DEVELOPMENT AND VALIDATION OF A MODIFIED H-FLUME FOR ACCURATE FLOW MEASUREMENT IN RECTANGULAR CHANNELS

Abstract

The study aimed to examine, from theoretical and experimental perspectives, the modified H-Flume as a flow measurement device for rectangular open channels. By introducing a vertical V-notch at the terminal section, the modified H-Flume allows for the derivation of theoretical relationship governing the discharge coefficient (C_d) and the stage-discharge relationship, overcoming the limitations of the original design. These relationships depend on the dimensionless parameter M₁ = mh₁/B, which encapsulates the key geometric and flow characteristics of the device.

Solely depending on M₁, the study introduces the relative upstream flow depth h₁^∗, which is a dimensionless parameter defined as the ratio of the upstream flow depth (h₁) to the critical flow depth (h_2,c) at the V-notch, capturing the hydraulic state of the upstream flow relative to critical conditions. This dimensionless parameter plays a pivotal role in determining the discharge coefficient (C_d). Indeed, the discharge coefficient (C_d) is fundamentally governed by h₁^∗, as it encapsulates the energy transformation and flow behavior from the upstream subcritical state to the downstream critical state. This relationship ensures that C_d is a precise function of the hydraulic conditions at the approach channel and the geometry of the V-notch. The relationship between h₁^∗and C_d is mathematically linked through energy principles and dimensionless parameters, emphasizing their interdependence. In addition, since C_d is directly influenced by h₁^∗, the flow rate (Q) can be uniquely determined by measuring the upstream depth h₁. This dependency eliminates ambiguity in the stage-discharge relationship and enables accurate flow rate predictions. As practical implications, the explicit dependence of C_d on h₁^∗(M₁)simplifies flow measurements, as a single depth reading at the upstream section suffices to determine the discharge. This relationship enhances the practicality of the modified H-Flume, ensuring reliability across a broad range of flow conditions.

An increase in h₁^∗ corresponds to changes in flow dynamics and directly affects C_d, enabling the accurate estimation of the discharge rate (Q).

Explicit approximate equations for h₁^∗(M₁) were developed, simplifying the calculation of C_dwhile maintaining remarkable accuracy. These equations revealed that h₁^∗ is a critical intermediary variable, as it reflects the flow’s evolution through the flume and its approach to the critical state at the V-notch. This link establishes the modified H-Flume as a semi-modular device where C_d depends not only on the geometric characteristics of the flume but also on the upstream flow conditions represented by h₁^∗.

The strong theoretical and experimental foundation of this study confirms the reliability and practicality of the modified H-Flume. The established relationships between h₁^∗, C_d, and Q offer a robust framework for precise flow measurement, providing significant advancements in open-channel hydraulics. This makes the modified H-Flume an invaluable tool for applications requiring high accuracy and versatility across a wide range of flow conditions. Indeed, four modified H-Flumes, with varying geometries, were subjected to experimental testing across 1480 flow conditions. Results show excellent agreement between theoretical and experimental discharge coefficients, with maximum deviations of only 0.185%. This validates the modified H-Flume's accuracy and reliability, making it a practical and theoretically sound tool for open-channel flow measurement.