Modern vision for critical flow in an egg-shaped section

Abstract

The critical regime plays a primordial role in the study of gradually varying flows by classifying flow regimes and slopes. Through this work, a new approach is proposed to analyze critical flow regime in an egg-shaped channel. Based on both the definition of Froude number and Achour and Bedjaoui general discharge relationship, a relation between critical and normal depths is derived and then graphically represented for the particular case of a smooth channel characterized by a generating diameter equal to 1 m. The results show the influence of the slope on the frequency of occurrence of the critical regime. At the same time and independently of the flow rate, a very advantageous approach for the calculation of the Froude number has been proposed. The study shows that there are six zones to differentiate the various flow states, namely: on the one hand for steep slopes two subcritical zones interspersed by a supercritical zone and on the other hand for mild slopes a zone corresponding to uniform flow, an area where the flow is probably gradually varied and finally an area where the flow is abruptly varied. Based on the specific energy equation, a validation process concluded that the proposed relationships were reliable. HIGHLIGHTS Determination of the frequency of occurrence of the critical regime.; The nature of the flow regime can be deduced from the value of the slope.; New theoretical approach for the study of the critical regime in an egg-shaped conduit considered as a form with several advantages.; The Froude number can be determined independently of the flow rate. Establishment of an abacus to define the flow domain including non-uniform flows.;

Keywords

• critical flow
• egg-shaped conduit
• froude number
• normal flow
• rate flow
• slope