Analytic expression for partially-filled flow velocity in pipe of circular section

The pipelines with circular cross section are widely used in the pract ical engineering. It is necessary to determine the flow discharge and the velocity under the partially filled condition. Most of the existing formulations use hydraulic radius as a characteristic-length parameter to reflect the influence of cross-section shape. The studies indicate that the results calculated from these types of formulations represent poorly the actual flow characteristics,especialy when the flow depth reaches the top of pipe. Based upon the principle of hydrodynamics and the experimental study,the dyadic characteristics between the flow discharge and the degree of fullness for the partially fil ed uniform flow in circular-section pipelines are fully analyzed,and a more accurate expression using discharge as the shape parameter is developed.