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.

  • $\begingroup$ Is this an existing turbine, or are you designing a new turbine? $\endgroup$ – David White Mar 14 '19 at 2:52
  • $\begingroup$ @DavidWhite It is an existing (scale model) turbine that I built. $\endgroup$ – Gnumbertester Mar 14 '19 at 2:53
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    $\begingroup$ 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. $\endgroup$ – David White Mar 14 '19 at 5:42
  • $\begingroup$ 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. $\endgroup$ – Gnumbertester Mar 14 '19 at 15:25
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    $\begingroup$ There are published data on turbine and generator efficiencies. You can assume efficiencies from such data, and back-calculate maximum theoretical power from there. $\endgroup$ – David White Mar 14 '19 at 16:38

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