I've got an inground swimming pool, and was inspired by an ill-formed question that was recently posted. I would like to non-invasively measure the volume of water my pump is circulating through the pool over a given period of time. By non-invasively, I mean I would rather not have to hack into the plumbing and embed a sensor into the stream, but rather I'd like to measure it inferentially somehow (e.g. perhaps the water current actually has an electrical current that can be measured through the PVC pipe with a hall effect sensor an an instrumentation-amp — not to bias the answers or anything).
For the sake of bounding the problem with some requirements, I'd be happy with an accuracy of ±1 gallon/min and a component cost of less than $100. To be clear though, these are artificial requirements, since I just want to build something like this for myself.