A CRITICAL APPRAISAL OF THE PRESENT STATE OF KNOWLEDGE OF GRADUALLY VARIED STEADY FLOW IN UN.IFORI -OHENNELS ON MILD SLOPES

Abstract

"Gxradual ,y varied*" steady flow sometimes referred to as "Non-uniform" steady flow is defined briefly as steady flow in a channel where `the water surface and the total energy line are not parallel to the bed of the channel. In uniform steady flow, the .water surface and the total energy line are parallel to the bed of the channel. Uniform flow, which is usua-lly assumed by the average civil engineer in making hydraulic computations, i8 more often atheoretical abstraction than an actuality. Therefore, it is imperative that the civil engineer lear'n#t to think in terms of gradually varied flow. Most of the problems in gradually varied flow are con-cerned with the computation of surface profiles of flow in both natural nonuniform channels and artificial uniform channels. The most important practical problem in gradually varied flow is the calculation of the backwater, curve resultting from the construction of a barrage or a dam across a river to determine the extent of land submergence and to evaluate uiiother and to what degree the tail.•race of the hydro_po or plant up` stream will be affected. - The Judicious spacing of the intermediate regulators on irrigation canals, which serve during the low season to raise the water levels behind them to levels allowing free...flow irri-gation and the design of the canal outlets, are dependent on the levels of the calculated back-water curves in between every couple of intermediate regulators. So a thorough knowledge of the technique of -computation of water surface profiles is very essential for a modern hydraulic design engineer engaged in the planning, design and ,operation of water resources develop_ meat projects i.e. irrigation,bydro-power, navigation and flood control. The theory of gradually varied flow was first postulated in a complete and comprehensive manner by J.N. Belanger in 1$28 in a paper which is considered as the foundation of the theory of gradually varied flow. Belanger's theory of gradually varied flow does not represent the true conditions as the flow approaches the critical depth, yc, as he assumed that the pressure would be hydrostatically distributed over every, normal section where_ as the stream lines in the region of critical depth become appreciably curvilinear. Subsequently the theory of gradually varied flow was improved by BoussinesgFawer[:eiJ] who included the curvature of stream tubes in the analysis of water surface profiles. The equations of Boussinesq and Fawer are useful only for the theo_ retical analysis of water surface profiles near the critical depth but they are not useful for the numerical analysis as it is extremely difficult - to ilitegrate them. So Belangert s differential equation of gradually varied flow remains the basis of various methods of computation of 3 water surf ace profiles. Ate„ recent investigations have been confined to the experimental verification of the validity of the assumption underlying the derivation of Belanger' $ differential equation of gradually varied flow and to the methods of solution of the differential equation by direct, approximate and graphical Integra_. tion. The purpose of the present study is make a critical app_ raises, of the present state of knowledge of gradually varied steady . flow in uniform channels on i~[ild slopes.