Division of flow in open channels

Abstract

This thesis deals with the problem of division of flow when a branch channel bifurcates from a main channel. The effects of both the angle of off-take and the relative widths of the main and branch channels are considered. In this project, comprising about 800 runs, five angles of off-take (30°, 45°, 60°, 75°, and 90°) and four b/B ratios (0.25, 0.50, 0.75, 1.00) for each off-take were studied, and a total of 26 channel junctions were investigated. Separate solutions have been obtained for subcritical and supercritical flows. The influence of streamlining on right-angled off-takes is studied in some detail. Part I presents an extensive critical review of earlier investigations. The previous investigations are discussed in the light of the author's experimental observations. Part II gives a solution to supercritical branch channel flow based on an analysis of wave formation in supercritical flow. The problem is treated as a particular case of transition in supercritical flow. The graphical method of characteristics is used to facilitate the computations of discharge distribution. A comparison with experimental observations shows that the agreement between theory and experiments is generally good except for 90° off-takes, which is explained as due to the increasing influence of separation for right-angled off-takes. A complete analysis of dividing flow is given in Part III. Secondary effects such as separation in the branch channel, curvature of streamlines, etc., are also considered. The solution involves the use of an experimental coefficient, which has been obtained for 90° off-takes for subcritical flows. A much simpler solution for subcritical dividing flow is obtained based on dimensional analysis. Experiments have shown that the Froude number in the main channel downstream of the branch (Fd) gives a better correlation for the discharge distribution than the upstream Froude number. Equations of the form: log?QbQm=K?x\log \frac{Q_b}{Q_m} = K \cdot xlogQm?Qb??=K?x have been obtained for the discharge distribution, where K and x are constants determined experimentally and are functions of the angle of off-take and the relative widths of the main and branch channels. The values of K and x are given for various angles of off-take and b/B ratios. Detailed studies have been reported on the effect of the angle of off-take on discharge distribution and the flow patterns at the junctions. The effects of streamlining right-angled off-takes are also studied. It was found that streamlining helps considerably in increasing the discharge distribution (Qb/Qm) and in improving the flow conditions in the branch channel. Streamlining the upstream edge of the branch inlet has a decided advantage over streamlining the downstream edge of the inlet. Circular curves were found to be more advantageous compared to elliptical curves. For higher Froude numbers in the subcritical range, it may be preferable to adopt a hockey spur at the downstream end of the branch inlet together with circular streamlining at the upstream end. Besides giving a quantitative solution to the problem, an attempt has been made in this thesis to study the characteristics of the flow at the junction in detail. Flow phenomena like separation in the branch channel, disturbance wave patterns in the main and branch channels, the variation of the inlet profile, and the drop in the water surface just upstream of the junction are discussed in detail.