EDIT: Fixed the Base unit of water.
Did a post on the spell "Route the Turbulent River" and realized it was too big when I hit the post size limit.
The reason you need Size is because of the average size and flow rate of a river verse how much this spell can affect. Without Size this spell can affect 200 cubic paces of water.
While the spell is active how much of the flow rate you can overcome determines how much of the river you can divert. This is what the spell is targeting, since this is the "currents". Some fraction of that would compound over the duration giving you how big a diversion you created, which would be compared to the total volume of the river that is diverted after the spell expires, assuming it does not just dead end and create a side branch. To avoid that requires your split reach somewhere lower than the river with enough capacity to take the rivers volume up to that point. This would result in the original path becoming a side branch that eventually transitions into marshlands or a dead branch lake most likely (over a very long time period, talking years at the fastest).
Note that cutting through solid rock will not happen with this spell since you are talking about something that takes centuries or millennia. At best you will be cutting through rocky soil or clay (~10%), which would be a fraction of the lengths listed later which are for soft soil or sand.
Base 4 water is walking speed, while Base 5 is jogging/running speed. That is roughly a 4x increase, so without Size the spell could affect about 800 cubic paces per second of currents [using round number for ease of math]. Note that the maximum here is the flow of the river you are diverting, since you can not flow more water than is available. Even if there is more total capacity in a section you would rapidly burn through that and be left with the flow rate.
Let us compare that to the Nile, which is the greatest river in ME. A 1 pace long section of the Nile is on average ~36,600 cubic paces of water and flows at ~3,700 cubic paces per second on average (it is a very slow river). While the spell is active it could divert ~21.6% of the Nile's flow and cuts a path that could hold at best 1.1 miles of its total capacity every day. Moon last between 15 and 29 days depending on when it is cast verse the phase of the moon. If you are trying to take all of the Nile you would end up with a 16~31 mile side branch.
The Rhine is about ~3,800 cubic paces per second and ~4,400 cubic paces per 1 pace length. While active the spell could divert ~21% of the Rhine's flow and cut a path 9 miles at best capable of holding its total capacity every day. At best (again cutting through soft material) after a Moon you would have something that could divert all of the Rhine for 135 to 270 miles.
The Grand Rhone is about ~2,240 cubic paces per second. However getting historical numbers for its average volume per pace is proving difficult, since it has been so heavily manipulated to make it suitable for shipping and avoiding it being marshland. This is actually good and bad for the spell. Areas with strong buildup are basically immune, while those with minimal buildup are more vulnerable. Those sections of the Grand Rhone are the only area where this spell might work on a river without size, though it would most likely take the full Moon duration.
While comparatively tiny you are not diverting the Petite Rhone because it is through deep solid rock canyons. However a version of this spell with some degree of Unnatural and +1 Size could cause its water to flow up one of those canyon faces while it lasted.
Results with Size
- Nile: +2 Size would give you your max diversion. That would give you ~5 miles per day through soft terrain (~0.5 miles per day rocky/clay) of sufficient size to reroute the whole river. As the Nile is the only river I did math on with far larger capacity than flow, thought I would include why the flow is the limit. Its extra capacity would give you about 2 minutes of 4,000 cubic paces per second flow before it was all used and you were capped at the 3,700 cubic paces per second of the river.
- Rhine: +2 Size would give you your max diversion. That would give you ~43 miles per day through soft terrain (~4.29 miles per day rocky/clay) of sufficent size to reroute the whole river.
- Grand Rhone: +1 Size would give you 17.8% of your max diversion. You need +2 Size to hit 100%. The spell has no effect in strong (fitted stone) buildup and slow chipping through weak (rocky soil/clay) buildup like earthen berms.
- Petite Rhone: Spell has no effect. It would take an Unnatural version that could flow water up a cliff to do anything and only have an effect while the spell lasted.
Overall it looks like +2 Size is what is needed to fully divert the current of a river. More doesn't help you since you are moving water away faster than the river can replenish it and less gives you something around 10% (+1 Size) or 1% (no Size).