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This paper is devoted to nonlinear observer and controller design for water level control of open-channel flow in irrigation canals or dam-river systems. A finite-dimensional model, previously developed by orthogonal collocation methods, based on Saint Venant equations and used for control design, is now further used for online flow rate and water infiltration estimation. This is done by a so-called state observer. In particular, the estimates obtained in this way can successfully be used in a controller previously proposed, resulting in a water level control law using only two level measurements along the canal (instead of the four measurements previously needed). The study is restricted to the case of a rectangular wetted section and subcritical flow. The results have been validated by simulations, on an implicit finite difference simulator based on a Preissmann scheme for various scenarios. DOI: 10.1061/(ASCE)0733-9429(2008) 134:9(1267) CE Database subject headings: Open channel flow; Shallow water; Water levels; Control systems; Approximation methods.

A method is proposed for predicting the backwater effect due to a single, submerged spur dike located within an open channel flow. A theoretical analysis based on the momentum principle relates the backwater effect to the drag force exerted by the spur dike on the flow. Experimental data obtained in laboratory flumes having subcritical flow conditions throughout the flow field have been used in developing predictive relationships for the spur dike drag coefficient, which is found to be strongly correlated to the blockage created by the spur dike within the flow cross section. The predictive relationships provide a means of obtaining a first-level estimate of the backwater effect due to a single, submerged spur dike in an open channel flow. DOI: 10.1061/(ASCE)0733-9429(2008)134:8(1153) CE Database subject headings: Dikes; Groins, structures; Drag; Submerged flow; Open channels; Backwater.

The specific energy equation has many applications in rectangular open-channel flow problems. The existing methods of solving this equation are as follows: trial-and-error solution, graphical solution, and design tables prepared from the specific energy equation expressed in dimensionless form. No direct solutions are available in the technical literature for this equation to date because it was presumed that finding roots of this equation requires a series of substitutions. In this technical note, the writer develops an analytical solution for transitions located in rectangular open channels: (1) to avoid the inconvenience in available solutions; (2) to derive a less time consuming method; and (3) to achieve more accurate results than those as a result of using existing methods. DOI: 10.1061/(ASCE)0733-9437(2008)134:4(533) CE Database subject headings: Channel design; Contraction; Control structures; Critical flow; Hydraulic engineering; Open channel.

This paper deals with the underlying mechanism of flow resistance in an alluvial channel: The effects of sidewall and bed form on flow resistance, Einstein's divided hydraulic radius approach and Engelund's energy slope division approach are reexamined. These two approaches assume that the shear stress on a mobile bed is the summation of shear stresses caused by skin friction and bed form. Using a different approach, this paper presents a theoretical relationship between the total bed shear stress with grain and bed-form shear stresses. The contribution of sidewall on the total bed shear stress is also discussed. The writers found that the size of bed form plays a significant role for the flow resistance, and developed relevant expressions for the length of the separation zone behind the bed forms. In addition, a systematical approach has been developed to compute the flow velocity in an alluvial channel. This approach is tested and verified against 5,989 flume and field measurements. The computed and measured discharge/velocity are in good agreement and 83.0% of all data sets fall within the [+ or -] 20% error band. CE Database subject headings: Boundary shear; Velocity; Open channel flow; Turbulent diffusion; Flow resistance.

Maintenance or repair of water mains may require the interruption of flow. Reinitiation of flow may present opportunities for the interaction of air and the accelerating water, resulting in undesirable pressure transients. This study focuses on air intrusion during flow startup in an initially filled horizontal pipeline supplied by a constant-head reservoir. Flow was initiated by opening the downstream end, allowing a free discharge at that point. During the initial phases of flow startup, an air cavity intruded in the upper portion of the pipe cross section while water exited the pipeline through the lower portion. The initial reservoir head controlled the rate of water velocity increase and, thus, the air intrusion advance. Air intrusion occurred until the water velocity was sufficient to arrest the intrusion. Higher reservoir heads resulted in the subsequent expulsion of the intrusion from the pipeline. However, for lower reservoir heads, the intrusion was not expelled, but readvanced to a final position that was controlled by shear forces. Criteria are developed for the flow conditions necessary to arrest the air intrusion in a horizontal pipeline as well as the intrusion lengths to be expected. CE Database subject headings: Transient flow; Water Pipelines; Open channel flow; Pressurized flow; Intrusion.

Abstract: A flooding probability based cost effective design of open channel section has been proposed using freeboard as an additional design variable. The freeboard of the channel is calculated based on the flooding probability value. The proposed model is solved using classical optimization techniques as well as a nondominated sorting genetic algorithm. The results of the model are compared with an earlier reported model to demonstrate its superiority and field applicability. DOI: 10.1061/(ASCE)0733-9437(2008)134:3(405) CE Database subject headings: Channel design; Open-channel flow; Optimization; Uniform flow; Cross sections.

Abstract: A power-law channel section is very versatile. It can model a wide range of familiar man-made or natural channel shapes. However estimating the wetted perimeter of a power-law channel section is difficult. The problem gets complicated further when considering the freeboard in the design process. In this paper, the wetted perimeter is estimated using the isoperimetric theorem which results in a simple and accurate expression for the wetted perimeter that does not lead to discontinuity in the optimal solution. For unconstrained optimum power-law channels, it is shown that the exponent and side slope at the water surface have values of 0.314 and 0.352, respectively, independent of either the maximum side slope or the relative freeboard. The analyses have also shown that the most hydraulically efficient power-law channel sections come closest to the semicircle. They tend to be U shaped and narrow with small relative freeboard ([less than or equal to] 0.30). A design procedure and two design charts are presented together with two illustrative examples to demonstrate the simplicity of the method. DOI: 10.1061/(ASCE)0733-9437(2008)134:3(380) CE Database subject headings: Channel design; Open-channel flow; Optimization; Uniform flow; Cross sections.

The singular point is a physical phenomenon consistent with critical flow conditions, and, consequently, the real control section of a water surface profile. A general method to study the location, type, and water surface slope of a singular point is described. This method, in addition to improving the classic gradually-varied flow theory, can be used for the design of channel contractions involving transcritical flows, as in the case of chute spillways and inlets to river diversion tunnels. The method is explained in the case of a chute spillway and verified against experimental data recorded in a Venturi channel. DOI: 10.1061/(ASCE)0733-9429(2008)134:4(492) CE Database subject headings: Open channels; Gradually-varied flow; Spillways; Transcritical flow.