Programmable Water (2003) (blikstein.com)

I think if no water leaks away it looks like it can be infinite, but the article mentions lots of leaks. Also, the amount of water doubles after AND, that could escalate into a problem unless excess can be removed somewhere...

The pressure head will likely fall off very rapidly with the number of gates.

You could probably build "amplifiers" down the line by adding more water to circuits with positive flow.

You can certainly plug them in complement style, so that water does not run when it's not switching (except for leaks), and that pressure does not drop from one gate to the other (but you must consider fan-in and fan-out).

You could install delay pieces between stages of your computer, like those Japanese fountain pieces that collect water and tip over when they get full. Put them all on one axle, and the different logic components of your stage will stay synched.

The concept of logic systems themselves have far preceeded the first electrical circuits. I am sure this was put to physical use somewhere in history, but to call it a "computer" would be kind of a stretch. Very doubtful in my opinion, certainly not a computer to any extend we would imagine one today.

What enables computers we know today is not just logical circuits - primarily, it's that we're able to pack a shit ton of them in a very, very small volume. Each processor today has close to a billion logic gates in it (assuming ~4 transistors per gate).

Well, the https://en.wikipedia.org/wiki/Antikythera_mechanism is arguably pretty computery and is thousands of years old.

To build something we'd consider a 'computer' requires a huge amount of conceptual background. Boolean logic, binary arithmetic, memory, Von Neumann architecture... and to be useful, it really has to exist in a society with lots of things being recorded and tallied on paper.

yeh the thing being programmed not same as thing title said was being programmed, am annoyed too