Ultrasonic Sensor to detect water flow
There are many types of ultrasonic flow flow meters such as in-line, clamp-on and Doppler flow-meters. As you cannot make any modification to your pipe, Clamp-on type is a good choice for your application.
Ultrasonic flow metes have three main part which are sensors (ultrasonic transducers), electronic part (it includes the MCU and Time to digital converter) and the spool piece.
In clamp-on type, first you must find suitable ultrasonic transducers that fit your requirements, and the rest is all about good measurement and processing of time difference between upstream and downstream signal from sensors (AMS, Maxim, TI and some Chinese company have special designed ICs for this purpose). You can mount sensors on your pipe, depend on the pipe size, one of the following configuration may be suitable for your application.

To have an accurate flow meter, apart from designing process, you need to calibrate it and calibration systems are two much expensive.