In reply to woolsack:
> Individual waterways that are 60% silted up have 60% less capacity to hold water. 60% less storage irrespective of actually getting the water away.
But the total volume of rivers is usually irrelevant, in that it is much smaller than the total volume of water that falls on the watershed in a 'rain event' (whether that is a single heavy burst of rain or a few weeks over a winter). If you took 'dredging' to extremes, you would need colossal storm drains that would dwarf the rivers.
Consider the River Severn. It has a watershed of 11,420 km^2. It also has an average flow of 61.17 m^3/s, and a maximum recorded flow of 533.48 m^3/s. Now if heavy rain (40mm) falls over only 20% of the catchment area, the total volume of rain is 91.36 million m^3, which is 414 hours or about 17 days at the average rate of flow (or just under 2 days at the highest recorded flow, which was presumably associated with flooding). The River Severn has a lag time of about 3-4 days according to Google (quite slow I think).
If you (hypothetically) dredged, straightened and canalised every mile of river and every major tributary so that water which previously took days to reach the mouth now took (say) 12 hours, you would need a channel that could take 2114.8 m^3/s, roughly the average flow of the Rhine, and ~17 times larger than the current Severn's average flow.
Water comes from upstream. If it comes quickly, you will get flooding; if it comes slowly you are fine.
PS if you assume a high flow rate of (say) 300 m^3/s, and that the time this water takes to flow out is roughly equal to the lag time (4 days), you get a total volume of ~100,000,000 m^3, fairly (surprisingly!) close to my estimated 'rainfall' event, which suggests my estimates aren't too insane.
Post edited at 17:24