It is proven that the momentum deposition flux and vertical diffusion caused by ''saturated'' gravity waves are related to each other by a simple expression: This expression is KRa =2k2z (kxkH)2Dzz, where Dzz is the vertical diffusion coefficient, kz is the vertical wavenumber of the gravity wave, kx/kH is the ratio of zonal wavenumber to horizontal wavenumber and KRa is a friction coefficient expressed as KRa≡ (momentum deposition flux)/(u0-Ck), with u0 the mean wind and Ck the wave horizontal phase speed. We refer to KRa as a ''generalized friction coefficient'' because it differs from ordinary Rayleigh friction, but is sometimes similar-depending on wave parameters and wind. The coefficient KRa is not sensitive to wave incoherency (variations of the sign of kz with time) because it depends on the square of kz, whereas the momentum deposition flux KRa(u0-Ck) is sensitive to such incoherency because it is an odd function of (u0-Ck). A model for KRa in the mesosphere is proposed, based on the model of Dzz recently derived by Ebel. It is emphasized that when KRa and Dzz are large, then the heat transport caused by gravity waves is also large and must be accounted for.