Application correlation algorithm to create a new critical depth equation for gradually varied flow in trapezoidal channel using teaching–learning and studying

Abstract

The critical depth is a hydraulic factor of the flow, it plays a particularly important role in studying and designing for open channels, especially during identification of water surfaces and analyzing to determine the phenomenon of a hydraulic jump in open channel. In practice, when calculating the critical depth, only the rectangular and isosceles triangle channels have the theory equation, in other circumstances in calculating by semi empirical equations. This paper presents the general method to compute the critical depth of trapezoidal channel, the case study methodology was chosen to analyze the application of existing formulas and then offering a new equation to compute the critical depth based on the optimization algorithm in MS Excel software. This new equation will help to obtain more accurate result, which relative error of the equation is less than 0.61%, this equation has a simple structure, easy to calculate with small errors to meet the conditions to quickly calculate the critical depth, this equation is also suitable for teaching–learning and studying in the field of hydraulics.

Keywords

• critical depth
• non-uniform flow
• trapezoidal chanel
• critical flow
• specific energy