The flow characteristics of rectangular and 1 : 1 and 1 : 2 trapezoidal weirs were investigated through hydraulic experiments in order calculate the exact overflow discharge of the broad-crested side weir. The flow was found to be most stable in trapezoidal shapes with the lowest incline. The 1 : 1 and 1 : 2 trapezoidal weirs had 5.67% and 8.57% increases, respectively, compared to the rectangular weir in terms of overflow amount, which suggests that they are more effective in preventing flood. An integrated discharge coefficient equation taking into account the discharge coefficient equation and shapes was proposed through a multiple linear regression analysis with an addition of a new parameter for the side wear, $L/L_H$, to the conventional discharge coefficient equation. Also, the applicability of the newly proposed discharge coefficient equation was reviewed by comparing the measured and calculated overflow amounts based on the experimental data of preceding researches and existing researchers and the research data of this study.