The Lighthill transpiration-velocity correction is commonly used in th
e analysis of viscous flows of aeronautical interest, in order to take
into account the perturbation to the potential flow caused by the pre
sence of the vorticity in the boundary layer. This correction consists
of considering the boundary as a permeable surface from which the flu
id flows through the boundary surface, with a velocity (named the tran
spiration velocity) determined on the basis of the local boundary-laye
r characteristics. Here, we use a new potential-vorticity decompositio
n in order to derive an exact representation of the effects of the vor
ticity on the external flow. The relationship between approximate tran
spiration-velocity representation and the exact one presented here is
analyzed: it is shown that, under typical boundary-layer assumptions,
the new representation reduces to that by Lighthill, except far a corr
ective field term. Finally, in order to quantify, in a simple case, th
e contribution of the corrective terms which arise in the new formulat
ion, we examine, as a numerical test case, the problem of an attached
boundary-layer flow over a flat plate: the numerical results indicate
that the corrective term is negligible for Reynolds numbers above 10(4
).