Circular- crested weirs are employed for flow measurement among their other wide applications in hydraulic engineering. They can also be used to control water level in farm ponds and reservoirs. Advantages of the circular crested weirs as compared to other weirs include the stable overflow pattern, the simplicity of design and their associated lower costs. In this study, the curvilinear flow past a circular-crested weir is analyzed using simplified Euler equations to determine the discharge coefficient. Also, velocity distribution profile and theoretical method were evaluated through physical models of circular-crested weirs of various radii and heights. It was found that the proposed method agrees well with the experimental observations. Also, it was seen that the estimations of discharge coefficient are close to their experimental values within 3 percentage of error.