There's a post I saw on reddit that points to the dimple on the side of a milk jug, and makes fun of all the people who don't know what that's for. In the comments are thousands of people giving dozens of different explanations, and all of them are wrong.
It is not there to indicate that the milk has spoiled by popping out due to gasses produced by spoiled milk. If there was enough gas to pop out the dimple, the whole jug would look like a balloon.
It is not there to provide structural integrity, like lateral support to prevent the bottles from crushing. The contents are under pressure, so if there was enough force on the jug from any direction, then the cap would pop off regardless of the shape in the sidewall.
The actual answer is that the dimple is added to ensure that all of the jugs contain the same volume of milk. Plastic jugs are blown into molds, and minor manufacturing variations over time would create jugs that hold different amounts of milk. Larger jugs would hold more than a gallon. They could just fill by volume, but consumers are wary of purchasing a bottle if it appears to be less full than the others. So they add the dimple to make it so that the level of milk is all the way at the top with minimal air between the milk and the cap.
You can verify this yourself by finding different jugs from the same supplier with dimples of different depths, or even no dimple at all. None of those other explanations would explain dimples of different sizes or jugs without dimples.
TLDR everybody is wrong. The milk jug dimples are added to ensure the jug contains the correct volume of milk.
You are correct that there is a connection to ensuring fill levels, but incorrect on it not being intended to provide structural integrity. It is both.
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