I saw my father once developing a liquid flow sensor, by that time was not water, but gasoline.
He was trying to measure the car gas consuption, you know, 20 years ago there was no comnputers on board like today.
He just used a differential temperature measurement method, that was nothing more than insert a PTC(or NTC) inside the pipe to be under flow and another also inside the pipe but just in contact with the fuild.
When no flow accured, both PTC were under same temperature and the differential between both was zero. When one of then as under flow, the heat was extract from it, cooled much more than the other and now the differential between both was enouth and proportional to measure the flow intensity.
I'm not sure how precise is this method.
Note: My father gave up of this project later, not sure why :roll: