Propellers are an arcane science practiced in the dark of night by naval architects by candlelight. The sun is up and I'm no prop expert, but here are some generalities:
The diameter of a propeller is only one measurement of its size. Equally important is pitch--easiest visualized as the theoretical distance the propeller would move the ship forward in one revolution if there were no slip. A 34-foot pitch would move the ship 34 feet, not accounting for slip.
Slip is usually expressed as a percentage of the theoretical pitch distance. At 22+ knots, Titanic probably had 12% to 15% slip. Surprisingly, slip goes down as speed increases. But, it never reaches zero.
Another critical dimension is surface area of the blades. The more area, the more power the prop can impart to the water. Tugboats typically have blades with extremely large surface area that rotate extremely slowly. Race boats must keep engine revolutions high, so may have blades only an inch or two wide.
Increasing pitch has the theoretical benefit of increasing speed because the ship will go farther with each revolution of the prop. There is a negative to this, however. The engine must work all that much harder. At some point, the increase of pitch overcomes the engine's ability to keep the prop rotating at the desired revolutions.
One way to overcome this problem is to reduce the diameter of the propeller. That has the effect of reducing the surface area of the blades. Another way to accomplish the same thing is to make the blades narrower. The disadvantage in both cases is that a prop with less blade surface area can impart less thrust into the water.
There is quite an art and a science to picking the correct diameter, pitch and blade area for a given ship. And, the right prop for one day may be wrong on another. For instance, Titanic was lightly loaded on its maiden voyage. Its engines could have driven rather deep pitch props. On a fully-laden trip, however, the right prop would have to have been of lighter pitch.
-- David G. Brown