cedarlakeinstruments:
That part right there tells me to expect development costs to exceed $10,000 USD.
Depends on how fancy a user interface you want, that's where usually most of the work goes. OP is not asking for app control (or worse: not just Android, but also an app for iOS!), that saves half the budget already.
The expectation of a cheap uncalibrated water flow sensor to be able to reasonably accurately reflect the volume measured by the main calibrated water meter, that's where it really goes wrong. Everything else is quite sensible.