Internal cooling air systems of turbomachines contain various fluid flow components, i.e., rotating holes, tapping configurations, coverplates, labyrinth seals, etc., for which only the basic aerodynamics are known. Numerical calculations for these elements are carried out and compared with test results showing fair agreement in general. For most of the components of internal air systems there is a serious lack of test data. It is shown that the situation can be relieved by applying numerical methods, which also should be used to improve and extend the empirical correlations in the air systems computer programs.