If an individual drinks a high enough volume of water in a short enough period of time, it is possible for them to dilute their blood to the point that they become seriously ill or die.
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This is sometimes referred to as water intoxication. Though incredibly rare, it is possible to drink enough water to dilute the blood to dangerous levels faster than the kidneys can filter it back out. This is one of the reasons for the development of sports drinks that contain salts and sugars.