I'm doing a science project that involves moving water through a 2cm pipe with graphene aerogel capacitors in it, but I don't know how to get the water flowing through the pipe. Should I use a pump? The ones I search for online are $200 and not what I'm looking for. Is there a way to get the water to flow through or should I just use gravity?

Depends on how much pressure you need and what volume of water is involved.

 

I suspect something from a local arts and crafts store or even a local home and garden store could do the job (I'd probably look for a pump used in small fountains or indoor water features, like something you'd put on a kitchen counter or above a fireplace). Most of those can be found for less than $20: http://www.amazon.com/b?node=3735941

You could siphon if you bought some tubing.