The short answer to this is…
Rivers never stop flowing because they never run out of water.
Ridiculous, but that’s what it is. The long answer is that they do actually run out of water.. or those that do are called intermittent.
In the case of those rivers that run perpetually, there is enough land at a higher elevation in the watershed.. that at any one moment there’s still water on its way out. There’s also flow rates of ground in a watershed, and usually this slows the rate of water on its path from landing at a particular place as precipitation to entering a stream or river. These sponge like characteristics of ground have the effect of averaging out the water flow out of the watershed between those moments when precipitation is falling and when it is not.
And there are watersheds which *shed* their water quickly. All at once. These are more likely to sometimes go dry as they tend to not absorb water, and hence evacuate water in bursts downstream, closer to the time that the water came down as precipitation.
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