Direct solutions for normal depths in curved irrigation canals

• New direct formulas for normal depth in curved-shaped irrigation canals making use of Marquardt method.
• Proposed formulas with maximum relative error less than 1%.
• The formulae accounting for both simplicity and accuracy.

The normal depth is an important hydraulic element for canal design, operation and management. Curved irrigation canals including parabola, U-shaped and catenary canals have excellent hydraulic performance and strong ability of anti-frost heave, while the normal depths in the governing equations of the current common methods have no explicit analytical solution. They are only indirect methods by using trial procedures, numerical methods, and graphical tools. This study presents new direct formulas for normal depth in curved irrigation canals by applying for Marquardt method. The maximum relative error of the proposed formulas is less than 1% within the practice range by comparative analysis, and they are simple and convenient for manual calculations. The results may provide the reliable theoretical basis and useful reference for the design and operation management of irrigation canals.