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Updated: Sep 11, 2025

Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure

Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure

Published on: April 25, 2025

Modified discharge capacity calculation method for piano key weirs.

Zhiqi Cheng^1,2, QianKe Xu^3,4,2, Xiaolong He⁵

¹School of Environmental Science and Engineering, Southwest Jiaotong University, Chengdu 610065, China.

Water Science and Technology : a Journal of the International Association on Water Pollution Research

|August 14, 2025

Summary

Estimating discharge capacity for piano key weirs (PKWs) is complex. This study introduces a modified equation, improving accuracy for PKW hydraulic design and engineering applications.

Keywords:

dimensional analysis discharge capacity modified discharge equation piano key weir theoretical analysis

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Area of Science:

Hydraulics and Fluid Mechanics
Civil Engineering
Water Resource Management

Background:

Piano key weirs (PKWs) exhibit complex hydraulic behaviors and numerous geometric parameters.
Accurate estimation of PKW discharge capacity is challenging, often requiring extensive experimental or computational analysis.

Purpose of the Study:

To compare and analyze existing discharge equations for PKWs.
To develop new relationships between key geometric parameters (weir height P, width W, crest length L) and discharge capacity.
To propose a modified theoretical discharge equation for PKWs.

Main Methods:

Dimensional analysis was used to derive a modified theoretical discharge equation.
The proposed equation was validated against existing experimental data and prototype observations.
Analysis of key parameters including weir height (P), width (W), and effective crest length (L).

Main Results:

The modified discharge equation shows good agreement with experimental and prototype data.
For a relative water head (H/P) range of 0.1 to 1.5, the mean absolute percentage error is less than 8%.
The new equation accurately describes the influence of PKW geometric parameters on discharge capacity.

Conclusions:

The proposed modified discharge method provides a highly accurate and simple approach for estimating PKW discharge capacity.
This method enhances the practical applicability for engineering designs involving PKWs.
It offers a more precise understanding of how geometric factors affect PKW hydraulic performance.