# Finding force exerted on a turbine blade by water flow

I am trying to find the maximum theoretical rotational power of a turbine from the following quantities: $$\omega$$, $$r$$, $$\gamma$$, $$I$$, and $$t$$.

This is in an experimental setting, not an assignment, so I am not sure if I am missing any necessary quantities.

My problem: I know that $$P=\tau\omega$$, but I am having trouble finding torque in this scenario. More specifically, I have $$r$$, but I do not know how to go about finding $$F$$. I have $$\gamma$$, which is the angle between the turbine blade and the water inflow vector. I would use this once I find $$F$$. The only forces on the rotating bodies are water inflow and centripetal force. I did some research and found that centripetal force would be negligible in this case as the blades are rigid bodies.

I have velocity and mass flow rate, although I cannot find a formula to find impact force on a water turbine blade, $$F$$.

Any guidance as to how to find $$F$$ would be greatly appreciated.

I know that once I find the power of a single blade, I can calculate the rotational power of the turbine.

• Is this an existing turbine, or are you designing a new turbine? – David White Mar 14 at 2:52
• @DavidWhite It is an existing (scale model) turbine that I built. – Gnumbertester Mar 14 at 2:53
• If you can hook this turbine up to a generator and put it into service, you could measure the electrical power output and back your way into an answer. – David White Mar 14 at 5:42
• Thank you @DavidWhite. I believe that can work, however, I am wondering (and probably should have included this in my question originally), how to calculate maximum theoretical power. – Gnumbertester Mar 14 at 15:25
• There are published data on turbine and generator efficiencies. You can assume efficiencies from such data, and back-calculate maximum theoretical power from there. – David White Mar 14 at 16:38