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Solutions for choke-free flow in a trapezoidal channel, with rise in bed elevation that may occur with partial filling up of the channel bottom, are discussed. In this analysis, the side slopes of the channel are assumed to be the same before and after the transition. Considering smooth and gradual transition zones, equations of energy and continuity are solved for subcritical and supercritical upstream flow conditions to determine the maximum limiting rise in bed elevation. The ranges of the upstream flow depths are also obtained for the choke-free condition, using the continuity equation of the upstream flow.

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Sadhana - Academy Proceedings in Engineering Sciences

Choke-free flow in trapezoidal channels with change in bed elevation

Physical solutions for the flow through circular channels due to increase in bed elevations are obtained, satisfying the condition of choke-free flow. In this analysis, three different cases of channel transitions, commonly found in practice, are considered. They are (1) when the channel bed is raised with the formation of a flat base; (2) when the channel bed is raised due to change in position of the centerline; and (3) when the channel bed is raised due to decrease in channel diameter. Considering a smooth and gradual transition zone, the equations of energy and continuity are solved for the subcritical approaching flow regime to determine the maximum limiting rise in bed elevation. Using the continuity equation of the upstream flow, the ranges of the upstream flow depths are also obtained for the choke-free condition.

Journal of Irrigation and Drainage Engineering

Choke-free flow in circular channels with increase in bed elevations

The flow upstream of a free overfall from smooth circular channels is theoretically analyzed to calculate the end-depth ratio (EDR), applying the momentum equation based on the Boussinesq approximation. The present approach eliminates the need for an empirical pressure coefficient. In subcritical approaching flows, the EDR is related to the critical depth, which occurs upstream of the end section, and the value of EDR is found to be around 0.75 for a critical depth-diameter ratio up to 0.82. On the other hand, in supercritical approaching flows, the end depth is expressed as a function of the streamwise slope of the channel using the Manning formula. Simple methods are presented to estimate the discharge from the end depth in subcritical and supercritical approaching flows. A relationship of discharge to the end depth and the channel characteristics parameter is also proposed. Streamline curvature at the free surface is used to compute the flow profiles upstream of a free overfall. This paper also presents a theoretical model to analyze the free overfall from horizontally laid rough circular channels with the aid of an autorecursive search scheme. The flow upstream of a free overfall from smooth circular channels is theoretically analyzed to calculate the end-depth ratio (EDR), applying the momentum equation based on the Boussinesq approximation. The present approach eliminates the need for an empirical pressure coefficient. In subcritical approaching flows, the EDR is related to the critical depth, which occurs upstream of the end section, and the value of EDR is found to be around 0.75 for a critical depth-diameter ratio up to 0.82. On the other hand, in supercritical approaching flows, the end depth is expressed as a function of the streamwise slope of the channel using the Manning formula. Simple methods are presented to estimate the discharge from the end depth in subcritical and supercritical approaching flows. A relationship of discharge to the end depth and the channel characteristics parameter is also proposed. Streamline curvature at the free surface is used to compute the flow profiles upstream of a free overfall. This paper also presents a theoretical model to analyze the free overfall from horizontally laid rough circular channels with the aid of an autorecursive search scheme.

Journal of Hydraulic Engineering

End depth in circular channels

A model is presented that enables us to estimate the temporal variation of sediment pick-up in evolving scour holes around circular cylinders, for uniform sediments, under a clear water scour. The procedure developed for computing the pick-up rate of sediment is based on the fundamental equation of local scour considering the horseshoe vortex system in front of the cylinder to be the main scouring agent. The present model agrees satisfactorily with experimental flume data.

Applied Mathematical Modelling

Sediment pick-up for evolving scour near circular cylinders

The three-dimensional quasi-steady vortex flow field around circular piers in a quasi-equilibrium scour hole under a clear water regime has been investigated experimentally. The main characteristic features of the flow, to be modeled, are a relatively large secondary vortex flow within the scour hole and skewed velocity distributions along the circumference of the pier. The flow field has been divided into a number of parts according to the flow characteristics. The components of quasi-steady velocity for different parts have been theoretically expressed in the form of equations satisfying the continuity equation and the requirements of fitting an individual profile of the measured velocity components. Using the suitable functions, the equations of the velocity components derived for different parts have been combined and matched at the junctions of these parts to get a single equation for each velocity component. The measured data have been utilized to determine the coefficients and exponents used in these equations through curve fittings. The proposed flow model, which corresponds closely with the observations, can be utilized to simulate the flow field in prototype. © ASCE.

Clear water scour at circular piers: A model

The three-dimensional flow field around a circular cylinder in a quasi-equilibrium scour hole under a clear water regime has been investigated experimentally. The distribution patterns of tangential, radial and vertical components of velocity upstream and longitudinal component of velocity downstream of a cylinder have been presented in this paper. The flow simulation results show the existence of a helical motion of fluid around the cylinder. © 1995 Indian Academy of Sciences.

Sadhana

Three-dimensional vortex flow field around a circular cylinder in a quasi-equilibrium scour hole

The bed shear stress for a horseshoe vortex in the equilibrium scour hole around the base of a circular cylinder, embedded in a loose bed with a uniform approach flow under a clear water regime, is computed from turbulent boundary layer analysis by integrating the Navier-Stokes equations. Inside the thin boundary layer, which is developed by the reverse flow at the bed due to swirl motion, Pohlhausen's method is applied with an arbitrary 1/7th power distribution of velocity, as was assumed by Weber in solving turbulent boundary layer. Outside the boundary layer, the expressions of 3-D flow field given by Dey are used. Finally the above technique produces two unknowns, namely bed shear stress and boundary layer thickness. The expression of wall shear stress given by Blasius for turbulent flow in pipes as well as over flat plates is assumed for solving boundary layer thickness, and subsequently bed shear stress. The computational results of bed shear stress and boundary layer thickness are presented. © 1994.

Bed shear in equilibrium scour around a circular cylinder embedded in a loose bed

No-choke flow in a trapezoidal channel with a change in bed elevation is analyzed assuming there is no change in channel sections before and after the transition. The energy and continuity equations are solved for the subcritical and supercritical approach-flow regimes to obtain the maximum limiting dimensions of bed elevation, considering there is no head loss in the transition zone. Also, the ranges of upstream-flow depths are obtained from this approach. © ASCE.

Journal of Engineering Mechanics

No-choke flow in trapezoidal channels

The rainfall data analysis in Teesta catchment shows that the river discharge is motivated by the heavy rainfall. It is also shown from stage and discharge analysis that the time of occurrence of peak floods for different years is commonly during the end of June. The variations of discharge with stage along with looping property are presented graphically at Coronation bridge, Teesta Bazar and Domohani. Analysis of annual peak discharge data at Domohani on the bank of the Teesta river helps to arrive at a conclusion with regard to the probable maximum magnitude of flood that may occur in near and remote future. -from Author

Indian Journal of Earth Sciences

Design flood of the River Teesta in north Bengal

Presents a graphical solution in SI units for the optimum shapes of trapezoidal and circular irrigation channels. (C.J. U.)