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, Cd, 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, Cd must be determined by analysis and calibration tests. For standard weirs, Cd is well defined or constant for measuring within specified head ranges.