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Before I begin the question: I am in no way judging this movie, just happened to be casually watching it and saw the scene (referred to below) and thought to post this question.

The scene: Boy falls into a 'river of chocolate', there is a tube that sucks up the chocolate. The forces of suction are so great as to create a vortex, and when the boy is sucked up, it clogs the tube. Willy Wonka mentions that the chocolate is aerated by the 'waterfall' portion of the river to make it very light.

My thoughts: There are so many things wrong with this, but let's just entertain the fact that this is a kid's movie or fiction and that machines / gadgets within the factory could be extremely advanced (or highly developed) in terms of material sciences, usage of physics, engineering, process design and control, and various other technologies.

My question is a multi-part question as follows:

PARAMETERS OF THE QUESTION NEED TO BE CALCULATED FIRST: In order to answer this and make sure we are all using similar parameters I will obviously have to edit this question at some point in the future, however, for now, assume the following:

  • Tube length:10 m
  • Tube height above liquid: 8 m
  • Tube below liquid:2 m
  • Tube internal diameter: 40 cm
  • Material tube is constructed of: Bullet-proof glass (or better?) with stainless steel reinforcements / rings.
  • Tube wall thickness: ?? (start with bullet proof glass)
  • Property of liquid: 'liquid chocolate aerated by a waterfall'. Here are two resources - industrial chocolate manufacture and use and bubble included chocolate.
  • Density of liquid: It is liquid chocolate, which has been aerated by a waterfall-type drop, so it has very tiny bubbles of air to make it 'lighter', i.e. it has been 'micro-aerated'. I am going to go with 0.7g/cm3 as per the info from 'industrial chocolate manufacture and use'.
  • Temperature & Pressure of room: usual - say 25C, pressure at sea level.
  • Temperature of liquid: 30C (lower melting point of chocolate)
  • Mass of boy: 65kg (he's fat for his age).

QUESTIONS:

  1. What is the MINIMUM force needed to lift up a column of liquid chocolate by 10m under these conditions?
  2. Assuming that 10% extra force can be created before the tube gets 'stuck', what would be the resulting difference in pressure between the suctioned portion of the tube, and the chocolate (ie. boy is the blockage)?
  3. Would this not kill him / pop his eyes / cause severe breathing difficulties? Does the force of the suction need to be less once the chocolate has already been sucked up into the tube - ie. it is pulling up a liquid rather than creating a vacuum to suck up a gas and then a liquid?
  4. Assuming the tube is made of the material specified above, how thick would it need to be in order to allow for it to withstand the pressure difference without shattering. Note that there are reinforcing struts / metal rings.
  5. What velocity / speed of suction (assuming an unlimited supply of liquid chocolate, and a tube of given internal diameter, and a depth below the surface of 2m) would be required to form a vortex which is about 5m in diameter and 2m deep in the liquid.

I hope to see some answers regarding this as it is a weird scene in a weird movie.

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closed as off-topic by ACuriousMind, Kyle Kanos, Kyle Oman, yuggib, Ryan Unger Jun 26 '15 at 16:11

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – ACuriousMind, Kyle Kanos, yuggib, Ryan Unger
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ We need the density of the liquid chocolate. Remember that "lifting by suction" is really "pushing by the atmosphere"; this puts the maximum height you can lift the liquid as $h = \frac{P}{\rho \cdot g}$ ; for water and normal atmospheric pressure, that puts the height at 10 m. If liquid chocolate is more dense (it sinks) it will be able to lift less high. The vortex will further lower the inlet pressure I presume. Not sure I can visualize this part of the question... $\endgroup$ – Floris Jun 23 '15 at 16:28
  • $\begingroup$ Just ammended my question, assume 0.7g/cm3 density of the micro-aerated chocolate. I think the suction/vortex will change that, however, the vortex only appears after the initial suction is done, hence, it will not affect the minimum amount of force required to start. $\endgroup$ – Darren R. Jun 23 '15 at 16:37
  • $\begingroup$ You are concerned with the pump in Willy Wonka's factory when there are worse violations of science/physics in movies? $\endgroup$ – Kyle Kanos Jun 23 '15 at 17:40
  • $\begingroup$ Just to be clear: we're talking about the 1971 movie "Willy Wonka & the Chocolate Factory" starring Gene Wilder, not the 2005 movie "Charlie and the Chocolate Factory" starring Johnny Depp? $\endgroup$ – Daniel Griscom Jun 23 '15 at 22:51
  • $\begingroup$ @DanielGriscom Thank you for your comment. I was referring to the 2005 one starring Johnny Depp though I guess I might have to see the original as well if there is a similar scene. The problem parameters are specified in the question just in case they are different, I will defer to the 2005 version of this as that is the one I was initially referring to. I edited question to clarify. $\endgroup$ – Darren R. Jun 24 '15 at 2:46
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The physical absurdity - or at least highly hyperbolic situations - of most of Roald Dahl's scenarios is the essential Dahl - it's wholesale a part of his humor and his lack compliance with physical laws is, in this respect, quite deliberate.

