Wow! At last I found a good question & that too with a sensible asker who is wiling to do the research part. Here is my answer just for you-
In case of a flood, the flow of river is most of the times "turbulent". Do a Google search on "turbulence"+"fluids". Also search for "Mechanics of fluids".
But, the force in case of turbulent motion is pretty complicated so, I'll explain it in case of a slower speed of flood when the flow is "streamline" i.e. when the flow is not irregular.
While flowing, the magnitudes of the velocities of streamliness are inversely proportional to the spacing between two streamlines in a plane. So, the narrower the hole is, more speedily the water will pass from it & thus, would exert more force.
Now, try and do a Google search on these topics-
1- Bernoulli's Principle
2- Torricelli's Law of Efflux
Those laws will help you with your report a lot.