Can water be made to flow through a pipe using only gravity and resulting in a higher elevation at the end of the pipe from its starting point? 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
 A: 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.
A: A perpetual motion machine is out of the question. You can't get something for nothing, but if you have a flowing stream of water coming down a hill in say a steel pipe, by use of a "Hydraulic ram pump" you can pump some water higher in altitude than where the water is entering the steel pipe. Look it up in google, see videos in youtube.com of this.
Boy Scouts built a Hydraulic ram pump using the water flowing down hill, down in the valley to pump water to a reservoir tank at the top of the hill to fight fires with. They placed a long steel pipe in the stream bed, built a little dam at the entrance to the pipe, (to keep the pipe filled with water) put the ram pump at the bottom (a pair of spring loaded valves) and a much smaller pipe going up to the tank at the top of the hill. When the spring loaded valves were "Tuned" correctly the water coming down the hill would accelerate faster and faster until the velocity would overcome the spring of the first valve and it would slam shut, stopping the water stream suddenly, it's momentum would cause suddenly cause the "Hydraulic ram pressure" to rise exorbitantly(Very high psi). The second valve (going up to the hill top tank) would open under this pressure, and release the pressure up the hill into the tank. With the pressure relieved, the maim (First valve) would open due to the spring, and would allow the main mountain stream to start flowing again, until it's velocity was high enough to once again over come the spring on the main valve, and start the hydraulic ram cycle to start all over again.
See it in Wikipedia, google, youtube.... very fun and useful if you need one. 
A: I have done this before and am getting ready to do it again. The creek that runs by my house comes from uphill. Not steep but gradually uphill. As it went through a culvert under the road I arranged the rocks so that the flow was concentrated in one spot. Then I used a 6" elbow (probably 45 degree would be better than the 90 I used but my results were perfect anyway.). After a length of 6" pipe (which I attached to the elbow) I reduced it to 4".Then every length of pipe (PVC) from there on I reduced till I ended up with a 1" or half. It was a lot of pressure so that I could run the pipe up the embankment. Then I put an on/off spigot on the pipe so it wasn't constantly on. I found though that crayfish can get stuck in the pipe so next time I'm going to put screen or hog wire (and secure it with a huge hose clamp or something) so I don't hurt any crayfish again. Worked like a charm. Have fun and goodluck, Cathy  
