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Let's begin by making it plain that water does not weigh 8.34 lbs per gallon. A gallon is eight pints; ok, so what's a pint? Well, an English pint is twenty ounces, and has been since time immemorial. Generations of English kids learnt it by chanting "a pint of water's a pound and a quarter" in school. This makes an "imperial gallon" weigh ten pounds. An American pint is sixteen ounces. This makes a US gallon eight pounds.

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Q: I am aware that water weighs 8.34 pounds per gallon but where is the number derived from?
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