There is a law on this. It is called the law of continunity, or the law of mass continuity.
the amount mass flowing in the stream is density*areastream*velocity.
So if velocity of a falling stream increases, what happens to the area of the stream?
A continuous stream of water is flowing out of a faucet and falling into a sink below. Explain why this stream of water is narrower at the bottom (near the sink) than at the top (near the faucet).
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