The velocity profile of a streaming hydrogen plasma with a temperature of 15 eV and a density of 3*1020 m-3 is measured by means of laser-induced fluorescence spectroscopy (LIFS). The LIFS method takes advantage of the fact that the wavelength of an argon fluoride excimer laser coincides with a transition within the singlet system of neutral carbon. The Doppler shift and width of the fluorescence radiation at 247.9 nm provide local values of the plasma velocity and the ion temperature. The measurements confirm earlier assumptions that the flow profile is determined by equilibrium of electrical forces and viscosity which allows one to extract information on the ion viscosity.