A proposal of the formulas of discharge and upstream head of free fall flow over a sharp crested weir

Calculation of water level of the rivers in which weir(s) exist uses the water level just upstream of the weir as the boundary condition. In this case precision of the weir formula becomes problem frequently. In this study, free fall flow over a sharp crested weir, as the fundamentals of weir hydraulics, has been discussed on the basis of the momentum theorem. The relationship between discharge and upstream head has been given as the equally dependent relationship each other given by dimensionless parameters derived from momentum theorem. Firstly, unique relationship between the ratio of upstream head to weir height and the ratio of critical depth to weir height has been obtained using the previous experimental data. Then the relationship has been corrected considering Reynolds number effect for small scale flow. Reynolds number effect on the correction is similar to that on the drag coefficient of obstacle. The resultant formula showed better agreement than the previous standard formula in wide experimental range.

sharp crested weir

momentum theorem

free fall flow

discharge evaluation

Reynolds number