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).
- What is the MINIMUM force needed to lift up a column of liquid chocolate by 10m under these conditions?
- 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)?
- 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?
- 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.
- 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.