New experimental results, and a plausible theoretical understanding thereof, are presented for the flow-induced currents and voltages observed in single-walled carbon nanotube samples. In our experiments, the electrical response was found to be sublinear-nearly logarithmic-in the flow speed over a wide range, and its direction could be controlled by an electrochemical biasing of the nanotubes. These experimental findings are inconsistent with the conventional idea of a streaming potential as the efficient cause. Here we present Langevin-equation based treatment of the nanotube charge carriers, assumed to be moving in the fluctuating field of ions in the flowing liquid. The resulting ``Doppler-shifted″ force-force correlation, as seen by the charge carriers drifting in the nanotube, is shown to give a sublinear response, broadly in agreement with experiments.