Any given river varies in depth from bank to bank as well as along its length. The same river will vary in current speed with certain stretches being faster than others. The two characteristics are related. To understand the relationship we can assume that a river contains a constant amount of water that moves downstream*. Another way of looking at this is that there is a steady volume of water flowing past any point in the river. This is actually the definition of current and a characteristic that is very important for a river. The term used to describe this amount of water in a river is flow.
Cubic meters per second (often abbreviated ‘Cumecs’) is a measure of flow in New Zealand and most countries using SI units. In the US they use cubic feet per second (CFS) as a measure of flow which is the same idea only smaller (there are roughly 30 CFS in one Cumec). Many rivers will have gauges in them that actually measure this flow. When such a gauge says that the flow of a river is 30 Cumecs, this simply means that if you were to capture all of the water that flowed past the point of the gauge in one second, it would take up 30 cubic meters.
In the absence of any new water coming into a river through tributaries, the flow will theoretically be constant along a river’s length. This provides us with a few handy relationships regarding a river’s depth, width, and the current speed. Whenever the river gets deeper or wider the current speed will decrease (so that the flow remains the same). Conversely, whenever the river gets shallower or more narrow, the current speed will increase. As you you gain experience paddling you will get to see this in action–deeper sections of the river will move slowly, a narrowing of canyon walls signify faster moving water and often bigger more violent rapids as a result.
This relationship is not only useful while paddling on a river, but also in other situations like trying to determine where to cross a river on foot. Whereas those with little experience in the outdoors will sometimes assume that the best place to ford a river might be where it is narrowest, application of the above rules shows the opposite. By looking for the widest part of the river to cross you’re actually ensuring that the current and/or depth will be minimized, and having less of either/both is what you’re looking for in a safe spot to cross.
To sum it up, deep and wide sections of a river are slower moving whereas narrow and shallow sections will be faster moving.