Stomach and intestines are surrounded by a serious amount of blood vessels, and liquids (water, alcohol) pass through the lining into the blood relatively quickly (within half an hour I believe). Nutrients in the food may take up to 24 hours to be broken down by the acids and enzymes and pass through.
Once in your blood, things reach your brain as quickly as your heart pumps them, probably less than a minute.
RE: dehydration-induced migrane, you may have a different mechanism, namely your body senses that water is incoming because it washed over your mouth, and your heart beats faster just because of that, increasing blood pressure and affecting your migraine.
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