I was thinking, in an open system, one could pump water up past a pipe's pressure capacity if you just pump it up to a reservoir to a height that is less than the pipe's pressure capacity, and then pump up the water further from that reservoir to the next one. The following picture describes what I am talking about.
My question is, can this be done in a closed system, where the reservoir is not exposed to the external atmosphere? Would it matter if a thick valve is used to try and isolate the succeeding columns, or would the pressure still transfer from the upper column of water to the lower column of water?
As it is a closed system, there would have to be a loop at each level so as the water is pumped up, a gas (water vapour) would be pumped down. Something like this: The white boxes are the reservoirs. The green pipes would pump liquid water up. The pink pipes would allow gaseous water vapour down. On each end of each pipe, you could have a heavy valve which can open and close. Actually, would such a valve be even necessary? With this configuration, the height of the column is now just the height of each pipe for pumping water up, right? But if that were the case, then you could just have a pipe that would go up, down, and then up again. Is the gas doing something or am I missing something?