Nonuniform Laminar Free-Surface Flow

Industrial flow processes involving molten substances or other highly viscous liquids frequently make use of conveyance by open channels. A one-dimensional analysis is undertaken of laminar flow in horizontal open channels of rectangular cross-section. A closed-form analytical solution is obtained for the non-dimensional surface profile of type H₂ and H₃. The non-dimensional profiles are independent of the Reynolds number of flow but are a distinct function of the aspect ratio of the flow but are a distinct function of the aspect ratio of the flow cross-section. The analytically predicted profiles are found to be in good agreement with the results of experimental observations, except in the immediate vicinity of the critical depth where small discrepancies occur. In distinct contrast to turbulent flow, the location of the critical depth upstream from the brink of a vertical channel drop is found to increase with the Reynolds number of flow.