In the present study, a practical method is developed to predict the radial velocity of the flow towards circular and square intakes. It is shown that one single spherical sink surface passing from the desired points that have radial velocity vectors of identical magnitude within the ambient fluid can be used for the prediction of the radial velocity. The specific imaginary center of the corresponding spherical sink surface should be located on the center-line axis downstream of the entrance of the intake. As opposed to the previous studies, the proposed method does not require the solution of equations in closed-integral form, and it can also be used for the orifice-intake not opening into the atmosphere (submerged outlet), and an intake with a pipe, or intake-pipe projecting into the ambient fluid. It is shown that velocity field can be predicted with the introduced method even in the case of circulation imposed or induced ambient fluid flow. The agreement between the theoretical results and the available experimental/numerical results was found to be good.