Abstract: The boundary layer momentum integral equation including higher-order effects,those associated with normal pressure gradient s, Reynolds normal pressure gradients and Reynolds normal stresses,is adopted,and the conventional entrainment equation and lag equation are cor-rected to contain those effects correspondingly So the improved integral equations can be ob-tained and are used to calculate the boundary flows over aerofoils at high subsonic and transonic speeds.It is shown that tlie inclusion of high-order tenn leads to much better agreement with ex-periment of flow with separation obviously.

Key words: turbulent boundary layer, integral equation, pressure gradient, Reynolds stressentrainment