In hydrology and water resources engineering, predicting the flow coefficient is a crucial task that helps estimate the precipitation resulting in a surface flow. Accurate flow coefficient prediction is essential for efficient water management, flood control strategy development, and water resource planning. This investigation calculated the flow coefficient using models based on Simple Membership functions and fuzzy Rules Generation Technique (SMRGT) and an Adaptive Neuro-Fuzzy Inference System (ANFIS) model. The fuzzy logic methods are used to model the intricate connections between the inputs and the output. Statistical parameters such as the coefficient of determination (R2), the root mean square error (RMSE), the mean absolute error (MAE), and the mean absolute percentage error (MAPE) were used to evaluate the performance of models. The statistical tests outcome for the SMRGT model was (RMSE:0.056, MAE:1.92, MAPE:6.88, R2:0.996), and for the ANFIS was (RMSE:0.96, MAE:2.703, MAPE:19.97, R2:0.8038). According to the findings, the SMRGT, a physics-based model, exhibited superior accuracy and reliability in predicting the flow coefficient compared to ANFIS. This is attributed to the SMRGT's ability to integrate expert knowledge and domain-specific information, rendering it a viable solution for a diverse range of issues.