Annecdotally I have a well-point (pump at top) that lifts water 2 to 3 metres. And I have an agricultural pump that sucks about 4m,and then pushes water up a hill the next 50 vertical metres or so. And its a pretty small pump.
Of course there's a limit. If there were no limit we'd have infinite free power generation.
Without looking up the actual equation, I would guess that this is never true (or at least practically never) when pushing water, because you’re not limited by atmospheric pressure.
When pushing you have to provide enough energy to move all the water in front of you, but if you do provide that energy the water will move. At some point I suppose the pressure will get so high the water will solidify in the pipe though?
You're missing the fundamentals of physics.
>At some point I suppose the pressure will get so high the water will solidify in the pipe though?
Before (way way way before) the water solidifies you will reach the maximum pressure that a given pump can deliver.
If you think the little 1/2 horse sump pump you can buy at home Depot will push a column of water up to the stratosphere then I have a bridge to sell you.
This is basic high school physics.