Having said this, the "Great Big Greedy Nincompoop" disappearing up the tube is wholly possible, given the right kind of pump. He would likely not survive the ordeal, though.

A reciprocating pump, that completely seals its intake as it expels its output, can build up a near perfect vacuum in the tube above the doomed Augustus, so that it could support a column of liquid of density $700{\rm kg\,m^{-3}}$ with height $h$ given by $\rho\,g\,h=10^5{\rm N\,m^{-2}}$, or about 14m high. There is also a drag component in this, given by the Hagen-Poiseuille Equation when the fluid is flowing, with the pressure drop proportional to the fluid's viscosity, but this will simply govern his speed up the pipe: if the fluid is too thick, Master Gloop will slow down until the pressure drop owing to viscosity is small enough to support the fluid weight and that of Master Gloop. For the same reason, the depth of the pipe's intake below the lake surface influences only how fast doomed Augustus goes, but it won't influence the ultimate weight-supporting limit. When he reaches a height of $8m$, if the pump pulls near to a full vacuum, then the force pushing him upwards is equivalent to the weight of six meters of chocolate above him (the 14 meters maximum column height, less the eight meters tube height). For a $40{\rm cm}$ diameter tube, this corresponds to an upward force of $\pi\times 0.2^2\times 700$ kilograms of weight: the weight of about 90kg. This may just be supported by friction between Master Gloop and the walls, so he might not get quite to $8m$, but it would certainly be possible to raise him to a height of that order.

The last relevant variable here is the wall thickness: it needs to be enough to support the crush of the atmosphere around a vacuum. This is an engineering problem, and thick glass will certainly do this. The compressive force $F$ supported in the walls of a cylinder in the face of a pressure difference $P$ is found by drawing a free body force diagram on a arc section subtending angle $\theta$: the inward crush of $P\,\theta\,r\,\ell$ (for $\theta\ll 1$) on a such an arc of axial length $\ell$ and radius $R$ is offset by the normal components $2\,F\,\sin(\theta/2)$ of the compressive wall force, thus, if the wall is of thickness $t$, the compressive stress is $P\,r/t$. This works out to be only a mild requirement for $t$ of a few centimeters. For a one centimeter thick wall, the compressive stress is 20 atmospheres: well below the yield stress of glass.

In the tube, Master Gloop will have about eight seconds of consiousness if the pump does pull a full vacuum. He'll need to be gotten out of there within a minute or even less before permanent brain damage arises, but, given Dahl's undertext was that Gloop's brain was not a vital organ, he might have longer. He'll almost certainly need hyperbaric oxygen therapy for treatment for acute decompression sickness afterwards if he survives. Hopefully Wonka has installed a Gloop screen in the pump intake to prevent Master Gloop from being mangled by the pump's workings.

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  • $\begingroup$ A worthy answer! $\endgroup$ – Floris Jun 25 '15 at 2:55
  • $\begingroup$ Great answer.. would you like to try and say something about the vortex as well please? :) $\endgroup$ – Darren R. Jun 26 '15 at 1:17
  • $\begingroup$ @DarrenR. Fluid mechanics is not a strength of mine. In particular, the formation of vortices is a pretty complicated topic. If you google "Vortex Formation" and "Vortex Formation Numerical analysis" and the like, you'll find that the main techniques here are experimental and numerical. I'm not altogether sure what effect on vortices that the viscosity of chocolate would have. Usually one would design an intake like this to avoid vortices, as these can lead to air in the intake, which can make pumping difficult. $\endgroup$ – WetSavannaAnimal Jun 26 '15 at 8:43

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