CRITICAL FLOW IN A TRIANGULAR-SHAPED CHANNEL

Abstract

The functional y(y_c;m;S₀;e;n) = 0 relationship has been well defined and theoretically established for the triangular-shaped channel, where y_cis the critical depth, m is the side slope, S₀ is the channel bottom slope, e is the absolute roughness, and n is the kinematic viscosity of the flowing water. A thorough investigation of the function revealed that the critical depth y_cis governed by a cubic equation without second order term. Its analytical resolution is very easy when one uses the circular or hyperbolic trigonometry.

The article ends with the study of the special case of the smooth triangular-shaped channel of a 90° apex angle by examining the equation that governs the critical depth It turned out that y_c is given by an explicit equation, as a function of m, S₀, and n . In addition, it has been demonstrated that, for such a canal, the more the slope S₀ increases, the more the critical depth decreases. Moreover, it was observed that, for the same slope S₀, the critical depth decreases as the side slope m increases, i.e. when the apex angle of the channel increases. For slopes S₀ less than 0.0012, the critical depths are so high that they are outside the practical context. As a matter of fact, for the slope S₀ = 0.0012, the critical depth already reaches more than 5m.