The present invention provides a system for measuring flow of a fluid through a line. In the system, a region of fluid along the line is isolated from pressure effects outside of the region. A source region contains a measurement gas in communication with the isolated region, such that the source means and the isolated region together define a fixed volume, and such that a change in volume of fluid in the isolated region produces a complementary change in the volume of the source means with a resulting change in the pressure of the measurement gas contained in the source region. Further provided is a reservoir in communication with the source means for containing a known volume of measurement gas, and means for pumping measurement gas from the reservoir. The pressure of the measurement gas in the reservoir and the source region is monitored. This pressure data is then analyzed to determine the volume of fluid in the isolated region.