D’Alembert paradox and Stokes paradox are the classical contents in fluid mechanics, which are also the confusing parts in teaching. Using a fixed sphere in a uniform flow field as an example, we present the key assumptions, governing equations, solutions of flow velocity and pressure for potential flow and low Reynolds number flow, respectively. The contours are plotted to compare the hydrodynamics of flows. The qualitative and quantitative analysis clarifies the origins of D’Alembert paradox and Stokes paradox. The combination of paradox and formula derivation could stimulate students’ interesting and further improve the understanding of theory.