Looks an awfully complicated equation your energy balance.

The gravitational potential energy is converted to two types of energy, if we neglect friction and second order effects like vena contracta.

1) The ??????? Energy of the moving water at the exit

2) The power takeoff of the turbine.

1) is determined by the water velocity v = √(2gH) by Torricelli's theorem. (This can also be derived from Bernoulli's theorem.)

2) The power takeoff is given.

Does this help?