If it is an ideal case, assume No energy loss and all the potential energy convert to rotational energy of the turbine.

mgh=(1/2) I w[sup]2[/sup].

where m is the mass of the water flow into turbine, I is the Moment of inertia of the turbine, w is the angular velocity.

Since the water flow into the turbine is increasing all the time, then the angular velocity will keep increasing.

d/dt(mgh)=I w dw/dt i.e. dw/dt=(dm/dt)gh / (I w)

where dm/dt is the water flow into the turbine per unit time.

It means that the angular velocity of the turbine will keep increase if there is no energy loss.

However, in real turbine, there are internal impedance.

And for a turbine to generate electric power, we would like it to rotate at a constant angular velocity ( f=60Hz per seconds-- w=2*?*f).

The impedance of the turbine should produce an angular acceleration = -(dm/dt)gh / (I w) ,

so that the turbine can be rotated at a constant angular velocity at a fixed (dm/dt) and h.

The system should keep dm/dt at the same rate.

For different height of the hole , different turbine machine should be designed so that the angular velocity will be the same, but the output electric power will be different.