Ok, I said I'd make a spreadsheet to figure out the velocity of floodwaters, so here it is:
It's just a quick and dirty calculation, assuming a triangular river cross-section, and absolutely not taking into account that the slope of the riverbed at its normal height and the slope of the adjacent area might not be the same, but it'll get you close enough for game purposes.
Note that if you already know the width, depth, and slope of a river, you can use the flood calculation pages to work out the velocity; just fill in the yellow areas and the green area will be your output. It doesn't even have to be a flooded river, just any flowing water with known parameters. The other cells in the spreadsheet are really just intermediate calculations that I didn't bother hiding. It's just easier that way. Besides, this calculation is a lot more straightforward than the first two pages, so a couple of unimportant but visible cells isn't going to busy up the spreadsheet too bad.
All that said, I was going to write a post working out all the details of meandering rivers. Meanders follow certain mathematical rules, and knowing them can help you draw more realistic rivers. But I'm not going to, because this guy has already done it. Thanks, Dave Richeson.