My understanding is that the purpose of the overflow holes is twofold–
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To allow water to flow down you drain faster.
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To prevent overflow if the sink is filling faster than it's draining.
If #1 was true, wouldn't you also see the overflow holes on kitchen sinks?
If #2 was true, wouldn't you also see the overflow holes on bathroom tubs?
So–why do I never see overflow holes on tubs or kitchen sinks?
Edit: To clarify, my familiarity is primarily with sinks/tubs in the United States.
Best Answer
Most sinks and tubs in North America do have an overflow device, it's simply cleverly hidden.
Bathroom sink overflows (which aren't always present -- ours lack them) are visible as North American bathroom sinks are almost universally single basin. However, North American kitchen sinks are often double basin -- and in a double basin sink, the divider doesn't extend up to the full height of the sink, so the two sinks use each other for an overflow. A rather clever design if you ask me, provided you aren't filling all the basins up that is.
As to the bathtub? There's usually an overflow hiding in the drain-stopper selector mechanism.