What are some ideas for experiments on a dripping faucet?
If you have a high speed camera, determining what the water does when it strikes different surfaces: water surface (there are thousands of photos of that already), flat hard surface, flat soft surface, etc.
Is the path for the drips straight down? Put different objects near the path(hint, change air flow caused by the falling drop).
determining the smallest, and largest size of drops that will drip. (you can do this by counting the drops in a given time, and measuring then the volume of liquid collected