IN-DEPTH INVESTIGATION OF FLOW MEASUREMENT USING SHARP-EDGED WIDTH CONSTRICTION IN TRAPEZOIDAL OPEN CHANNELS

Abstract

Flow measurement in open channels is a critical aspect of hydraulic engineering, essential for effective water resource management, irrigation, environmental monitoring, and industrial applications. The present study investigates the feasibility of using a sharp-edged width constriction as a reliable and efficient flow measurement device in trapezoidal open channels. The proposed device, which has already demonstrated its effectiveness in rectangular channels, consists of two thin vertical plates forming a full central rectangular opening, creating a lateral flow contraction. Its geometric simplicity, cost-effectiveness, and ease of implementation make it a promising alternative to conventional flow measurement structures.

The primary objective of this study is to establish a rigorous theoretical framework governing the discharge coefficient (C_d) of the device and validate it experimentally. The discharge coefficient, a crucial parameter in flow measurement, accounts for contraction effects, energy losses, and variations in velocity distribution. A comprehensive theoretical analysis is conducted using two independent methodologies. The first method is based on the energy equation, reformulated in dimensionless terms to explicitly incorporate the influence of approach flow velocity—an essential factor in accurate flow estimation. The second method employs the kinetic factor, which characterizes the relative approach velocity head. Both analytical approaches converge to the same result, demonstrating that the discharge coefficient (C_d) is governed exclusively by the compound dimensionless parameter ψ (β, M₁), which is intrinsically linked to the section reduction ratio. The parameter β, referred to as the contraction rate, is defined as β = b_o/b, where b_o denotes the opening width of the device, and b represents the base width of the trapezoidal approach channel. The dimensionless parameter M₁ is expressed as M₁= mh₁/b, incorporating the influence of the trapezoidal approach channel’s side slope (m), i.e., 1 vertical to m horizontal, and the relative upstream flow depth (h₁/b), both of which play a crucial role in determining the flow behavior and discharge characteristics. The contraction rate b provides critical insight into how geometric changes affect hydraulic behavior, and overall flow dynamics in open-channel systems. The exclusive dependence of C_d on b and M₁is further confirmed through dimensional analysis.  

The theoretical predictions are subjected to rigorous experimental validation. A large-scale experimental campaign was conducted under controlled laboratory conditions using a custom-built test setup equipped with precise measuring instruments. Seven different devices with varying contraction rates 0.15 ≤ β ≤ 0.45 were tested, and an extensive dataset of 1,012 measurement points was collected. The experimental discharge coefficient values (C_d,Exp) were compared with theoretical predictions (C_d,Th), revealing a remarkable agreement, with a maximum deviation of only 0.301%. This minimal discrepancy underscores the reliability and the robustness of the derived (C_d) theoretical relationship and confirms that the device can be applied confidently in real-world hydraulic applications. This outstanding outcome enables practitioners to accurately estimate the desired flow rates conveyed through a trapezoidal channel with a high degree of confidence, eliminating the need for additional calibration efforts.

The findings of this study contribute significantly to the field of open channels flow measurement by providing a simple yet highly accurate alternative to conventional devices. The proposed device's self-cleaning ability, ease of installation, and precise theoretical predictability make it particularly suitable for applications in water distribution networks, drainage systems, irrigation canals, and environmental monitoring such as helping estimate river discharges, or providing accurate real-time hydrological data that supports decision-making in flood management.