We consider the accuracy of the velocity approximation with respect to the pressure approximation using various standard finite element methods for incompressible fluid flow. Of particular interest is the case where the hydrostatic part of the pressure is dominating, which implies that the pressure may be large relative to the velocity. Some standard mixed elements like the Mini element and the Taylor-Hood element handle this case well, while others like the P\_2-P\_0 element and the Crouzeix-Raviart element do not. This seems to be related to the fact that the Taylor-Hood and the Mini elements yield a stable approximation of the mixed Poisson problem.