Water pressure & amount of flow?
Just a quick pass at this...
Pressure is easy. The overwhelming factor is depth. Pressure/depth is about 14.7 psi per 33 feet depth.
Given that there is a 3" choke point at the end of a 12" diameter run, pressure loss through the 12" section is porbably small, possibly negligible.
That said, a starting point would be to determine flow through the 3" section at the pressure due to the depth of the pond. You might be able to find literature giving the headloss coefficients of the fittings and pipe. Machinery's Handbook might have some of this.
Flow is proportional to the SQUARE of pressure. To get 2x the flow, you need 4x the pressure.