I am not a physics guy, so be nice to the layman, guys! Please note: not a homework type problem. This is a scenario being considered for real-world application.
I have not yet considered details like diameter of pipe on the decline, smaller diameter pipe on the incline, ratio of distance decline versus incline, etc. please feel free to fill in those blanks for me and make assumptions as appropriate.
Based on my initial research of related concepts, it appears gravity can in fact be used as a sort of pump to raise water from a lower to a higher elevation using only gravity over the distance and an initial boost from an electric powered pump from the lowest elevation into the pipe to get the process started. Do you concur with this assertion? And if so, please explain the process.
Would the following scenario accomplish this goal? Please fill in the blanks is with relevant calculations.
1000 foot distance, 10 foot decline evenly over this distance; followed by 100 foot distance, 20 foot incline evenly over this distance; copy entire 1100 foot distance including decline and incline and repeat beginning now 10 feet higher than original elevation; repeat multiple times.
Questions:
Is the assumed degree of decline reasonable? (10 feet decline over 1000 feet)
Is the assumed degree of incline reasonable? (20 feet incline over 100 feet)
Would the diameter of the pipe over the declining distance need to be greater and the diameter of the pipe over the incline and distance need to be smaller? If so, please address.
Would the rate of flow and speed of flow transitioning from the decline to the incline be reasonable?
What factors need to be considered for friction, drag, etc. as far as interior of the pipe and material the pipe is made out of and it's effect on flow of water?
Could a system of suspension wires similar to a suspension bridge effect minimizing surface ground disturbance, minimize cost of construction and simultaneously accommodate the sheer weight of the system plus water flowing through the pipe?
Additional questions:
Feel free to bring up other issues or questions I am not considering or listing herein. Thank you in advance for your input. DS
Best Answer
If my understanding is correct, you are hoping to design a tubing configuration that, once started (by a temporary boost from an electric pump), will pump water uphill without additional power input. Unfortunately, that would never work, as it would be a perpetual motion machine of the first kind, and would violate the first law of thermodynamics. Were it to be possible, then you could take the water flow out of the end of the pipe, use it to drive a turbine, and then generate electricity forever.
Now, if you are only hoping to briefly drive water to a higher elevation than you started, then that's quite likely possible with your system. Absent large amounts of friction in the pipe, if you start with it empty and fill it up from the lower end, the water will be moving fairly quickly once the leading edge had returned to the height of the entrance, and the momentum of the moving water would likely drive some of the water up that last 50 feet and out the upper end. However, inevitably the water flow would slow, stop, and reverse until the level equalized. A system that does this repeatedly is called a ram pump.