You can google and find multiple sources of what the definition of slip is, I used this one but all the definitions are the same (quote below)
http://www.halepropeller.com/PropellerTerminology.html
Prop slip definition:
I said "the higher the prop slip, the higher the thrust" and I think this is correct.
If the vessel speed is constant, if we increase rpm, the theoretical distance the prop should travel in one revolution INCREASED. This accelerates more water backwards and increased thrust AND by the definition above, this also increased the slip ratio.
"
If the vessel speed is constant, if we increase rpm"....
here is where we are having the problem.... what you are doing is,
increasing the rpm to get the higher thrust, and yes, the slip is also being increased, but it is only a by-product of the action, dependent not on the amount of thrust, but on the size of the blades, the pitch of the blades, the rpm, and the restriction of the forward movement of the vessel. one needs to examine all these things in an attempt to measure the slip that a prop has. "
thrust" is only measured as the amount of force the prop developes as it turns at any given rpm, and makes no difference at all how much the prop is slipping.... although it needs to be noted that if you have too high of percentage of slip, it means that the thrust is lower...
and yes, IF the boat hull is restrained in some manner, such as towing an object, the prop slip percentage will increase quicker than the thrust will, when more rpm/power is applied... the prop slip will actually increase even if the rpm remains constant, and if no gain/loss of rpm, the thrust will also remain constant, even when the slip increases.
the vessel speed will naturally want to increase when more rpm is applied, and IF the vessel is allowed to run free and not be restrained when the rpm is increased, percentage of slip will increase, but at a
slower rate, while the amount of available thrust will quickly rise and be restrained only by the amount of throttle given
and then, if you were to change to a fat bladed prop with very little slip, you can get just as much or more thrust with even less rpm and less percentage of slip.... it should be clear that slip and thrust are not related, but due to the medium that the
propeller operates in (water), you can have/create slip without any thrust, but you can not have thrust without at least some small amount of slip.
slip is largely an undesirable and energy wasting characteristic, but because it is always present in this usage and cant be eliminated and is hard to predictably measure, it has allowed a whole industry to grow from the science of propeller design and theoretical formulas, in an attempt to find a way to use the slip to its best advantage in an attempt to save/create more energy from it.
slip is the wild card in the equation, and without propeller slip, the formula for sizing props to a boat would be as predictable and simple as choosing gear ratios for an automobile... where the wheels dont normally slip.
or think of it this way... how would you know what is the proper gear ratio you would need in a car if you were forever driving around with the wheels spinning and slipping in the mud?... there are a lot of variables that need to be addressed before one could come up with a reasonable choice, and it would not work efficiently for all speeds and rpm ranges that one wants to use... or if one decides to tow a trailer thru the slippery stuff also...