Submerged flow exists in a measuring flume when a change in flow depth downstream from the flume causes a change in flow depth upstream for any particular constant value of discharge. When a change in tailwater depth does not affect the upstream depth, free flow exists. To evaluate the discharge under free-flow conditions, it is necessary to measure only a flow depth upstream from the contracted section (throat) of the flume, whereas two flow depths must be measured to evaluate the discharge under submerged-flow conditions. The two flow depths normally measured when submerged flow exists consist of the same upstream depth used for free flow and a depth measured in the throat, although this need not be the case as will be shown later. Most of the earlier investigations regarding measuring flumes have emphasized the development of free-flow calibrations or ratings for various flume geometries. Notable free flow investigations have been made by V. M. Cone, Parshall, Engel, Khafagi, Robinson and Chamberlain, and Ackers and Harrison, to mention a few. Various methods of analyzing submerged flow have been presented by Parshall, Khafagi, Villemonte and Gunaji, Robinson and Chamberlain, and Robinson. Parameters describing submergence in flow-measuring flumes will be developed from dimensional analysis. A combination of empiricism and dimensional analysis will be used to develop a submerged flow discharge equation. The resulting discharge equation will be compared with the theoretical submerged-flow equation developed from momentum relationships. A rectangular flat-bottomed flow measuring flume was used to generate data necessary for establishing the parameters describing submerged flow. The form of the discharge equations describing submerged flow in a rectangular flume has been verified for a trapezoidal flat-bottomed flume, a rectangular flat-bottomed flume, and a Parshall flume.
Skogerboe, Gaylord V. V. and Hyatt, M. Leon, "Analysis of Submergence in Flow Measuring Flumes" (1967). Reports. Paper 94.