Power is measured in Watts (W), which is one Joule (J) per second; distance or displacement is measured in metres, and time is measured in seconds.
Power (W) = Work (J) / Time (s)
Power (W) = Force (N) x Displacement (m) / Time (s)
And because displacement travelled over time is called speed, or velocity, v (m/s), we can simplify this further as follows:
The force exerted on the turbine is as follows:
so Power (W) = Hnet (m) x 𝛾 (N/m³) x A (m²) x velocity (m/s)
Power (W) = Hnet (m) x 𝛾 (N/m³) x Q (m³/s)
This is the power supplied to a turbine. If the turbine were 100% efficient, it would also be the power delivered by the turbine to the turbine shaft. No mechanical device is 100 % efficient, but water turbines have high efficiencies.
If the turbine efficiency is η, the turbine output power is
Pt = 𝛾 H Q η
Watts are a rather small measure for hydropower, so this value is divided by 1e3, 1e6 or 1e9 to get kilowatts, megawatts or gigawatts.
(1e3 denotes 10³, for example)