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unbalanced props always cause vibrations...
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I disagree completely. I am sure a drastically unbalanced prop would matter, but balancing it "by eye" is good enough.
Try it for yourself. Cut down a prop as evenly as you can by eye with scissiors, it will not be any louder or vibrate any more than it did before you cut it down.
I have modified tons of propeller pumps and always go with a prop that is a bit too big and trim it down. The only pumps that vibrate or make noise are those where the hole in the magnet is off center.
It does seem logical that balance of the prop would be very critical, but close is good enough. I think this is due to the high RPMs of the pump. The weight difference of the prop being slightly off is insignificant compared to manufacturing inconsistencies in the magnet (look at how inconsistent the hole in a MJ magnet is... those can't be even close to balanced). Heck... the super glue you use to glue the tube in the magnet probably introduces more weight variation than cutting down the prop.
I think that balancing the weight doesn't matter at all - getting it close is important because you want the two blades to have about the same surface area. Inconsistencies in the amount of water each blade pushes would result in way more vibration and noise than a fraction of a gram difference between each blade.
Please try the exact experiment I suggest before you tell me I am wrong - build a mod, try it, then trim the prop down as evenly as possible by eye, and try it again. Is there more vibration or noise?