Unfortunately no one has mentioned the effect of "PITCH" on changing sizes of propellers.
What follows is a typical Engineers "back of the envelope" style of calculation. No claims for absolute accuracy but it's often good enough to avoid serious problems and show if you are moving in the right direction.
If the the propellers are geometrically similar, then doubling the the diameter will increase the cross sectional area of the cylinder of water that the propeller tries to push rearwards in one revolution by four times. But, doubling the diameter also doubles the pitch, so this cylinder is twice as long. Hence, doubling a propellers diameter would in this situation actually increase the volume (and so mass) of this cylinder by no less than eight times.....
In this situation doubling the diameter (and pitch) would result in astronomic increase in the power demand to maintain the same shaft speed. Using this idea, doubling the rate at which water is pushed rearwards only requires the propeller diameter to be increased by around a quarter.
I remember writing something along these lines in "Model Boats" a few years ago. I wanted to show that it was worthwhile to take a few propellers along when carrying out sailing trials on a new model. A slight change can have a drastic effect on a models speed and power consumption. Testing is the only way we can be sure our models are working well and it is never "obvious" which way to go. I remember changing down to a slightly smaller propeller, which allowed the electric motor to spin faster with less current drawn, yet still the model still ran at the same speed.
Glynn Guest