We present a series of detailed experimental observations of saline and turbidity currents flowing in a straight channel. Experiments are performed by continuously feeding the channel with a dense mixture until a quasi-steady configuration is obtained. The flume, 12 m long, is characterized by a concrete fixed bed with a uniform slope of 0.005. Longitudinal velocity profiles are measured in ten cross sections, 1 m apart, employing an ultrasound Doppler velocity profiler. We also measure the density of the mixture using a rake of siphons sampling at different heights from the bottom in order to obtain the vertical density distributions in a cross section where the flow already attained a quasi-uniform configuration. We performed 27 experiments changing the flow discharge, the fractional excess density, the character of the current (saline or turbidity) and the roughness of the bed in order to observe the consequences of these variations on the vertical velocity profiles and on the overall characteristics of the flow. Dimensionless velocity profiles under quasi-uniform flow conditions were obtained by scaling longitudinal velocity with its depth averaged value and the vertical coordinate with the flow thickness. They turned out to be influenced by the Reynolds number of the flow, by the relative bed roughness, and by the presence of sediment in suspension. Unexpectedly, the densimetric Froude number of the current turned out to have no influence on the dimensionless velocity profiles.