No Site would give out the design for free except this one and especially when you are with engineer is Terminator to help you out.Just give me teh specification like size and capacity all and I'll chuck out the formula for you.It's a free deal. Just tell me a few details, What's the out put do you want? What's the rate of flow you want? What capacity of output is the steam outback is of.

The water wheel would be moving with the force applied by the water flow.So the energy of the water flow is the driving force. Now the relation between Energy and Moment of inertia and angulat velelocity is E=1/2I*w^2 Where E is the kinetic energy of the flow and I is the moment of inertia of the Wheel = 1/2 MR^2 Now the energy Rotational kinetic enegy of the Wheel is derived from the stream flow. Now the rate of flow is Q=AV Kinetic energy of flowing water is 1/2PQV^2 Here P is the density of water and Q is rate of flow and V is the velocity of flow. Now,putting Q=AV KE=1/2PAV^3 Now equating both the equations we get I/4MR^2W^2=1/2PAV^3 =>MR^2W^2=2PAV^3 Taking all SI Units P= 1000Kg/M^3 So The Radius or the size of the Wheel is dependent on mass You said the surface flow is 10 feet isn 5 secs ie 3 Meters in 5 sec so the velocity is 0.6 mts /sec so we can replace the value in our formula MR^2W^2=2000A(0.6)^3 =>MR^2W^2=432A Now A is the area of flow. Now you have to play around with 4 things Mass,Area,Radius and Angular velocity. If you want your Water wheel to rotate at 1 rev?minute ie 2piR radians per second, You'll get 6.28R/60 = speed of revolution in Mts /sec Now the formula reduces to 0.010955R^2 *R^2*M=432A Now MR^4=432A/ =39434.048A Now teh area of water flow would be the area of the cup surface or the flat surface. Asuming it to me 1feet^2 i.e 0.09 meter^2 we get MR^4=3549.4 Now we are only left with mass and radius. Here let the mass be 10Kgs You get a wheel radius of 4.3 mts If you go for a 100Kg Weight,The radius will be in between some 2.2 mts. I'd advise you to go.Id advise you to go for the design where you use massive wheel of smaller radius. Trust me.They are easy to maintain. The above design is based on a lot of assumptions.I didn't consider the variation in current and the friction between the moving parts. It will give you 10% error but,that much is good enough for a home made water wheel. The formula for you to play around is MR^2W^2=432A Please ask me in case of doubts.