A database containing more than 16,300 discharge values and ancillary hydraulic attributes was assembled from summaries of discharge measurement records for 391 USGS streamflow-gauging stations (streamgauges) in Texas. Each discharge is between the 40th- and 60th-percentile daily mean streamflow as determined by period-of-record, streamgauge-specific, flow-duration curves. Each discharge therefore is assumed to represent a discharge measurement made for near-median streamflow conditions, and such conditions are conceptualized as representative of midrange to baseflow conditions in much of the state. The hydraulic attributes of each discharge measurement included concomitant cross-section flow area, water-surface top width, and reported mean velocity. Two regression equations are presented: (1) an expression for discharge and (2) an expression for mean velocity, both as functions of selected hydraulic attributes and watershed characteristics. Specifically, the discharge equation uses cross-sectional area, water-surface top width, contributing drainage area of the watershed, and mean annual precipitation of the location; the equation has an adjusted R-squared of approximately 0.95 and residual standard error of approximately 0.23 base-10 logarithm (cubic meters per second). The mean velocity equation uses discharge, water-surface top width, contributing drainage area, and mean annual precipitation; the equation has an adjusted R-squared of approximately 0.50 and residual standard error of approximately 0.087 third root (meters per second). Residual plots from both equations indicate that reliable estimates of discharge and mean velocity at ungauged stream sites are possible. Further, the relation between contributing drainage area and main-channel slope (a measure of whole-watershed slope) is depicted to aid analyst judgment of equation applicability for ungauged sites. Example applications and computations are provided and discussed within a real-world, discharge-measurement scenario, and an illustration of the development of a preliminary stage-discharge relation using the discharge equation is given.