Discharge formula based on brink depth over sharp-crested weirs

Abstract

Weirs are among the most essential hydraulic structures for measuring water discharge in open channels. The prediction of water discharge over weirs should be as precise and straightforward measured as feasible. The experimental investigation of flow prediction over varied heights of a conventional rectangular sharp-crested weir was conducted in the present work. The investigation evaluated five ratios of weir height to length, P/b, of 0.33, 0.4, 0.47, 0.53, and 0.6, different water discharges, Q, of up to 17.25 L/s, and different bed slopes, S, between 0.001 and 0.01. The experiment's findings reveal that a change in the bed slope has no significant effect on the brink depth, hb, for a constant water discharge. However, it influences the head over the weir, h, which is usually measured upstream of the weir location and used to predict water discharge. A simple, accurate formula was developed for predicting water discharge over rectangular sharp-crested weirs depending on the brink depth with mean absolute percent error (MAPE) and root-mean-square error (RMSE) of 1.714% and 0.229, respectively. In addition to having a simple form, the developed formula performs well, is unaffected by the bed slope, and applies to a wide range of h/P values, from 0.158 to 0.945. HIGHLIGHTS The discharge equation for a sharp-crested weir was predicted according to the brink depth.; The normal water depth affects when reduced or increased channel bed slope. Therefore, the discharge equations which depend on normal depth were affected.; The relationship between brink depth and critical depth was developed statically.;

Keywords

• sharp-crested weirs
• simple formula
• open channel
• weir
• brink depth
• predicting discharge