This study compares three approaches to deriving the downstream hydraulic geometry (DHG) relationships: one by Leopold and Maddock (1953), a second by Huang and Nanson (2000), and the third in this study. The DHG relationships are the power function relationships between the downstream discharge and various variables, which include the flow velocity, channel width, channel depth, channel slope, and roughness coefficient. The DHG relationships can be described using a set of equations, including the continuity equation, flow velocity equation, and sediment transport equation. The derived relationships are then compared with the empirical results from previous studies worldwide, as well as those from two basins in Korea. As a result, first, all the theoretically derived exponents for peak velocity are found to be very small at around 0.1. This result supports the assumption that for a given rainfall event, the peak velocity in a basin remains unchanged. Simple regression analysis in this study also confirms that the change of peak flow velocity downstream is statistically insignificant. Through this, the assumption of a constant flow velocity within specific storm events may hold a certain degree of validity. Second, the range of the exponent for the channel width is found to be rather smaller at (0.4–0.6) than the those of the other two exponents. The range of the exponent for the channel depth is found to be (0.2–0.6), while that of the peak velocity to be (0.0–0.4). Possible reasons for this tendency have also been investigated in several studies, but have not yet been universally accepted.