Closed-Form Expression of the Response Time of an Open Channel

Computing accurately the response time of an open-channel is of extreme importance for management operations on canal networks, such as feed-forward control problems. The methods proposed in the literature to approximate the response time do not always account for the influence of a cross-structure at the downstream end of a canal pool, which may have a significant impact on the response time. This paper proposes a new approach to compute the response time, accounting explicitly for the backwater and the feedback effects due to the downstream cross structure. The method provides a distributed analytical expression of the response time as a function of the characteristics of the canal (geometry, roughness) and of the downstream cross structure. A test canal with a weir or a gate at the downstream end is used to compare the new method with some others. Results show that the proposed expression accurately reproduces the response time for various backwater and downstream boundary conditions. CE Database subject headings: Open channel flow, Analytical model, Response time, Flow control, Canal design. Introduction The response time of an irrigation canal or a regulated river is usually defined as the time required for the system to transit from an initial steady state to a final steady state Cemagref, UMR G-EAU, 361 rue J.F. Breton, B.P. 5095, 34196 Montpellier Cedex 5, France. E-mail: [email protected]. IRD, UMR G-EAU, Maison des Sciences de l’Eau, 300 Avenue Emile Jeanbrau, 34095 Montpellier Cedex 5, France. E-mail: [email protected]. Cemagref, UMR G-EAU, 361 rue J.F. Breton, B.P. 5095, 34196 Montpellier Cedex 5, France. E-mail: [email protected]. 1 S. Munier Author-produced version of the article published in Journal of Irrigation and Drainage Engineering, 2010, Volume 136, Issue 10, pp. 677-684. The original publication is available at http://ascelibrary.aip.org/iro/ doi: 10.1061/(ASCE)IR.1943-4774.0000241