An analytical or numerical solution of this differential equation gives the flow depth y as a function of x for a given set of parameters, and the function yx is the surface profile. In this paper, a closedform solution of gradually varied flow equation is derived for ordinary rectangular and triangular channels using. Open channel flow florida international university. Introduction a steady nonuniform flow in a prismatic channel with gradual changes in its water surface elevation is named as gradually varied flow gvf. The backwater produced by a dam or weir across a river and drawdown produced at a sudden drop in a channel are few typical examples of gvf. Introduction a steady nonuniform flow in a prismatic channel with gradual changes in its water surface elevation is named as graduallyvaried flow gvf. Pdf accurate gradually varied flow model for water surface profile. The gradually varied flow equations are first derived.
Uniform flow serves as the standard reference for experimental and theoretical work e. For a given value of specific energy, e1, the discharge may pass through the channel section at either depth d1 supercritical flow or d2 subcritical flow. Equation for uniform flow uniform flow occurs in a channel when the depth and velocity do not vary along its length where. Gradually varied flow is defined as steady nonuniform flow in a channel in which there are gradual changes in the water depth.
The depth associated with uniform flow is designated y 0. Energy, specific energy, and gradually varied flow. Introduction a steady nonuniform flow in a prismatic channel with gradual changes in its watersurface elevation is named as gradually varied flow gvf. Gradually varied openchannel flow profiles normalized by critical. Development of an analytical benchmark solution to assess various. Restore flow profile symmetry and eliminate distortions. Allows much shorter meter runs to be used with much higher repeatability. Introduction to gradually varied flow flood modeller.
This is followed by a presentation of procedures for qualitatively sketching the watersurface profiles and for determining the discharge from a reservoir. The momentum and energy principles are equally applicable in the derivation of spatially varied flow equations. Steady, gradually varied flow is discussed in this chapter and the rapidly varied flow in chapter 7. Graduallyvaried flow profiles in open channels analytical. Natural channels are of irregular shape, varying from. Box 5969, kuwait the gradually varied flow profile in a circular channel section is computed using the direct step method and the integration method. Advances in engineering software 15 1992 3342 gradually varied flow in circular channels with variable roughness nabil a. Gradually varied flow in circular channels with variable. Using this property it is possible to compute the water flow profile passing through the critical stage. Pdf computation of gradually varied flow in a channel system. At a larger depth the same discharge may be delivered through the section with a smaller velocity and a higher specific energy than a critical depth.
Helps balance the pressure, velocity and flow rate of meter tubes running. The equations for gradually varied flow it should be noted that the slope is defined as the sine of the slope angle and that is assumed positive if it descends in the direction of flow and negative if it ascends. The main objective of computation is to determine the shape of flow profile. Spatially varied flow equations chow 1969 water resources. Isolates the flow meter from upstream disturbances. Graduallyvaried flow in open channels lecture notes 06 1. Graduallyvaried flow in open channels lecture notes 06. How high water will rise in piezometers at points a, b, c, and d. Improves the benefits of many usm diagnostics by providing flow stabilty. Gradually varied flow in open channels lecture notes 06 1. Computational issues of solving the 1d steady gradually varied flow. Broadly classified, there are three methods of computation. Graduallyvaried flow gvf is a steady nonuniform flow in an open channel with.