CHAPTER 2 - BASIC CONCEPTS RELATED TO FLOWING WATER AND MEASUREMENT

9. Thin Plate Weir Relationships

Most investigators derive the equation for sharp-crested rectangular weirs by mathematical integration of elemental orifice strips over the nappe (Bos, 1989). Each strip is considered an orifice with a different head on it. The resulting rectangular weir equation for theoretical discharge is:

A correction factor is needed to account for simplifications and assumptions. Thus, a discharge coefficient, C_d, is added to obtain actual discharge, expressed as:

This relationship is the basic weir equation and can be modified to account for weir blade shape and approach velocity. However, C_d must be determined by analysis and calibration tests. For standard weirs, C_d is well defined or constant for measuring within specified head ranges.