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I just saw a YouTube video about Non-Newtonian fluids where people could actually walk on the surface of the fluid but if they stood still, they'd sink. Cool stuff.

Now, I'm wondering: Could a pool of Non-Newtonian fluid stop a bullet? Why or why not?

If so, if you put this stuff inside of a vest, it would make an effective bullet-proof vest, wouldn't it?

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Yes, here is an example where they made a bullet proof vest by soaking Kevlar fabric in a non-newtonian fluid:

http://www.youtube.com/watch?v=LlEo5MbcaX0

The video is from 2006, I don't know if this has been developed further.

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This would be a great answer if you write about the contents of the video. –  David Z Jul 11 '12 at 22:05
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BAE Systems have already done this. Annoyingly there seems to be some problem on the BAE web server at the moment, but there's a description here with links to the BAE site. Alternatively Google for something like "liquid armour site:baesystems.com".

Dilatant fluids are very good at absorbing energy as forcibly shearing them requires evaporating the water between the particles, and this absorbs a lot of energy. There is more info about dilatant fluids in the answers to Why do non-Newtonian fluids go hard when having a sudden force exerted on them?

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Actually non-neutonian fluids are a bit heavy and massive with regard to their bullet stopping efficiency. They could work with other approaches.

This does not mean their tension surface is infinite. They are penetrable and a bullet applies huge surface tension

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