Methods used so far to assess the flow velocities of the water commonly assumed to be responsible for forming the major outflow channel systems on Mars have relied widely on various versions of the Manning equation. This has led to problems in allowing for the difference between the accelerations due to gravity on Mars and Earth and for the differences of scale between Martian floods and most river systems on Earth. We reanalyze the problem of estimating water flow velocities in Martian outflow channels using equations based on the Darcy-Weisbach friction factor instead of the Manning n factor. We give simplified formulae appropriate to Mars for the Darcy-Weisbach friction coefficient as a function of bedrock size distribution. For a given channel floor slope and water flood depth, similar mean flow velocities are implied for a wide range of values of the ratio of bed roughness to water depth relevant to Martian outflow channels. Using a recent rederivation of Manning's equation based on turbulence theory, we obtain a new value of 0.0545 s m-1/3 for the Manning n coefficient appropriate to Martian channels and show that previous analyses have generally overestimated (though in some cases underestimated) water flow velocities on Mars by a factor of order two. Combining the consequences of this flow velocity overestimate with likely overestimates of flow depth from assuming bank-full flow, we show that discharges may have been overestimated by a factor of up to 25, leading to corresponding overestimates of subsurface aquifer permeabilities, rates of filling of depressions with water, and grain sizes of sediments on channel floors. Despite the availability of an improved value for the Manning n coefficient for Mars, we strongly recommend that modified forms of the original version of the Manning equation should be replaced by the modern form or, preferably, by the Darcy-Weisbach equation in future work.