It's common for shorter/smaller conveyors to assume a high friction coefficient of .75-1 on which to base the motor size. That's a lot but when dealing with a small motor it doesn't hurt you/cost much to oversize the motor by a factor of 2+.
You're still approaching the problem backwards. You need to figure out or specify how much mechanical energy/power you have available, and then you simply match the generator to it. @DaveE gave you most of the answer and how to figure that out in Post #5.
For the generator selection; there...
Fair enough, guys. Elevators too. What triggered me is that lack of understanding of mechanical advantage is the secret sauce in that classic pmm. @berkeman told me that he's in a pm discussion with OP and OP has something legit in mind for storing the energy.
BTW, I'm willing to humor the OP for a bit because they seem willing to learn but this still looks like the old classic pmm to me:
motor -> pulley -> generator -> Profit!
The wiki might be enough. It's a pretty simple/straightforward concept:
https://en.m.wikipedia.org/wiki/Mechanical_advantage
The key is simply recognizing that conservation of energy always applies, so you can't just assume if you spin at nameplate rpm you'll generate nameplate power...
In order to find that answer, you need to design/solve the whole cycle. I dont think it has a simple answer and I'm skeptical that the way you are using simplifying assumptions will work. For starters:
Point 1: Top of cold column. 90C, 1Bar.
Process 1-2: Adiabatic compression through 1,000 m...
You're not giving us all the details of the cycle and making us guess. We don't like that. We can't tell if the numbers work unless we see them in the context of the rest of the cycle.
What is your next step? It would be better if you gave us a diagram with all the states and processes labeled. Those two processes alone don't tell us much in isolation.
Well you haven't connected that in any way to the first part. You didn't say anything about P0.
I'm skeptical that you know how to design a thermodynamic cycle, because you haven't even started/aren't trying. You're just pointlessly manipulating disembodied equations.
No. If you can design a steam cycle you can design this one too. But if you have trouble, we can help you through it(that's PF's mission). Regardless, your diagram has no numbers so we couldn't answer that even if we wanted to!
You have four states associated with the four normal processes in...
He's assuming an oxymoron: that an incompressible fluid can have variable density, so the density differences (weight difference between the water columns) would drive the flow.
That is the correct conservation of energy statement, showing that there is no inequality/"too much energy". The details....well, you'd need to design the cycle. It's not a simple/single equation, you need to analyze the state of the water at every point in the cycle.
Note though that...