Divemaster, Wow, ok as a full time water wheel builder (
www.waterwheelplace.com )I sometimes get envolved in the gearing and generator setups ( currently building 2 now )so I see a lot of variables (primarly the water speed and depth) which make this kinda tough so let's say that your water speed is 7.3 fps (5 mph). Generaly a undershot wheel runs @ about 65% of the water's speed when under light load so the water will move the wheel's rim @ about 4.7fps. This means a 6' diameter wheel (6 x 3.14 = 19 ft circumference)will turn @ 14.8rpm when under light load. As you probably know you need to overspeed a pm motor about 7% to get the rated voltage out when using it as a generator so we want to turn the motor/generator @ 1340 rpm using a water wheel rotating @ 14.8 rpm to get 190v out of it. So... You are looking for about a 90 to 1 ratio.
By these same calculations we can see that if the stream is running @ 30 mph (flood stage) the wheel will be turning @ 89 rpm (under light load) which is pretty darn fast, and probably unsafe. I'm not really sure it would get spinning that fast due to the water turbulance from the blades lowering into and lifting out of the water but worth thinking about.
Ok, how wide to make the wheel. 190v x 15amps = 2850 watts of energy fed to the generator to produce 2850 watts of electricity (assuming 100% generator efficency)(I'm not sure hoe efficient pm motor/generators are) Before feeding the 2850 watts to the generator you must gear things up 90 to 1 which will rob about 15% to 20% of the water wheel's energy so the water wheel needs to produce about 3420 watts of energy @ the shaft to get the generator/motor up to 190v. You're going to need a very wide wheel to drive that generator, 10' wide at least using an undershot wheel. There are several reasons for this, first off while a well made overshot wheel can be 80% efficient @ converting the water's energy onto power an undershot wheel is only 10%-20% efficient. In addition to this an undershot wheel's head can be calculated as 1.5 times the depth the paddle goes into the water so you only have 15" of head to make the power if the paddle dips 10" into the water.
A better option may be to use a smaller generator or plan on using a lower voltage with that generator/motor. Your generator/motor will probably hit 90v @ about 600 rpm which would he high enough to minimize voltage drop over the 400' to your shop. If you're willing to put in the fairly large amount of civil engeneering required you could use a Poncelet undershot wheel (65% eff.) of an overshot wheel (80% eff.) Either way the process will be fun.
Below is a picture of an adjustable gearing setup currently set @ 114 to 1.
