- #36
houlahound
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I'm impressed, but I see nowhere in the equation the optimal cooking time for spaghetti at STP??
I always use 10 minutes.houlahound said:I'm impressed, but I see nowhere in the equation the optimal cooking time for spaghetti at STP??
You're making me hungry.houlahound said: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.
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?Chestermiller said: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.
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).Low-Q said: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.
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 said: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).
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 said: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.
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.Chestermiller said:can not capitalize on the free end pressure pointing directly into the person's mouth.
Chestermiller said: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.
Are you saying that you are not willing to accept a fluid mechanics explanation of what is happening?jbriggs444 said: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.
Can you please provide a diagram?Stephen Tashi said: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.
I have seen no supporting reasoning for the mechanism that you have offered. So no, I do not accept it.Chestermiller said:Are you saying that you are not willing to accept a fluid mechanics explanation of what is happening?
What would it take to convince you? The. derivation of the basic equations? The solution to the equations? Or what?jbriggs444 said:I have seen no supporting reasoning for the mechanism that you have offered. So no, I do not accept it.
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.Chestermiller said:What would it take to convince you? The. derivation of the basic equations? The solution to the equations? Or what?
See the following quote about pushing on a wet noodle from the link https://en.wikipedia.org/wiki/Wet_noodle:jbriggs444 said: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 said: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).
This was addressed in a subsequent post.Stephen Tashi said: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 said:This was addressed in a subsequent post.
No. Post #52Stephen Tashi said:Are you referring to post #43 ?
Chestermiller said:No. Post #52
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 said: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 said: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.
Of course, that is wrong. The pressure differential multiplied by the cross section of the noodle is the net force that applies.Stephen Tashi said:As you indicated in another post, the small area of the free ends makes the net forces on them negligible.
jbriggs444 said:Of course, that is wrong. The pressure differential multiplied by the cross section of the noodle is the net force that applies.
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?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 said:It seems to me that the effects of "pressure" aren't easily analyzed as set of vectors.
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.Stephen Tashi said: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.
Chestermiller said: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.
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:Andy Resnick said: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.