do with string theory.

and

2. If in space nobody can hear you scream, can you still slurp spaghetti as ∆P < 0.

 

[Chestermiller]

Cheers thanks, I have one further question;

1. Does this have anything to do with string theory.

and

2. If in space nobody can hear you scream, can you still slurp spaghetti as ∆P < 0.

You're making me hungry.

 

[Low-Q]

The present hydrodynamic lubrication model recognizes the fact that the most important physical mechanism responsible for the noodle being sucked through the lips and into the mouth is provided by the viscous drag and pressure flow of the fluid in the annular gap between the lips and noodle. When the liquid advances axially through the gap, it drags fluid with it. Additional fluid flow is provided by the pressure difference between air outside and the air inside the mouth. Both these components of the fluid flow contribute to the axial shear force on the surface of the noodle. The model takes all this into account.

Will the same force be applied to a stiff short steel rod - if the rod is lubricated with tomato sauce first? Or is it more forces applied to suck that rod into the mouth - such as surface pressure on the rods flat end?
The rod will stop moving when the end inside the mouth hits something, but the spagetti will not stop due to its flexible nature.

 

[Chestermiller]

Will the same force be applied to a stiff short steel rod - if the rod is lubricated with tomato sauce first? Or is it more forces applied to suck that rod into the mouth - such as surface pressure on the rods flat end?
The rod will stop moving when the end inside the mouth hits something, but the spagetti will not stop due to its flexible nature.

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).

 

[jbriggs444]

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).

I am not following this. As I understand your contention, the pressure difference on a thin ring of air surrounding a rod passing through the lips is sufficient to propel both air and rod into the mouth, but the pressure difference on a thick cylinder is inadequate to do so.

 

[Chestermiller]

I am not following this. As I understand your contention, the pressure difference on a thin ring of air surrounding a rod passing through the lips is sufficient to propel both air and rod into the mouth, but the pressure difference on a thick cylinder is inadequate to do so.

Perhaps I spoke too hastily. But, in any event, the case of a relatively short rigid rod is certainly much different from a long flexible noodle, especially if the rigid rod has its end cut off while the noodle is much longer, curved, and can not capitalize on the free end pressure pointing directly into the person's mouth. My formal background is in fluid mechanics, and I've had lots of experience with lubrication flow. I am very confident that it is viscous shear and pressure flow in the narrow gap between the lips and the noodle that is responsible for the noodle suction effect.

 

[jbriggs444]

can not capitalize on the free end pressure pointing directly into the person's mouth.

If the noodle is stationary then the portion not pointing directly into the mouth is irrelevant and there is still a net pressure surplus on the side facing directly away from the mouth. If the noodle is in motion then centripetal acceleration is required, but that means that the noodle is already in motion as a result of the pressure differential.

 

[Stephen Tashi]

I am very confident that it is viscous shear and pressure flow in the narrow gap between the lips and the noodle that is responsible for the noodle suction effect.

People who have an attraction to classical mechanics will find it more attractive to explain the situation without using fluid flow. Can we think of an experiment that would highlight the critical role of pressure flow?

Suppose I imagine a cylinder partially inserted into a chamber so one end of the cylinder rests on the flat floor of the chamber (allowing no air between that end of the cylinder and the floor). The other end of the cylinder is outside the chamber. The cylinder passes through a round hole in the top of the chamber that allows no air between the sides of the hole and the cylinder. An explosive charge is set off in the chamber. Does classical mechanics predict the cylinder will be blown out of the chamber? I think the mechanics of rigid bodies doesn't predict any difference between the behavior of such a cylinder and the behavior of a cylindrical column that was cast as an integral part of the chamber.

 

[Chestermiller]

If the noodle is stationary then the portion not pointing directly into the mouth is irrelevant and there is still a net pressure surplus on the side facing directly away from the mouth. If the noodle is in motion then centripetal acceleration is required, but that means that the noodle is already in motion as a result of the pressure differential.

Are you saying that you are not willing to accept a fluid mechanics explanation of what is happening?

 

[Chestermiller]

People who have an attraction to classical mechanics will find it more attractive to explain the situation without using fluid flow. Can we think of an experiment that would highlight the critical role of pressure flow?

Suppose I imagine a cylinder partially inserted into a chamber so one end of the cylinder rests on the flat floor of the chamber (allowing no air between that end of the cylinder and the floor). The other end of the cylinder is outside the chamber. The cylinder passes through a round hole in the top of the chamber that allows no air between the sides of the hole and the cylinder. An explosive charge is set off in the chamber. Does classical mechanics predict the cylinder will be blown out of the chamber? I think the mechanics of rigid bodies doesn't predict any difference between the behavior of such a cylinder and the behavior of a cylindrical column that was cast as an integral part of the chamber.

Can you please provide a diagram?

 

[jbriggs444]

Are you saying that you are not willing to accept a fluid mechanics explanation of what is happening?

I have seen no supporting reasoning for the mechanism that you have offered. So no, I do not accept it.

 

[Chestermiller]

I have seen no supporting reasoning for the mechanism that you have offered. So no, I do not accept it.

What would it take to convince you? The. derivation of the basic equations? The solution to the equations? Or what?

 

[jbriggs444]

What would it take to convince you? The. derivation of the basic equations? The solution to the equations? Or what?

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.

 

[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.