Why do rivers not run out of mud?

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Since the Mississippi flows into the ocean and carries all that mud with it, why is the river getting deeper or wider over time eventually disappearing? Also where does its water come from?

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Rivers do get deeper over time.

The Grand Canyon is the result of thousands of years of the Colorado river digging down into the ground.

As to where the water comes from, that’s called a ‘watershed’ and it’s usually rain over a large area that drains down into the river, or snow that melts and flows down the mountains into a river.

So long as there is ground above the water, that ground will be washed into the river and can replace mud that is washed away. This is called erosion. This would only stop if everything eroded to make the world completely flat, but this would be disrupted by plate tectonics.

An rivers get their water from the water cycle you learn about in elementary school. Water flows into the ocean, it evaporates, becomes clouds, the clouds rain on the land which then becomes the river.

It does get wider and deeper upstream where it is much steeper. And this mud that is eroding away from the mountains does get deposited on the riverbed where the flow is calm. So rivers like the Mississippi does get shallower over time and naturally changes direction fairly regularly. But it will take quite a long time for the Rocky Mountains to erode away completely and end up in the Mississippi river delta, although it is slowly happening.

The Mississippi has lots of tributary rivers…. Ohio, Missouri, etc. The watershed covers pretty much half of the USA. So anywhere rain falls in that area will eventually end up in the river and the Gulf of Mexico.

https://en.wikipedia.org/wiki/Mississippi_River_System#/media/File:Mississippi_watershed_map_1.jpg

Rivers can move all the time. The lower Mississippi goes through relatively flat land, the river starts to meander (bend) as there’s not much of a downhill slope to follow. The river cuts into the outside of the bends and deposits silt/mud on the inside of the bends. Eventually some bends can meet and cut off the old course of the river, forming oxbow lakes.

https://www.thoughtco.com/oxbow-lakes-overview-1435835