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The speed of a river is affected by the amount of friction slowing down the water and the grade or fall of the river.

The amount of friction is determined by how rough the bed or wetted perimeter is, and how big the perimeter is.

A wide shallow river or a very deep and narrow river with the same volume and grade will be in contact with similar areas of river bed, causing the same amount of friction. But a river with a semi circular shape in cross section and the same volume and grade will have less contact area with the river bed and will therefore have less friction and be faster.

The steeper the grade of the river, the faster it will flow.

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Q: If a deep river is faster why doesnt the larger wetted perimeter increase friction and slow down the speed of the river?
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