American Society of Civil Engineers

Exact Equations for Critical Depth in a Trapezoidal Canal

by Prabhata K. Swamee, (corresponding author), (Emeritus Fellow, Dept. of Civ. Engrg., Indian Inst. of Technol. Roorkee, Roorkee 247 667, India E-mail: and Pushpa N. Rathie, (Prof., Dept. of Statistics, Univ. of Brasilia, Brasilia 70910-900, Brazil. E-mail:

Journal of Irrigation and Drainage Engineering, Vol. 131, No. 5, September/October 2005, pp. 474-476, (doi:

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Document type: Technical Note
Discussion: by A. R. Vatankhah and et al.    (See full record)
Discussion: by Rajesh Srivastava E-mail:    (See full record)
Closure:(See full record)
Abstract: Critical depth is an important parameter in the analysis of varied flow in canals and natural streams. For triangular, rectangular, and parabolic channel sections it is possible to express critical depth analytically. However, for many practical sections, including the trapezoidal section, the governing equations are implicit in the critical depth. For these sections the critical depth is presently obtained either by trial and error procedure, or by using empirical equations based on curve fitting. In this Technical Note exact analytical solutions of critical depth for the trapezoidal open channel section have been obtained in the form of fast converging infinite series.

ASCE Subject Headings:
Critical flow
Open channels
Rivers and streams
Water depth