In this paper we present the calculations of the time development of the magnetisation generated by the selected fluid layers and the total fluid volume in the rotating sample. It is assumed that the Couette flow model describes the angular velocity distribution of the fluid between the rotating concentric cylinders. The sample is placed in the external magnetic field gradient, where the component perpendicular to the rotation axis is the parabolic function of the distance from this axis. We discuss the shape of FID signals and NMR spectra for different values of the parameters describing the flow of the fluid. In addition, the special case of the constant magnetic field gradient is presented. The dependence of the amplitudes of the rotational sidebands in the NMR spectrum on the parameters of the external magnetic field inhomogenity is discussed as well.