A new approximate formula of critical water depth in circular cross-section

Aimed atthe problems of large error and narrowapplicable scope exiting in the trial and diagrammethods generally used, a newapproximate formula of criticalwater depth in circular cross-sectionwas proposed. The mathemati- cal model of critical water depth was set up through the mathematical transformation of critical flow formula in circular cross-section, and the new approximate formula of critical water depth in circular cross-section was obtained by using least squares for programming computation. The example computation and error analysis indicated that the largest relative error of this formulawas smaller than 1% in the practical scope of project. Comparedwith the existing formula of critical water depth in circular cross-section, the new formula is more convenient in computation and broader in applicable scope, and it can be applied for reference in engineering practices.