Including new field data in the slope range of torrents up to 63%, an empirical equation is developed to express the mean flow velocity in terms of the flow rate, the slope and a characteristic grain size. The proposed equation is applicable over a wide range of flow conditions, including mountain streams and torrents with a slope range of about 1% to 63% and relative flow depths as small as about 0.4. For gravel-bed rivers with slopes below about 1% and flow rates up to 2400 m³/s, a similar equation with somewhat different exponents is presented. The alternative velocity equation can be transformed into a form similar to the Manning-Strickler formula; the parameter corresponding to Manning's n is shown to be a function of the flow rate, the slope and a characteristic grain size of the bed.