The necessity of simultaneous measurement of the longitudinal T1 and transverse T2 relaxation times for monitoring the state of the flowing liquid during the study in the range of flow rate q changes by at least two orders of magnitude has been substantiated. A new method for measuring T1 has been developed. For its implementation, the design of a differential nuclear magnetic spectrometer has been proposed, which makes it possible to measure T1 in the entire range of measurement of flow rate q. The results of experimental studies are presented.