The paper contains theoretical considerations on the influence of axisymmetric swirl of the stream on characteristics of the measuring orifice. Equations of the mathematical model were solved with the finite volume method. Detailed calculations were done for the orifices with diameter ratios beta = 0.25, 0.5 and 0.75 for the Reynolds number Re = 100 000. It was found that the swirling flow strongly influenced the discharge coefficient C for the orifice.