CRESTLESS CONTRACTED V-NOTCH WEIR FOR FLOW MEASUREMENT IN TRIANGULAR OPEN CHANNELS

B. ACHOUR, L. AMARA, K.H. KULKARNI

Abstract


Accurate flow measurement in triangular open channels remains a significant challenge in hydraulic engineering, primarily due to the lack of simple and cost-effective devices tailored to these geometries. Existing solutions, such as non-intrusive flow measurement devices including laser Doppler velocimeter, ultrasonic, and electromagnetic flow meters, although highly accurate, are prohibitively expensive and require specialized maintenance and calibration. Furthermore, conventional weirs and flumes, including triangular, rectangular and trapezoidal designs, are ill-suited for triangular channel profiles, limiting their practical applicability in such contexts.

In response to this gap, the present study introduces a novel and economical approach for measuring discharge in triangular open channels, utilizing a contracted V-notch weir installed at the downstream end of the channel. Distinguished by its simplicity of construction and ease of implementation, the proposed device eliminates the need for a crest height, facilitating self-cleaning operation and minimizing maintenance demands. The study formulates a rigorous theoretical framework for the discharge coefficient (Cd), explicitly expressed as a function of the dimensionless section reduction ratio (ζ = m2 / m1 = b / T), where m1 and m2 are the side slopes of the approach channel and V-notch, respectively, and b and T are their corresponding top widths. The discharge coefficient derived from this relationship is shown to be invariant with respect to upstream flow depth h1, simplifying its practical use.

The validity of the theoretical formulation is assessed through an extensive experimental program involving nine different V-notch configurations, with section reduction ratios varying from 0.35 to 0.50. This carefully selected range ensures an optimal compromise between sustaining critical flow conditions within the V-notch and avoiding adverse surface tension effects, thereby safeguarding the precision and broader applicability of the proposed methodology.

A total of 2,879 experimental Cd values were collected under diverse flow conditions. The experimental discharge coefficients demonstrated remarkable agreement with the theoretical predictions, with a maximum deviation not exceeding 0.015%. This confirms the accuracy, robustness, and reliability of the proposed theoretical discharge coefficient relationship and its suitability for practical applications.

The findings of this study offer a simple, inexpensive, and highly accurate alternative for flow measurement in triangular open approach channels, making the crestless contracted V-notch a practical solution for use in irrigation canals, water distribution networks, and field monitoring programs.

Future research should explore the adaptation of this methodology to other non-standard channel geometries and flow conditions.


Keywords


V-notch weir, Triangular open channels, Flow measurement, Discharge coefficient, Section reduction ratio.

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References


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