A paddle switch is an easy and cheap method. IIRC "GEMS" makes inexpensive ones.
Vortex shedding is a bit more complicated but less intrusive.
A pressure dropping orifice or restriction of some sort and a differential pressure switch will work too. This is probably the least expensive way to go.
A rotating paddle wheel would work.
Alittle more info would help greatly. Is this water flowing in a river, a trough, or a pipe. If it is a pipe what diameter?What pressure?
There is a commercially available water flow switch if it is in a pipe.
Yes, many details of the actual configuration to be worked on are needed.
Vertical or horizontal or both if in pipes, existance of a pump, or float valve, the possibility of insertion of sensors in the flow or must be non-invasive, industrial or household environment, derivations/branches of flow, minimum flow to be detected, material, flexibility of pipes, buried or exposed, presence of air when flow ends, in general a detailed schematic of the system.
Differential pressure sensing, microphones, temperature sinking by flow, differential temperature sensing, buoyancy, insertion of devices inside pipe, optical windows... come to mind.
Does the water pipe end pours into an atmospheric reservoir ?
If yes, for 'cost effective', the simplest way, the stream exiting the pipe may hit a pivoting paddle that can bang on a bell when flow starts, and the same paddle returning to rest position when flow stops, can bang onto another bell.
There is dozens of ways, but will not be suggested until you come back with details of the installation.
Circuit planned for a domestic potable water, 1 inch diameter PVC pipe , initial water flow will be at very low pressure and once the water flow is sensed then the motor will be started manually and the water flow will be at good pressure. Next detection of now flow water will be on the motor flow water.
I trust this could help any one of us to design a circuit
"motor" or pump ? "now flow" or no flow ? Come on, put some effort to it !
The "next detection" cannot happen as the pump is on and there is flow at 'good pressure'. There is no change of state to be sensed to manually turn off the pump !
If you answer all the questions and expose your plan, something can be resolved. Seems you want a third world suction pump from municipal water mains with not much effort in digging and inserting things in pipe and perhaps keeping it undetectable. Your neighbors will not have water supply. You will. If a neighbor did not leave a faucet open to find out when will water be available again. Then your pump may suck air from the neighbor.
AC current detection for the pump can tell if there is water of not in the pipe. There will be low current if there is no water to pump and higher current if there is.
A plain ampermeter can show presence of water in the pump. Start it and check current. If low; turn it off and try later when current shows higher.